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th5/_dev/boring/sidh_ff433815b51c34496bb6bea13e73e29e5c278238.patch

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SIDH: Align codepoints with the ones in latest version
2018-12-05 14:20:21 +00:00
diff --git a/CMakeLists.txt b/CMakeLists.txt
index bfde5d588..a0f0da3b2 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -520,6 +520,7 @@ add_subdirectory(ssl/test)
add_subdirectory(fipstools)
add_subdirectory(tool)
add_subdirectory(decrepit)
+add_subdirectory(third_party/sidh)
if(FUZZ)
add_subdirectory(fuzz)
diff --git a/crypto/CMakeLists.txt b/crypto/CMakeLists.txt
index b1ca70e15..7135f55fc 100644
--- a/crypto/CMakeLists.txt
+++ b/crypto/CMakeLists.txt
@@ -396,6 +396,7 @@ add_library(
../third_party/fiat/curve25519.c
$<TARGET_OBJECTS:fipsmodule>
+ $<TARGET_OBJECTS:sidh>
${CRYPTO_ARCH_SOURCES}
${CRYPTO_FIPS_OBJECTS}
diff --git a/include/openssl/nid.h b/include/openssl/nid.h
index afeb2dea4..effe19205 100644
--- a/include/openssl/nid.h
+++ b/include/openssl/nid.h
@@ -4234,6 +4234,12 @@ extern "C" {
#define LN_auth_any "auth-any"
#define NID_auth_any 958
+#define SN_X25519_SIDHp503 "X25519-SIDHp503"
+/* This ID is only needed by kNamedGroups (ssl_key_share.c). It isn't
+ used in kObjects array (obj_dat.h). It can't be smaller than than
+ NUM_NID (obj_dat.h)
+*/
+#define NID_X25519_SIDHp503 960
#if defined(__cplusplus)
} /* extern C */
diff --git a/include/openssl/ssl.h b/include/openssl/ssl.h
index 17c559259..9cbf536e1 100644
--- a/include/openssl/ssl.h
+++ b/include/openssl/ssl.h
@@ -2177,6 +2177,7 @@ OPENSSL_EXPORT int SSL_set1_curves_list(SSL *ssl, const char *curves);
#define SSL_CURVE_SECP384R1 24
#define SSL_CURVE_SECP521R1 25
#define SSL_CURVE_X25519 29
+#define SSL_CURVE_X25519_SIDHp503 0xFE30
// SSL_get_curve_id returns the ID of the curve used by |ssl|'s most recently
// completed handshake or 0 if not applicable.
diff --git a/ssl/CMakeLists.txt b/ssl/CMakeLists.txt
index d6c1294f1..8d7cfa14f 100644
--- a/ssl/CMakeLists.txt
+++ b/ssl/CMakeLists.txt
@@ -1,4 +1,4 @@
-include_directories(../include)
+include_directories(../include ../third_party/sidh/include)
add_library(
ssl
diff --git a/ssl/handshake_client.cc b/ssl/handshake_client.cc
index c1d54bd8f..d141cc399 100644
--- a/ssl/handshake_client.cc
+++ b/ssl/handshake_client.cc
@@ -1011,6 +1011,7 @@ static enum ssl_hs_wait_t do_read_server_key_exchange(SSL_HANDSHAKE *hs) {
!hs->peer_key.CopyFrom(point)) {
return ssl_hs_error;
}
+ hs->key_share->SetInitiator(true);
} else if (!(alg_k & SSL_kPSK)) {
OPENSSL_PUT_ERROR(SSL, SSL_R_UNEXPECTED_MESSAGE);
ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_UNEXPECTED_MESSAGE);
diff --git a/ssl/handshake_server.cc b/ssl/handshake_server.cc
index c4f3b75e5..1c93fd16d 100644
--- a/ssl/handshake_server.cc
+++ b/ssl/handshake_server.cc
@@ -932,7 +932,10 @@ static enum ssl_hs_wait_t do_send_server_certificate(SSL_HANDSHAKE *hs) {
hs->new_session->group_id = group_id;
// Set up ECDH, generate a key, and emit the public half.
- hs->key_share = SSLKeyShare::Create(group_id);
+ if ((hs->key_share = SSLKeyShare::Create(group_id)) == nullptr) {
+ return ssl_hs_error;
+ }
+ hs->key_share->SetInitiator(false);
if (!hs->key_share ||
!CBB_add_u8(cbb.get(), NAMED_CURVE_TYPE) ||
!CBB_add_u16(cbb.get(), group_id) ||
diff --git a/ssl/internal.h b/ssl/internal.h
index f8a2ea70a..ddd6bb397 100644
--- a/ssl/internal.h
+++ b/ssl/internal.h
@@ -998,12 +998,20 @@ class SSLKeyShare {
// Deserialize initializes the state of the key exchange from |in|, returning
// true if successful and false otherwise. It is called by |Create|.
virtual bool Deserialize(CBS *in) { return false; }
+
+ // Sets flag indicating role of the key share owner. True for initiator of the
+ // handshake, false for responder.
+ void SetInitiator(bool flag) { is_initiator_ = flag; }
+
+ protected:
+ bool is_initiator_ = false;
};
struct NamedGroup {
int nid;
uint16_t group_id;
- const char name[8], alias[11];
+ const char name[16], alias[15];
+ uint16_t min_protocol_ver;
};
// NamedGroups returns all supported groups.
@@ -1019,6 +1027,10 @@ bool ssl_nid_to_group_id(uint16_t *out_group_id, int nid);
// true. Otherwise, it returns false.
bool ssl_name_to_group_id(uint16_t *out_group_id, const char *name, size_t len);
+// ssl_get_protocol_ver_for_group looks up the minimal version of a TLS that
+// supports |group_id|. In case |group_id| is not a valid ID of a group function
+// returns 0.
+uint16_t ssl_get_protocol_ver_for_group(uint16_t group_id);
// Handshake messages.
diff --git a/ssl/ssl_key_share.cc b/ssl/ssl_key_share.cc
index 55c74633c..f36e33bb5 100644
--- a/ssl/ssl_key_share.cc
+++ b/ssl/ssl_key_share.cc
@@ -30,6 +30,8 @@
#include "internal.h"
#include "../crypto/internal.h"
+#include "sidh/def_p503.h"
+#include "sidh/P503_api.h"
BSSL_NAMESPACE_BEGIN
@@ -207,12 +209,88 @@ class X25519KeyShare : public SSLKeyShare {
uint8_t private_key_[32];
};
+class SIDHp503X25519KeyShare : public SSLKeyShare {
+public:
+ ~SIDHp503X25519KeyShare() override {
+ OPENSSL_cleanse(private_x25519_, sizeof(private_x25519_));
+ OPENSSL_cleanse(private_SIDH_, sizeof(private_SIDH_));
+ }
+
+ uint16_t GroupID() const override {
+ return SSL_CURVE_X25519_SIDHp503;
+ }
+
+ bool Offer(CBB *out) override {
+ uint8_t public_x25519[32] = {0};
+ uint8_t public_SIDH[SIDHp503_PUB_BYTESZ] = {0};
+
+ X25519_keypair(public_x25519, private_x25519_);
+ if (EphemeralKeyPair_SIDHp503(private_SIDH_, public_SIDH, is_initiator_)) {
+ return false;
+ }
+
+ return
+ CBB_add_bytes(out, public_x25519, sizeof(public_x25519)) &&
+ CBB_add_bytes(out, public_SIDH, sizeof(public_SIDH));
+ }
+
+ bool Finish(Array<uint8_t> *out_secret, uint8_t *out_alert,
+ Span<const uint8_t> peer_key) override {
+ *out_alert = SSL_AD_INTERNAL_ERROR;
+
+ Array<uint8_t> secret;
+ if (!secret.Init(sizeof(private_x25519_) + SIDHp503_SS_BYTESZ)) {
+ OPENSSL_PUT_ERROR(SSL, ERR_R_MALLOC_FAILURE);
+ return false;
+ }
+
+ if (peer_key.size() != (32 + SIDHp503_PUB_BYTESZ) ||
+ !X25519(secret.data(), private_x25519_, peer_key.data())) {
+ *out_alert = SSL_AD_DECODE_ERROR;
+ OPENSSL_PUT_ERROR(SSL, SSL_R_BAD_ECPOINT);
+ return false;
+ }
+
+ if (is_initiator_) {
+ // Never fails
+ (void)EphemeralSecretAgreement_A_SIDHp503(private_SIDH_, peer_key.data() + 32, secret.data() + sizeof(private_x25519_));
+ } else {
+ (void)EphemeralSecretAgreement_B_SIDHp503(private_SIDH_, peer_key.data() + 32, secret.data() + sizeof(private_x25519_));
+ }
+
+ *out_secret = std::move(secret);
+ return true;
+ }
+
+ bool Serialize(CBB *out) override {
+ return (CBB_add_asn1_uint64(out, GroupID()) &&
+ CBB_add_asn1_octet_string(out, private_x25519_, sizeof(private_x25519_)) &&
+ CBB_add_asn1_octet_string(out, private_SIDH_, sizeof(private_SIDH_)));
+ }
+
+ bool Deserialize(CBS *in) override {
+ CBS key;
+ if (!CBS_get_asn1(in, &key, CBS_ASN1_OCTETSTRING) ||
+ CBS_len(&key) != (sizeof(private_x25519_) + sizeof(private_SIDH_)) ||
+ !CBS_copy_bytes(&key, private_x25519_, sizeof(private_x25519_)) ||
+ !CBS_copy_bytes(&key, private_SIDH_, sizeof(private_SIDH_))) {
+ return false;
+ }
+ return true;
+ }
+
+private:
+ uint8_t private_x25519_[32];
+ uint8_t private_SIDH_[SIDHp503_PRV_KEY_BYTESZ_MAX];
+};
+
CONSTEXPR_ARRAY NamedGroup kNamedGroups[] = {
- {NID_secp224r1, SSL_CURVE_SECP224R1, "P-224", "secp224r1"},
- {NID_X9_62_prime256v1, SSL_CURVE_SECP256R1, "P-256", "prime256v1"},
- {NID_secp384r1, SSL_CURVE_SECP384R1, "P-384", "secp384r1"},
- {NID_secp521r1, SSL_CURVE_SECP521R1, "P-521", "secp521r1"},
- {NID_X25519, SSL_CURVE_X25519, "X25519", "x25519"},
+ {NID_secp224r1, SSL_CURVE_SECP224R1, "P-224", "secp224r1", TLS1_VERSION},
+ {NID_X9_62_prime256v1, SSL_CURVE_SECP256R1, "P-256", "prime256v1", TLS1_VERSION},
+ {NID_secp384r1, SSL_CURVE_SECP384R1, "P-384", "secp384r1", TLS1_VERSION},
+ {NID_secp521r1, SSL_CURVE_SECP521R1, "P-521", "secp521r1", TLS1_VERSION},
+ {NID_X25519, SSL_CURVE_X25519, "X25519", "x25519", TLS1_VERSION},
+ {NID_X25519_SIDHp503, SSL_CURVE_X25519_SIDHp503, "X25519-SIDHp503", "x25519sidhp503", TLS1_3_VERSION},
};
} // namespace
@@ -237,6 +315,8 @@ UniquePtr<SSLKeyShare> SSLKeyShare::Create(uint16_t group_id) {
New<ECKeyShare>(NID_secp521r1, SSL_CURVE_SECP521R1));
case SSL_CURVE_X25519:
return UniquePtr<SSLKeyShare>(New<X25519KeyShare>());
+ case SSL_CURVE_X25519_SIDHp503:
+ return UniquePtr<SSLKeyShare>(New<SIDHp503X25519KeyShare>());
default:
return nullptr;
}
@@ -288,6 +368,15 @@ bool ssl_name_to_group_id(uint16_t *out_group_id, const char *name, size_t len)
return false;
}
+uint16_t ssl_get_protocol_ver_for_group(uint16_t group_id) {
+ for (const auto &group : kNamedGroups) {
+ if (group.group_id == group_id) {
+ return group.min_protocol_ver;
+ }
+ }
+ return 0;
+}
+
BSSL_NAMESPACE_END
using namespace bssl;
diff --git a/ssl/t1_lib.cc b/ssl/t1_lib.cc
index 678e4a3b7..6bfd21c82 100644
--- a/ssl/t1_lib.cc
+++ b/ssl/t1_lib.cc
@@ -324,7 +324,8 @@ bool tls1_get_shared_group(SSL_HANDSHAKE *hs, uint16_t *out_group_id) {
for (uint16_t pref_group : pref) {
for (uint16_t supp_group : supp) {
- if (pref_group == supp_group) {
+ if ((pref_group == supp_group) &&
+ (ssl_get_protocol_ver_for_group(pref_group)<=ssl_protocol_version(ssl))) {
*out_group_id = pref_group;
return true;
}
@@ -2177,7 +2178,10 @@ static bool ext_key_share_add_clienthello(SSL_HANDSHAKE *hs, CBB *out) {
group_id = groups[0];
}
- hs->key_share = SSLKeyShare::Create(group_id);
+ if ((hs->key_share = SSLKeyShare::Create(group_id)) == nullptr) {
+ return false;
+ }
+ hs->key_share->SetInitiator(true);
CBB key_exchange;
if (!hs->key_share ||
!CBB_add_u16(&kse_bytes, group_id) ||
diff --git a/third_party/sidh/CMakeLists.txt b/third_party/sidh/CMakeLists.txt
new file mode 100644
index 000000000..6befbfe47
--- /dev/null
+++ b/third_party/sidh/CMakeLists.txt
@@ -0,0 +1,54 @@
+cmake_minimum_required(VERSION 2.8.11)
+include_directories(../../include)
+
+set(ASM_EXT S)
+enable_language(ASM)
+add_definitions(-pedantic)
+
+# Compile to object files, we will link them with libssl
+add_library(
+ sidh
+
+ OBJECT
+
+ src/ec_isogeny.c
+ src/fpx.c
+ src/P503.c
+ src/sidh.c
+)
+
+# Architecture specific settings
+if(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "aarch64" OR ${CMAKE_SYSTEM_PROCESSOR} STREQUAL "arm64")
+ add_definitions(-lrt)
+endif()
+
+# Platform specific sources
+if(OPENSSL_NO_ASM)
+ target_sources(
+ sidh
+ PRIVATE
+ src/generic/fp_generic.c
+ )
+elseif(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "x86_64")
+ target_sources(
+ sidh
+
+ PRIVATE
+
+ src/AMD64/fp_x64.c
+ src/AMD64/fp_x64_asm.${ASM_EXT}
+ )
+elseif(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "aarch64" OR ${CMAKE_SYSTEM_PROCESSOR} STREQUAL "arm64")
+ target_sources(
+ sidh
+
+ PRIVATE
+
+ src/ARM64/fp_arm64.c
+ src/ARM64/fp_arm64_asm.${ASM_EXT}
+ )
+endif()
+
+target_include_directories(sidh PUBLIC
+ include
+)
diff --git a/third_party/sidh/LICENSE b/third_party/sidh/LICENSE
new file mode 100644
index 000000000..d76bde897
--- /dev/null
+++ b/third_party/sidh/LICENSE
@@ -0,0 +1,56 @@
+MIT License
+
+Copyright (c) Microsoft Corporation. All rights reserved.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE
+
+========================================================================
+
+Performance improvements and aligning the code to nicely fit to
+BoringSSL was done by Cloudflare and is licensed under BSD3 licence.
+
+========================================================================
+
+Copyright (c) 2018 Cloudflare. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+ * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+ * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+ * Neither the name of Cloudflare nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/third_party/sidh/include/sidh/P503_api.h b/third_party/sidh/include/sidh/P503_api.h
new file mode 100644
index 000000000..6b25196a5
--- /dev/null
+++ b/third_party/sidh/include/sidh/P503_api.h
@@ -0,0 +1,65 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: API header file for P503
+*********************************************************************************************/
+
+#ifndef P503_API_H__
+#define P503_API_H__
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/*********************** Ephemeral key exchange API ***********************/
+
+// Encoding of keys for KEX-based isogeny system "SIDHp503" (wire format):
+// ----------------------------------------------------------------------
+// Elements over GF(p503) are encoded in 63 octets in little endian format (i.e., the least significant octet is located in the lowest memory address).
+// Elements (a+b*i) over GF(p503^2), where a and b are defined over GF(p503), are encoded as {a, b}, with a in the lowest memory portion.
+//
+// Private keys PrivateKeyA and PrivateKeyB can have values in the range [0, 2^250-1] and [0, 2^252-1], resp. In the SIDH API, private keys are encoded
+// in 32 octets in little endian format.
+// Public keys PublicKeyA and PublicKeyB consist of 3 elements in GF(p503^2). In the SIDH API, they are encoded in 378 octets.
+// Shared keys SharedSecretA and SharedSecretB consist of one element in GF(p503^2). In the SIDH API, they are encoded in 126 octets.
+
+// SECURITY NOTE: SIDH supports ephemeral Diffie-Hellman key exchange. It is NOT secure to use it with static keys.
+// See "On the Security of Supersingular Isogeny Cryptosystems", S.D. Galbraith, C. Petit, B. Shani and Y.B. Ti, in ASIACRYPT 2016, 2016.
+// Extended version available at: http://eprint.iacr.org/2016/859
+
+// Alice's ephemeral public key generation
+// Input: a private key PrivateKeyA in the range [0, 2^250 - 1], stored in 32 bytes.
+// Output: the public key PublicKeyA consisting of 3 GF(p503^2) elements encoded in 378 bytes.
+int EphemeralKeyGeneration_A_SIDHp503(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA);
+
+// Bob's ephemeral key-pair generation
+// It produces a private key PrivateKeyB and computes the public key PublicKeyB.
+// The private key is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes.
+// The public key consists of 3 GF(p503^2) elements encoded in 378 bytes.
+int EphemeralKeyGeneration_B_SIDHp503(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB);
+
+// Alice's ephemeral shared secret computation
+// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
+// Inputs: Alice's PrivateKeyA is an integer in the range [0, 2^250 - 1], stored in 32 bytes.
+// Bob's PublicKeyB consists of 3 GF(p503^2) elements encoded in 378 bytes.
+// Output: a shared secret SharedSecretA that consists of one element in GF(p503^2) encoded in 126 bytes.
+int EphemeralSecretAgreement_A_SIDHp503(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA);
+
+// Bob's ephemeral shared secret computation
+// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
+// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,3^159)) - 1], stored in 32 bytes.
+// Alice's PublicKeyA consists of 3 GF(p503^2) elements encoded in 378 bytes.
+// Output: a shared secret SharedSecretB that consists of one element in GF(p503^2) encoded in 126 bytes.
+int EphemeralSecretAgreement_B_SIDHp503(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB);
+
+// Generates SIDH/P503 key pair. Internally uses BN_rand() for a entropy source.
+// Input: IsInitiator: 1 for generating public key type A, 0 for type B.
+// Output: the private (PrivateKey) stored in 32 bytes, public key (PublicKey) stored in 378 bytes
+// Returns: 0 on succes, -1 in case of failure
+int EphemeralKeyPair_SIDHp503(unsigned char* PrivateKey, unsigned char* PublicKey, int IsInitiator);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif
diff --git a/third_party/sidh/include/sidh/def_p503.h b/third_party/sidh/include/sidh/def_p503.h
new file mode 100644
index 000000000..1f39f5988
--- /dev/null
+++ b/third_party/sidh/include/sidh/def_p503.h
@@ -0,0 +1,70 @@
+#ifndef DEF_P503_H_
+#define DEF_P503_H_
+
+#include <stdint.h>
+#include "openssl/base.h"
+#include "../crypto/internal.h"
+#include "sidh/P503_api.h"
+
+// Basic constants
+#define SIDHp503_PRV_A_BITSZ 250 // Bit size of SIDH private key (type A)
+#define SIDHp503_PRV_B_BITSZ 252 // Bit size of SIDH private key (type B)
+#define SIDHp503_PUB_BYTESZ 378 // Byte size of SIDH public key
+#define SIDHp503_SS_BYTESZ 126 // Shared secret byte size
+#define SIDHp503_PRV_KEY_BYTESZ_MAX (((SIDHp503_PRV_A_BITSZ>SIDHp503_PRV_B_BITSZ?SIDHp503_PRV_B_BITSZ:SIDHp503_PRV_B_BITSZ)+7)/8)
+#define NBITS_FIELD 503
+#define NBITS_ORDER 256
+#define NWORDS_ORDER ((NBITS_ORDER+RADIX-1)/RADIX) // Number of words of oA and oB, where oA and oB are the subgroup orders of Alice and Bob, resp.
+#define NWORDS64_FIELD ((NBITS_FIELD+63)/64) // Number of 64-bit words of a 503-bit field element
+#define NWORDS64_ORDER ((NBITS_ORDER+63)/64) // Number of 64-bit words of a 256-bit element
+#define MAX_Alice 125
+#define MAX_Bob 159
+#define RADIX64 64
+
+#if defined(OPENSSL_64_BIT)
+ #define NWORDS_FIELD 8 // Number of words of a 503-bit field element
+ #define p503_ZERO_WORDS 3 // Number of "0" digits in the least significant part of p503 + 1
+ #define RADIX 64
+ #define LOG2RADIX 6
+ typedef uint64_t digit_t; // Unsigned 64-bit digit
+#else
+ #define NWORDS_FIELD 16
+ #define p503_ZERO_WORDS 7
+ #define RADIX 32
+ #define LOG2RADIX 5
+ typedef uint32_t digit_t; // Unsigned 32-bit digit
+#endif
+
+// Extended datatype support
+#if !defined(BORINGSSL_HAS_UINT128)
+ typedef uint64_t uint128_t[2];
+#endif
+
+struct params_t {
+ const uint64_t prime[NWORDS64_FIELD];
+ const uint64_t primeP1[NWORDS64_FIELD];
+ const uint64_t primeX2[NWORDS64_FIELD];
+ // Order of Alice's subgroup
+ const uint64_t Alice_order[NWORDS64_ORDER];
+ // Order of Bob's subgroup
+ const uint64_t Bob_order[NWORDS64_ORDER];
+ // Alice's generator values {XPA0 + XPA1*i, XQA0, XRA0 + XRA1*i} in GF(p503^2), expressed in Montgomery representation
+ const uint64_t A_gen[5*NWORDS64_FIELD];
+ // Bob's generator values {XPB0 + XPB1*i, XQB0, XRB0 + XRB1*i} in GF(p503^2), expressed in Montgomery representation
+ const uint64_t B_gen[5*NWORDS64_FIELD];
+ // Montgomery constant Montgomery_R2 = (2^512)^2 mod p503
+ const uint64_t Montgomery_R2[NWORDS64_FIELD];
+ // Value one in Montgomery representation
+ const uint64_t Montgomery_one[NWORDS64_FIELD];
+ // Value (2^256)^2 mod 3^159
+ const uint64_t Montgomery_Rprime[NWORDS64_ORDER];
+ // Value -(3^159)^-1 mod 2^256
+ const uint64_t Montgomery_rprime[NWORDS64_ORDER];
+ // Value order_Bob/3 mod p503
+ const uint64_t Border_div3[NWORDS_ORDER];
+ // Fixed parameters for isogeny tree computation
+ const unsigned int strat_Alice[MAX_Alice-1];
+ const unsigned int strat_Bob[MAX_Bob-1];
+};
+
+#endif // DEF_P503_H_
diff --git a/third_party/sidh/src/AMD64/fp_x64.c b/third_party/sidh/src/AMD64/fp_x64.c
new file mode 100644
index 000000000..62bb9692e
--- /dev/null
+++ b/third_party/sidh/src/AMD64/fp_x64.c
@@ -0,0 +1,88 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: modular arithmetic optimized for x64 platforms for P503
+*********************************************************************************************/
+
+#include "../internal.h"
+#include "../P503_internal.h"
+
+// Global constants
+extern const struct params_t kP503Params;
+
+inline void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular addition, c = a+b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+
+ fpadd503_asm(a, b, c);
+}
+
+
+inline void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular subtraction, c = a-b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ fpsub503_asm(a, b, c);
+}
+
+
+inline void fpneg503(digit_t* a)
+{ // Modular negation, a = -a mod p503.
+ // Input/output: a in [0, 2*p503-1]
+ unsigned int i, borrow = 0;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, ((digit_t*)kP503Params.primeX2)[i], a[i], borrow, a[i]);
+ }
+}
+
+
+void fpdiv2_503(const digit_t* a, digit_t* c)
+{ // Modular division by two, c = a/2 mod p503.
+ // Input : a in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ unsigned int i, carry = 0;
+ digit_t mask;
+
+ mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p503
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(carry, a[i], ((digit_t*)kP503Params.prime)[i] & mask, carry, c[i]);
+ }
+
+ mp_shiftr1(c, NWORDS_FIELD);
+}
+
+
+void fpcorrection503(digit_t* a)
+{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
+ unsigned int i, borrow = 0;
+ digit_t mask;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, a[i], ((digit_t*)kP503Params.prime)[i], borrow, a[i]);
+ }
+ mask = 0 - (digit_t)borrow;
+
+ borrow = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(borrow, a[i], ((digit_t*)kP503Params.prime)[i] & mask, borrow, a[i]);
+ }
+}
+
+
+void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
+{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
+
+ UNREFERENCED_PARAMETER(nwords);
+ mul503_asm(a, b, c);
+}
+
+
+void rdc_mont(const digit_t* ma, digit_t* mc)
+{ // Montgomery reduction exploiting special form of the prime.
+ // mc = ma*R^-1 mod primeX2, where R = 2^512.
+ // If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
+ // ma is assumed to be in Montgomery representation.
+ rdc503_asm(ma, mc);
+}
diff --git a/third_party/sidh/src/AMD64/fp_x64_asm.S b/third_party/sidh/src/AMD64/fp_x64_asm.S
new file mode 100644
index 000000000..4e8f3147a
--- /dev/null
+++ b/third_party/sidh/src/AMD64/fp_x64_asm.S
@@ -0,0 +1,1640 @@
+//*******************************************************************************************
+// SIDH: an efficient supersingular isogeny cryptography library
+//
+// Abstract: field arithmetic in x64 assembly for P503 on Linux
+//*******************************************************************************************
+
+.intel_syntax noprefix
+
+// Registers that are used for parameter passing:
+#define reg_p1 rdi
+#define reg_p2 rsi
+#define reg_p3 rdx
+
+// p503 + 1
+#define p503p1_3 0xAC00000000000000
+#define p503p1_4 0x13085BDA2211E7A0
+#define p503p1_5 0x1B9BF6C87B7E7DAF
+#define p503p1_6 0x6045C6BDDA77A4D0
+#define p503p1_7 0x004066F541811E1E
+// p503 x 2
+#define p503x2_0 0xFFFFFFFFFFFFFFFE
+#define p503x2_1 0xFFFFFFFFFFFFFFFF
+#define p503x2_3 0x57FFFFFFFFFFFFFF
+#define p503x2_4 0x2610B7B44423CF41
+#define p503x2_5 0x3737ED90F6FCFB5E
+#define p503x2_6 0xC08B8D7BB4EF49A0
+#define p503x2_7 0x0080CDEA83023C3C
+
+.text
+
+.extern OPENSSL_ia32cap_P
+.hidden OPENSSL_ia32cap_P
+
+p503p1_nz:
+.quad 0xAC00000000000000
+.quad 0x13085BDA2211E7A0
+.quad 0x1B9BF6C87B7E7DAF
+.quad 0x6045C6BDDA77A4D0
+.quad 0x004066F541811E1E
+
+.macro CSWAP16 IDX, M1, M2
+ movdqu xmm0, [\M1+\IDX*16]
+ movdqu xmm1, [\M2+\IDX*16]
+ movdqa xmm2, xmm1
+ pxor xmm2, xmm0
+ pand xmm2, xmm15
+ pxor xmm0, xmm2
+ pxor xmm1, xmm2
+ movdqu [\M1+\IDX*16], xmm0
+ movdqu [\M2+\IDX*16], xmm1
+.endm
+
+.global cswap503_asm
+cswap503_asm:
+ // Fill xmm15. After this step first half of XMM15 is
+ // just zeros and second half is whatever in RDX
+ movq xmm15, rdx
+
+ // Copy lower double word everywhere else. So that
+ // XMM15=RDX|RDX. As RDX has either all bits set
+ // or non result will be that XMM15 has also either
+ // all bits set or non of them. 68 = 01000100b
+ pshufd xmm15, xmm15, 68
+
+ // P[0].X with Q[0].X
+ CSWAP16 0, rdi, rsi
+ CSWAP16 1, rdi, rsi
+ CSWAP16 2, rdi, rsi
+ CSWAP16 3, rdi, rsi
+
+ // P[0].Z with Q[0].Z
+ CSWAP16 4, rdi, rsi
+ CSWAP16 5, rdi, rsi
+ CSWAP16 6, rdi, rsi
+ CSWAP16 7, rdi, rsi
+
+ // P[1].X with Q[1].X
+ CSWAP16 8, rdi, rsi
+ CSWAP16 9, rdi, rsi
+ CSWAP16 10, rdi, rsi
+ CSWAP16 11, rdi, rsi
+
+ // P[1].Z with Q[1].Z
+ CSWAP16 12, rdi, rsi
+ CSWAP16 13, rdi, rsi
+ CSWAP16 14, rdi, rsi
+ CSWAP16 15, rdi, rsi
+
+ ret
+
+//***********************************************************************
+// Field addition
+// Operation: c [reg_p3] = a [reg_p1] + b [reg_p2]
+//***********************************************************************
+.global fpadd503_asm
+fpadd503_asm:
+ push r12
+ push r13
+ push r14
+ push r15
+
+ xor rax, rax
+ mov r8, [reg_p1]
+ mov r9, [reg_p1+8]
+ mov r10, [reg_p1+16]
+ mov r11, [reg_p1+24]
+ mov r12, [reg_p1+32]
+ mov r13, [reg_p1+40]
+ mov r14, [reg_p1+48]
+ mov r15, [reg_p1+56]
+ add r8, [reg_p2]
+ adc r9, [reg_p2+8]
+ adc r10, [reg_p2+16]
+ adc r11, [reg_p2+24]
+ adc r12, [reg_p2+32]
+ adc r13, [reg_p2+40]
+ adc r14, [reg_p2+48]
+ adc r15, [reg_p2+56]
+
+ mov rcx, p503x2_0
+ sub r8, rcx
+ mov rcx, p503x2_1
+ sbb r9, rcx
+ sbb r10, rcx
+ mov rcx, p503x2_3
+ sbb r11, rcx
+ mov rcx, p503x2_4
+ sbb r12, rcx
+ mov rcx, p503x2_5
+ sbb r13, rcx
+ mov rcx, p503x2_6
+ sbb r14, rcx
+ mov rcx, p503x2_7
+ sbb r15, rcx
+ sbb rax, 0
+
+ mov rdi, p503x2_0
+ and rdi, rax
+ mov rsi, p503x2_1
+ and rsi, rax
+ mov rcx, p503x2_3
+ and rcx, rax
+
+ add r8, rdi
+ adc r9, rsi
+ adc r10, rsi
+ adc r11, rcx
+ mov [reg_p3], r8
+ mov [reg_p3+8], r9
+ mov [reg_p3+16], r10
+ mov [reg_p3+24], r11
+ setc cl
+
+ mov r8, p503x2_4
+ and r8, rax
+ mov r9, p503x2_5
+ and r9, rax
+ mov r10, p503x2_6
+ and r10, rax
+ mov r11, p503x2_7
+ and r11, rax
+
+ bt rcx, 0
+ adc r12, r8
+ adc r13, r9
+ adc r14, r10
+ adc r15, r11
+ mov [reg_p3+32], r12
+ mov [reg_p3+40], r13
+ mov [reg_p3+48], r14
+ mov [reg_p3+56], r15
+
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ ret
+
+
+//***********************************************************************
+// Field subtraction
+// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]
+//***********************************************************************
+.global fpsub503_asm
+fpsub503_asm:
+ push r12
+ push r13
+ push r14
+ push r15
+
+ xor rax, rax
+ mov r8, [reg_p1]
+ mov r9, [reg_p1+8]
+ mov r10, [reg_p1+16]
+ mov r11, [reg_p1+24]
+ mov r12, [reg_p1+32]
+ mov r13, [reg_p1+40]
+ mov r14, [reg_p1+48]
+ mov r15, [reg_p1+56]
+ sub r8, [reg_p2]
+ sbb r9, [reg_p2+8]
+ sbb r10, [reg_p2+16]
+ sbb r11, [reg_p2+24]
+ sbb r12, [reg_p2+32]
+ sbb r13, [reg_p2+40]
+ sbb r14, [reg_p2+48]
+ sbb r15, [reg_p2+56]
+ sbb rax, 0
+
+ mov rdi, p503x2_0
+ and rdi, rax
+ mov rsi, p503x2_1
+ and rsi, rax
+ mov rcx, p503x2_3
+ and rcx, rax
+
+ add r8, rdi
+ adc r9, rsi
+ adc r10, rsi
+ adc r11, rcx
+ mov [reg_p3], r8
+ mov [reg_p3+8], r9
+ mov [reg_p3+16], r10
+ mov [reg_p3+24], r11
+ setc cl
+
+ mov r8, p503x2_4
+ and r8, rax
+ mov r9, p503x2_5
+ and r9, rax
+ mov r10, p503x2_6
+ and r10, rax
+ mov r11, p503x2_7
+ and r11, rax
+
+ bt rcx, 0
+ adc r12, r8
+ adc r13, r9
+ adc r14, r10
+ adc r15, r11
+ mov [reg_p3+32], r12
+ mov [reg_p3+40], r13
+ mov [reg_p3+48], r14
+ mov [reg_p3+56], r15
+
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ ret
+
+
+///////////////////////////////////////////////////////////////// MACRO
+// Schoolbook integer multiplication, a full row at a time
+// Inputs: memory pointers M0 and M1
+// Outputs: memory pointer C
+// Temps: regs T0:T9
+/////////////////////////////////////////////////////////////////
+
+.macro MUL256_SCHOOL M0, M1, C, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9
+ mov rdx, \M0
+ mulx \T0, \T1, \M1 // T0:T1 = A0*B0
+ mov \C, \T1 // C0_final
+ mulx \T1, \T2, 8\M1 // T1:T2 = A0*B1
+ xor rax, rax
+ adox \T0, \T2
+ mulx \T2, \T3, 16\M1 // T2:T3 = A0*B2
+ adox \T1, \T3
+ mulx \T3, \T4, 24\M1 // T3:T4 = A0*B3
+ adox \T2, \T4
+
+ mov rdx, 8\M0
+ mulx \T5, \T4, \M1 // T5:T4 = A1*B0
+ adox \T3, rax
+ xor rax, rax
+ mulx \T6, \T7, 8\M1 // T6:T7 = A1*B1
+ adox \T4, \T0
+ mov 8\C, \T4 // C1_final
+ adcx \T5, \T7
+ mulx \T7, \T8, 16\M1 // T7:T8 = A1*B2
+ adcx \T6, \T8
+ adox \T5, \T1
+ mulx \T8, \T9, 24\M1 // T8:T9 = A1*B3
+ adcx \T7, \T9
+ adcx \T8, rax
+ adox \T6, \T2
+
+ mov rdx, 16\M0
+ mulx \T1, \T0, \M1 // T1:T0 = A2*B0
+ adox \T7, \T3
+ adox \T8, rax
+ xor rax, rax
+ mulx \T2, \T3, 8\M1 // T2:T3 = A2*B1
+ adox \T0, \T5
+ mov 16\C, \T0 // C2_final
+ adcx \T1, \T3
+ mulx \T3, \T4, 16\M1 // T3:T4 = A2*B2
+ adcx \T2, \T4
+ adox \T1, \T6
+ mulx \T4,\T9, 24\M1 // T3:T4 = A2*B3
+ adcx \T3, \T9
+ mov rdx, 24\M0
+ adcx \T4, rax
+
+ adox \T2, \T7
+ adox \T3, \T8
+ adox \T4, rax
+
+ mulx \T5, \T0, \M1 // T5:T0 = A3*B0
+ xor rax, rax
+ mulx \T6, \T7, 8\M1 // T6:T7 = A3*B1
+ adcx \T5, \T7
+ adox \T1, \T0
+ mulx \T7, \T8, 16\M1 // T7:T8 = A3*B2
+ adcx \T6, \T8
+ adox \T2, \T5
+ mulx \T8, \T9, 24\M1 // T8:T9 = A3*B3
+ adcx \T7, \T9
+ adcx \T8, rax
+
+ adox \T3, \T6
+ adox \T4, \T7
+ adox \T8, rax
+ mov 24\C, \T1 // C3_final
+ mov 32\C, \T2 // C4_final
+ mov 40\C, \T3 // C5_final
+ mov 48\C, \T4 // C6_final
+ mov 56\C, \T8 // C7_final
+.endm
+
+//*****************************************************************************
+// 503-bit multiplication using Karatsuba (one level), schoolbook (one level)
+//*****************************************************************************
+mul503_mulx_asm:
+ push r12
+ push r13
+ push r14
+ push r15
+ mov rcx, reg_p3
+
+ // r8-r11 <- AH + AL, rax <- mask
+ xor rax, rax
+ mov r8, [reg_p1]
+ mov r9, [reg_p1+8]
+ mov r10, [reg_p1+16]
+ mov r11, [reg_p1+24]
+ push rbx
+ push rbp
+ sub rsp, 96
+ add r8, [reg_p1+32]
+ adc r9, [reg_p1+40]
+ adc r10, [reg_p1+48]
+ adc r11, [reg_p1+56]
+ sbb rax, 0
+ mov [rsp], r8
+ mov [rsp+8], r9
+ mov [rsp+16], r10
+ mov [rsp+24], r11
+
+ // r12-r15 <- BH + BL, rbx <- mask
+ xor rbx, rbx
+ mov r12, [reg_p2]
+ mov r13, [reg_p2+8]
+ mov r14, [reg_p2+16]
+ mov r15, [reg_p2+24]
+ add r12, [reg_p2+32]
+ adc r13, [reg_p2+40]
+ adc r14, [reg_p2+48]
+ adc r15, [reg_p2+56]
+ sbb rbx, 0
+ mov [rsp+32], r12
+ mov [rsp+40], r13
+ mov [rsp+48], r14
+ mov [rsp+56], r15
+
+ // r12-r15 <- masked (BH + BL)
+ and r12, rax
+ and r13, rax
+ and r14, rax
+ and r15, rax
+
+ // r8-r11 <- masked (AH + AL)
+ and r8, rbx
+ and r9, rbx
+ and r10, rbx
+ and r11, rbx
+
+ // r8-r11 <- masked (AH + AL) + masked (AH + AL)
+ add r8, r12
+ adc r9, r13
+ adc r10, r14
+ adc r11, r15
+ mov [rsp+64], r8
+ mov [rsp+72], r9
+ mov [rsp+80], r10
+ mov [rsp+88], r11
+
+ // [rcx+64] <- (AH+AL) x (BH+BL), low part
+ MUL256_SCHOOL [rsp], [rsp+32], [rcx+64], r8, r9, r10, r11, r12, r13, r14, r15, rbx, rbp
+
+ // [rcx] <- AL x BL
+ MUL256_SCHOOL [reg_p1], [reg_p2], [rcx], r8, r9, r10, r11, r12, r13, r14, r15, rbx, rbp // Result C0-C3
+
+ // [rsp] <- AH x BH
+ MUL256_SCHOOL [reg_p1+32], [reg_p2+32], [rsp], r8, r9, r10, r11, r12, r13, r14, r15, rbx, rbp
+
+ // r8-r11 <- (AH+AL) x (BH+BL), final step
+ mov r8, [rsp+64]
+ mov r9, [rsp+72]
+ mov r10, [rsp+80]
+ mov r11, [rsp+88]
+ mov rax, [rcx+96]
+ add r8, rax
+ mov rax, [rcx+104]
+ adc r9, rax
+ mov rax, [rcx+112]
+ adc r10, rax
+ mov rax, [rcx+120]
+ adc r11, rax
+
+ // [rcx+64], x3-x5 <- (AH+AL) x (BH+BL) - ALxBL
+ mov r12, [rcx+64]
+ mov r13, [rcx+72]
+ mov r14, [rcx+80]
+ mov r15, [rcx+88]
+ sub r12, [rcx]
+ sbb r13, [rcx+8]
+ sbb r14, [rcx+16]
+ sbb r15, [rcx+24]
+ sbb r8, [rcx+32]
+ sbb r9, [rcx+40]
+ sbb r10, [rcx+48]
+ sbb r11, [rcx+56]
+
+ // r8-r15 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH
+ sub r12, [rsp]
+ sbb r13, [rsp+8]
+ sbb r14, [rsp+16]
+ sbb r15, [rsp+24]
+ sbb r8, [rsp+32]
+ sbb r9, [rsp+40]
+ sbb r10, [rsp+48]
+ sbb r11, [rsp+56]
+
+ add r12, [rcx+32]
+ mov [rcx+32], r12 // Result C4-C7
+ adc r13, [rcx+40]
+ mov [rcx+40], r13
+ adc r14, [rcx+48]
+ mov [rcx+48], r14
+ adc r15, [rcx+56]
+ mov [rcx+56], r15
+ mov rax, [rsp]
+ adc r8, rax
+ mov [rcx+64], r8 // Result C8-C15
+ mov rax, [rsp+8]
+ adc r9, rax
+ mov [rcx+72], r9
+ mov rax, [rsp+16]
+ adc r10, rax
+ mov [rcx+80], r10
+ mov rax, [rsp+24]
+ adc r11, rax
+ mov [rcx+88], r11
+ mov r12, [rsp+32]
+ adc r12, 0
+ mov [rcx+96], r12
+ mov r13, [rsp+40]
+ adc r13, 0
+ mov [rcx+104], r13
+ mov r14, [rsp+48]
+ adc r14, 0
+ mov [rcx+112], r14
+ mov r15, [rsp+56]
+ adc r15, 0
+ mov [rcx+120], r15
+
+ add rsp, 96
+ pop rbp
+ pop rbx
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ ret
+
+//***********************************************************************
+// Integer multiplication
+// Based on Karatsuba method
+// Operation: c [reg_p3] = a [reg_p1] * b [reg_p2]
+// NOTE: a=c or b=c are not allowed
+//***********************************************************************
+.global mul503_asm
+mul503_asm:
+ mov ecx, [rip+OPENSSL_ia32cap_P+8]
+ and ecx, 0x80100
+ cmp ecx, 0x80100
+ je mul503_mulx_asm
+
+ push r12
+ push r13
+ push r14
+ mov rcx, reg_p3
+
+ // rcx[0-3] <- AH+AL
+ xor rax, rax
+ mov r8, [reg_p1+32]
+ mov r9, [reg_p1+40]
+ mov r10, [reg_p1+48]
+ mov r11, [reg_p1+56]
+ add r8, [reg_p1]
+ adc r9, [reg_p1+8]
+ adc r10, [reg_p1+16]
+ adc r11, [reg_p1+24]
+ push r15
+ mov [rcx], r8
+ mov [rcx+8], r9
+ mov [rcx+16], r10
+ mov [rcx+24], r11
+ sbb rax, 0
+ sub rsp, 80 // Allocating space in stack
+
+ // r12-r15 <- BH+BL
+ xor rdx, rdx
+ mov r12, [reg_p2+32]
+ mov r13, [reg_p2+40]
+ mov r14, [reg_p2+48]
+ mov r15, [reg_p2+56]
+ add r12, [reg_p2]
+ adc r13, [reg_p2+8]
+ adc r14, [reg_p2+16]
+ adc r15, [reg_p2+24]
+ sbb rdx, 0
+ mov [rsp+64], rax
+ mov [rsp+72], rdx
+
+ // (rsp[0-3],r8,r9,r10,r11) <- (AH+AL)*(BH+BL)
+ mov rax, [rcx]
+ mul r12
+ mov [rsp], rax // c0
+ mov r8, rdx
+
+ xor r9, r9
+ mov rax, [rcx]
+ mul r13
+ add r8, rax
+ adc r9, rdx
+
+ xor r10, r10
+ mov rax, [rcx+8]
+ mul r12
+ add r8, rax
+ mov [rsp+8], r8 // c1
+ adc r9, rdx
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, [rcx]
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [rcx+16]
+ mul r12
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [rcx+8]
+ mul r13
+ add r9, rax
+ mov [rsp+16], r9 // c2
+ adc r10, rdx
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, [rcx]
+ mul r15
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [rcx+24]
+ mul r12
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [rcx+8]
+ mul r14
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [rcx+16]
+ mul r13
+ add r10, rax
+ mov [rsp+24], r10 // c3
+ adc r8, rdx
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, [rcx+8]
+ mul r15
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [rcx+24]
+ mul r13
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [rcx+16]
+ mul r14
+ add r8, rax
+ mov [rsp+32], r8 // c4
+ adc r9, rdx
+ adc r10, 0
+
+ xor r11, r11
+ mov rax, [rcx+16]
+ mul r15
+ add r9, rax
+ adc r10, rdx
+ adc r11, 0
+
+ mov rax, [rcx+24]
+ mul r14
+ add r9, rax // c5
+ adc r10, rdx
+ adc r11, 0
+
+ mov rax, [rcx+24]
+ mul r15
+ add r10, rax // c6
+ adc r11, rdx // c7
+
+ mov rax, [rsp+64]
+ and r12, rax
+ and r13, rax
+ and r14, rax
+ and r15, rax
+ add r12, r8
+ adc r13, r9
+ adc r14, r10
+ adc r15, r11
+
+ mov rax, [rsp+72]
+ mov r8, [rcx]
+ mov r9, [rcx+8]
+ mov r10, [rcx+16]
+ mov r11, [rcx+24]
+ and r8, rax
+ and r9, rax
+ and r10, rax
+ and r11, rax
+ add r8, r12
+ adc r9, r13
+ adc r10, r14
+ adc r11, r15
+ mov [rsp+32], r8
+ mov [rsp+40], r9
+ mov [rsp+48], r10
+ mov [rsp+56], r11
+
+ // rcx[0-7] <- AL*BL
+ mov r11, [reg_p1]
+ mov rax, [reg_p2]
+ mul r11
+ xor r9, r9
+ mov [rcx], rax // c0
+ mov r8, rdx
+
+ mov r14, [reg_p1+16]
+ mov rax, [reg_p2+8]
+ mul r11
+ xor r10, r10
+ add r8, rax
+ adc r9, rdx
+
+ mov r12, [reg_p1+8]
+ mov rax, [reg_p2]
+ mul r12
+ add r8, rax
+ mov [rcx+8], r8 // c1
+ adc r9, rdx
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, [reg_p2+16]
+ mul r11
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov r13, [reg_p2]
+ mov rax, r14
+ mul r13
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+8]
+ mul r12
+ add r9, rax
+ mov [rcx+16], r9 // c2
+ adc r10, rdx
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, [reg_p2+24]
+ mul r11
+ mov r15, [reg_p1+24]
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, r15
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [reg_p2+16]
+ mul r12
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [reg_p2+8]
+ mul r14
+ add r10, rax
+ mov [rcx+24], r10 // c3
+ adc r8, rdx
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, [reg_p2+24]
+ mul r12
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [reg_p2+8]
+ mul r15
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [reg_p2+16]
+ mul r14
+ add r8, rax
+ mov [rcx+32], r8 // c4
+ adc r9, rdx
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, [reg_p2+24]
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+16]
+ mul r15
+ add r9, rax
+ mov [rcx+40], r9 // c5
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+24]
+ mul r15
+ add r10, rax
+ mov [rcx+48], r10 // c6
+ adc r8, rdx
+ mov [rcx+56], r8 // c7
+
+ // rcx[8-15] <- AH*BH
+ mov r11, [reg_p1+32]
+ mov rax, [reg_p2+32]
+ mul r11
+ xor r9, r9
+ mov [rcx+64], rax // c0
+ mov r8, rdx
+
+ mov r14, [reg_p1+48]
+ mov rax, [reg_p2+40]
+ mul r11
+ xor r10, r10
+ add r8, rax
+ adc r9, rdx
+
+ mov r12, [reg_p1+40]
+ mov rax, [reg_p2+32]
+ mul r12
+ add r8, rax
+ mov [rcx+72], r8 // c1
+ adc r9, rdx
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, [reg_p2+48]
+ mul r11
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov r13, [reg_p2+32]
+ mov rax, r14
+ mul r13
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+40]
+ mul r12
+ add r9, rax
+ mov [rcx+80], r9 // c2
+ adc r10, rdx
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, [reg_p2+56]
+ mul r11
+ mov r15, [reg_p1+56]
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, r15
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [reg_p2+48]
+ mul r12
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, [reg_p2+40]
+ mul r14
+ add r10, rax
+ mov [rcx+88], r10 // c3
+ adc r8, rdx
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, [reg_p2+56]
+ mul r12
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [reg_p2+40]
+ mul r15
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, [reg_p2+48]
+ mul r14
+ add r8, rax
+ mov [rcx+96], r8 // c4
+ adc r9, rdx
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, [reg_p2+56]
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+48]
+ mul r15
+ add r9, rax
+ mov [rcx+104], r9 // c5
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, [reg_p2+56]
+ mul r15
+ add r10, rax
+ mov [rcx+112], r10 // c6
+ adc r8, rdx
+ mov [rcx+120], r8 // c7
+
+ // [r8-r15] <- (AH+AL)*(BH+BL) - AL*BL
+ mov r8, [rsp]
+ sub r8, [rcx]
+ mov r9, [rsp+8]
+ sbb r9, [rcx+8]
+ mov r10, [rsp+16]
+ sbb r10, [rcx+16]
+ mov r11, [rsp+24]
+ sbb r11, [rcx+24]
+ mov r12, [rsp+32]
+ sbb r12, [rcx+32]
+ mov r13, [rsp+40]
+ sbb r13, [rcx+40]
+ mov r14, [rsp+48]
+ sbb r14, [rcx+48]
+ mov r15, [rsp+56]
+ sbb r15, [rcx+56]
+
+ // [r8-r15] <- (AH+AL)*(BH+BL) - AL*BL - AH*BH
+ mov rax, [rcx+64]
+ sub r8, rax
+ mov rax, [rcx+72]
+ sbb r9, rax
+ mov rax, [rcx+80]
+ sbb r10, rax
+ mov rax, [rcx+88]
+ sbb r11, rax
+ mov rax, [rcx+96]
+ sbb r12, rax
+ mov rdx, [rcx+104]
+ sbb r13, rdx
+ mov rdi, [rcx+112]
+ sbb r14, rdi
+ mov rsi, [rcx+120]
+ sbb r15, rsi
+
+ // Final result
+ add r8, [rcx+32]
+ mov [rcx+32], r8
+ adc r9, [rcx+40]
+ mov [rcx+40], r9
+ adc r10, [rcx+48]
+ mov [rcx+48], r10
+ adc r11, [rcx+56]
+ mov [rcx+56], r11
+ adc r12, [rcx+64]
+ mov [rcx+64], r12
+ adc r13, [rcx+72]
+ mov [rcx+72], r13
+ adc r14, [rcx+80]
+ mov [rcx+80], r14
+ adc r15, [rcx+88]
+ mov [rcx+88], r15
+ adc rax, 0
+ mov [rcx+96], rax
+ adc rdx, 0
+ mov [rcx+104], rdx
+ adc rdi, 0
+ mov [rcx+112], rdi
+ adc rsi, 0
+ mov [rcx+120], rsi
+
+ add rsp, 80 // Restoring space in stack
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ ret
+
+///////////////////////////////////////////////////////////////// MACRO
+// Schoolbook integer multiplication
+// Inputs: memory pointers M0 and M1
+// Outputs: regs T0:T6
+// Temps: regs T7:T9
+/////////////////////////////////////////////////////////////////
+.macro MUL128x320_SCHOOL M0, M1, T0, T1, T2, T3, T4, T5, T6, T7, T8, T9
+ mov rdx, \M0
+ mulx \T1, \T0, \M1 // T0 <- C0_final
+ mulx \T2, \T4, 8\M1
+ xor rax, rax
+
+ mulx \T3, \T5, 16\M1
+ adox \T1, \T4
+ adox \T2, \T5
+ mulx \T4, \T7, 24\M1
+ adox \T3, \T7
+ mulx \T5, \T6, 32\M1
+ adox \T4, \T6
+ adox \T5, rax
+
+ mov rdx, 8\M0
+ mulx \T7, \T6, \M1
+ adcx \T1, \T6 // T1 <- C1_final
+ adcx \T2, \T7
+ mulx \T6, \T8, 8\M1
+ adcx \T3, \T6
+ mulx \T9, \T7, 16\M1
+ adcx \T4, \T9
+ mulx \T6, \T9, 24\M1
+ adcx \T5, \T6
+ mulx \T6, rdx, 32\M1
+ adcx \T6, rax
+
+ xor rax, rax
+ adox \T2, \T8
+ adox \T3, \T7
+ adox \T4, \T9
+ adox \T5, rdx
+ adox \T6, rax
+.endm
+
+
+//**************************************************************************************
+// Montgomery reduction
+// Based on method described in Faz-Hernandez et al. https://eprint.iacr.org/2017/1015
+// Operation: c [reg_p2] = a [reg_p1]
+// NOTE: a=c is not allowed
+//**************************************************************************************
+rdc503_mulx_asm:
+ push rbx
+ push r12
+ push r13
+ push r14
+ push r15
+
+ // a[0-1] x p503p1_nz --> result: r8:r14
+ MUL128x320_SCHOOL [reg_p1], [rip+p503p1_nz], r8, r9, r10, r11, r12, r13, r14, rbx, rcx, r15
+
+ xor r15, r15
+ add r8, [reg_p1+24]
+ adc r9, [reg_p1+32]
+ adc r10, [reg_p1+40]
+ adc r11, [reg_p1+48]
+ adc r12, [reg_p1+56]
+ adc r13, [reg_p1+64]
+ adc r14, [reg_p1+72]
+ adc r15, [reg_p1+80]
+ mov [reg_p1+24], r8
+ mov [reg_p1+32], r9
+ mov [reg_p1+40], r10
+ mov [reg_p1+48], r11
+ mov [reg_p1+56], r12
+ mov [reg_p1+64], r13
+ mov [reg_p1+72], r14
+ mov [reg_p1+80], r15
+ mov r8, [reg_p1+88]
+ mov r9, [reg_p1+96]
+ mov r10, [reg_p1+104]
+ mov r11, [reg_p1+112]
+ mov r12, [reg_p1+120]
+ adc r8, 0
+ adc r9, 0
+ adc r10, 0
+ adc r11, 0
+ adc r12, 0
+ mov [reg_p1+88], r8
+ mov [reg_p1+96], r9
+ mov [reg_p1+104], r10
+ mov [reg_p1+112], r11
+ mov [reg_p1+120], r12
+
+ // a[2-3] x p503p1_nz --> result: r8:r14
+ MUL128x320_SCHOOL [reg_p1+16], [rip+p503p1_nz], r8, r9, r10, r11, r12, r13, r14, rbx, rcx, r15
+
+ xor r15, r15
+ add r8, [reg_p1+40]
+ adc r9, [reg_p1+48]
+ adc r10, [reg_p1+56]
+ adc r11, [reg_p1+64]
+ adc r12, [reg_p1+72]
+ adc r13, [reg_p1+80]
+ adc r14, [reg_p1+88]
+ adc r15, [reg_p1+96]
+ mov [reg_p1+40], r8
+ mov [reg_p1+48], r9
+ mov [reg_p1+56], r10
+ mov [reg_p1+64], r11
+ mov [reg_p1+72], r12
+ mov [reg_p1+80], r13
+ mov [reg_p1+88], r14
+ mov [reg_p1+96], r15
+ mov r8, [reg_p1+104]
+ mov r9, [reg_p1+112]
+ mov r10, [reg_p1+120]
+ adc r8, 0
+ adc r9, 0
+ adc r10, 0
+ mov [reg_p1+104], r8
+ mov [reg_p1+112], r9
+ mov [reg_p1+120], r10
+
+ // a[4-5] x p503p1_nz --> result: r8:r14
+ MUL128x320_SCHOOL [reg_p1+32], [rip+p503p1_nz], r8, r9, r10, r11, r12, r13, r14, rbx, rcx, r15
+
+ xor r15, r15
+ xor rbx, rbx
+ add r8, [reg_p1+56]
+ adc r9, [reg_p1+64]
+ adc r10, [reg_p1+72]
+ adc r11, [reg_p1+80]
+ adc r12, [reg_p1+88]
+ adc r13, [reg_p1+96]
+ adc r14, [reg_p1+104]
+ adc r15, [reg_p1+112]
+ adc rbx, [reg_p1+120]
+ mov [reg_p1+56], r8
+ mov [reg_p2], r9 // Final result c0
+ mov [reg_p1+72], r10
+ mov [reg_p1+80], r11
+ mov [reg_p1+88], r12
+ mov [reg_p1+96], r13
+ mov [reg_p1+104], r14
+ mov [reg_p1+112], r15
+ mov [reg_p1+120], rbx
+
+ // a[6-7] x p503p1_nz --> result: r8:r14
+ MUL128x320_SCHOOL [reg_p1+48], [rip+p503p1_nz], r8, r9, r10, r11, r12, r13, r14, rbx, rcx, r15
+
+ // Final result c1:c7
+ add r8, [reg_p1+72]
+ adc r9, [reg_p1+80]
+ adc r10, [reg_p1+88]
+ adc r11, [reg_p1+96]
+ adc r12, [reg_p1+104]
+ adc r13, [reg_p1+112]
+ adc r14, [reg_p1+120]
+ mov [reg_p2+8], r8
+ mov [reg_p2+16], r9
+ mov [reg_p2+24], r10
+ mov [reg_p2+32], r11
+ mov [reg_p2+40], r12
+ mov [reg_p2+48], r13
+ mov [reg_p2+56], r14
+
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ pop rbx
+ ret
+
+//***********************************************************************
+// Montgomery reduction
+// Based on comba method
+// Operation: c [reg_p2] = a [reg_p1]
+// NOTE: a=c is not allowed
+//***********************************************************************
+.global rdc503_asm
+rdc503_asm:
+ mov ecx, [rip+OPENSSL_ia32cap_P+8]
+ and ecx, 0x80100
+ cmp ecx, 0x80100
+ je rdc503_mulx_asm
+
+ push r12
+ push r13
+ push r14
+ push r15
+
+ mov r11, [reg_p1]
+ mov rax, p503p1_3
+ mul r11
+ xor r8, r8
+ add rax, [reg_p1+24]
+ mov [reg_p2+24], rax // z3
+ adc r8, rdx
+
+ xor r9, r9
+ mov rax, p503p1_4
+ mul r11
+ xor r10, r10
+ add r8, rax
+ adc r9, rdx
+
+ mov r12, [reg_p1+8]
+ mov rax, p503p1_3
+ mul r12
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+ add r8, [reg_p1+32]
+ mov [reg_p2+32], r8 // z4
+ adc r9, 0
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, p503p1_5
+ mul r11
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_4
+ mul r12
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov r13, [reg_p1+16]
+ mov rax, p503p1_3
+ mul r13
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+ add r9, [reg_p1+40]
+ mov [reg_p2+40], r9 // z5
+ adc r10, 0
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, p503p1_6
+ mul r11
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_5
+ mul r12
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_4
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov r14, [reg_p2+24]
+ mov rax, p503p1_3
+ mul r14
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+ add r10, [reg_p1+48]
+ mov [reg_p2+48], r10 // z6
+ adc r8, 0
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, p503p1_7
+ mul r11
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_6
+ mul r12
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_5
+ mul r13
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_4
+ mul r14
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov r15, [reg_p2+32]
+ mov rax, p503p1_3
+ mul r15
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+ add r8, [reg_p1+56]
+ mov [reg_p2+56], r8 // z7
+ adc r9, 0
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, p503p1_7
+ mul r12
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_6
+ mul r13
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_5
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_4
+ mul r15
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rcx, [reg_p2+40]
+ mov rax, p503p1_3
+ mul rcx
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+ add r9, [reg_p1+64]
+ mov [reg_p2], r9 // z0
+ adc r10, 0
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, p503p1_7
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_6
+ mul r14
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_5
+ mul r15
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_4
+ mul rcx
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov r13, [reg_p2+48]
+ mov rax, p503p1_3
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+ add r10, [reg_p1+72]
+ mov [reg_p2+8], r10 // z1
+ adc r8, 0
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, p503p1_7
+ mul r14
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_6
+ mul r15
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_5
+ mul rcx
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_4
+ mul r13
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov r14, [reg_p2+56]
+ mov rax, p503p1_3
+ mul r14
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+ add r8, [reg_p1+80]
+ mov [reg_p2+16], r8 // z2
+ adc r9, 0
+ adc r10, 0
+
+ xor r8, r8
+ mov rax, p503p1_7
+ mul r15
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_6
+ mul rcx
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_5
+ mul r13
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+
+ mov rax, p503p1_4
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ adc r8, 0
+ add r9, [reg_p1+88]
+ mov [reg_p2+24], r9 // z3
+ adc r10, 0
+ adc r8, 0
+
+ xor r9, r9
+ mov rax, p503p1_7
+ mul rcx
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_6
+ mul r13
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+
+ mov rax, p503p1_5
+ mul r14
+ add r10, rax
+ adc r8, rdx
+ adc r9, 0
+ add r10, [reg_p1+96]
+ mov [reg_p2+32], r10 // z4
+ adc r8, 0
+ adc r9, 0
+
+ xor r10, r10
+ mov rax, p503p1_7
+ mul r13
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+
+ mov rax, p503p1_6
+ mul r14
+ add r8, rax
+ adc r9, rdx
+ adc r10, 0
+ add r8, [reg_p1+104] // z5
+ mov [reg_p2+40], r8 // z5
+ adc r9, 0
+ adc r10, 0
+
+ mov rax, p503p1_7
+ mul r14
+ add r9, rax
+ adc r10, rdx
+ add r9, [reg_p1+112] // z6
+ mov [reg_p2+48], r9 // z6
+ adc r10, 0
+ add r10, [reg_p1+120] // z7
+ mov [reg_p2+56], r10 // z7
+
+ pop r15
+ pop r14
+ pop r13
+ pop r12
+ ret
+
+//***********************************************************************
+// 503-bit multiprecision addition
+// Operation: c [reg_p3] = a [reg_p1] + b [reg_p2]
+//***********************************************************************
+.global mp_add503_asm
+mp_add503_asm:
+ mov r8, [reg_p1]
+ mov r9, [reg_p1+8]
+ mov r10, [reg_p1+16]
+ mov r11, [reg_p1+24]
+ add r8, [reg_p2]
+ adc r9, [reg_p2+8]
+ adc r10, [reg_p2+16]
+ adc r11, [reg_p2+24]
+ mov [reg_p3], r8
+ mov [reg_p3+8], r9
+ mov [reg_p3+16], r10
+ mov [reg_p3+24], r11
+
+ mov r8, [reg_p1+32]
+ mov r9, [reg_p1+40]
+ mov r10, [reg_p1+48]
+ mov r11, [reg_p1+56]
+ adc r8, [reg_p2+32]
+ adc r9, [reg_p2+40]
+ adc r10, [reg_p2+48]
+ adc r11, [reg_p2+56]
+ mov [reg_p3+32], r8
+ mov [reg_p3+40], r9
+ mov [reg_p3+48], r10
+ mov [reg_p3+56], r11
+ ret
+
+
+//***********************************************************************
+// 2x503-bit multiprecision subtraction
+// Operation: c [reg_p3] = a [reg_p1] - b [reg_p2]. Returns borrow mask
+//***********************************************************************
+.global mp_sub503x2_asm
+mp_sub503x2_asm:
+ xor rax, rax
+ mov r8, [reg_p1]
+ mov r9, [reg_p1+8]
+ mov r10, [reg_p1+16]
+ mov r11, [reg_p1+24]
+ mov rcx, [reg_p1+32]
+ sub r8, [reg_p2]
+ sbb r9, [reg_p2+8]
+ sbb r10, [reg_p2+16]
+ sbb r11, [reg_p2+24]
+ sbb rcx, [reg_p2+32]
+ mov [reg_p3], r8
+ mov [reg_p3+8], r9
+ mov [reg_p3+16], r10
+ mov [reg_p3+24], r11
+ mov [reg_p3+32], rcx
+
+ mov r8, [reg_p1+40]
+ mov r9, [reg_p1+48]
+ mov r10, [reg_p1+56]
+ mov r11, [reg_p1+64]
+ mov rcx, [reg_p1+72]
+ sbb r8, [reg_p2+40]
+ sbb r9, [reg_p2+48]
+ sbb r10, [reg_p2+56]
+ sbb r11, [reg_p2+64]
+ sbb rcx, [reg_p2+72]
+ mov [reg_p3+40], r8
+ mov [reg_p3+48], r9
+ mov [reg_p3+56], r10
+ mov [reg_p3+64], r11
+ mov [reg_p3+72], rcx
+
+ mov r8, [reg_p1+80]
+ mov r9, [reg_p1+88]
+ mov r10, [reg_p1+96]
+ mov r11, [reg_p1+104]
+ mov rcx, [reg_p1+112]
+ sbb r8, [reg_p2+80]
+ sbb r9, [reg_p2+88]
+ sbb r10, [reg_p2+96]
+ sbb r11, [reg_p2+104]
+ sbb rcx, [reg_p2+112]
+ mov [reg_p3+80], r8
+ mov [reg_p3+88], r9
+ mov [reg_p3+96], r10
+ mov [reg_p3+104], r11
+ mov [reg_p3+112], rcx
+
+ mov r8, [reg_p1+120]
+ sbb r8, [reg_p2+120]
+ sbb rax, 0
+ mov [reg_p3+120], r8
+ ret
+
+
+//***********************************************************************
+// Double 2x503-bit multiprecision subtraction
+// Operation: c [reg_p3] = c [reg_p3] - a [reg_p1] - b [reg_p2]
+//***********************************************************************
+.global mp_dblsub503x2_asm
+mp_dblsub503x2_asm:
+ push r12
+ push r13
+ push r14
+
+ xor rax, rax
+ mov r8, [reg_p3]
+ mov r9, [reg_p3+8]
+ mov r10, [reg_p3+16]
+ mov r11, [reg_p3+24]
+ mov r12, [reg_p3+32]
+ mov r13, [reg_p3+40]
+ mov r14, [reg_p3+48]
+ mov rcx, [reg_p3+56]
+ sub r8, [reg_p1]
+ sbb r9, [reg_p1+8]
+ sbb r10, [reg_p1+16]
+ sbb r11, [reg_p1+24]
+ sbb r12, [reg_p1+32]
+ sbb r13, [reg_p1+40]
+ sbb r14, [reg_p1+48]
+ sbb rcx, [reg_p1+56]
+ adc rax, 0
+ sub r8, [reg_p2]
+ sbb r9, [reg_p2+8]
+ sbb r10, [reg_p2+16]
+ sbb r11, [reg_p2+24]
+ sbb r12, [reg_p2+32]
+ sbb r13, [reg_p2+40]
+ sbb r14, [reg_p2+48]
+ sbb rcx, [reg_p2+56]
+ adc rax, 0
+ mov [reg_p3], r8
+ mov [reg_p3+8], r9
+ mov [reg_p3+16], r10
+ mov [reg_p3+24], r11
+ mov [reg_p3+32], r12
+ mov [reg_p3+40], r13
+ mov [reg_p3+48], r14
+ mov [reg_p3+56], rcx
+
+ mov r8, [reg_p3+64]
+ mov r9, [reg_p3+72]
+ mov r10, [reg_p3+80]
+ mov r11, [reg_p3+88]
+ mov r12, [reg_p3+96]
+ mov r13, [reg_p3+104]
+ mov r14, [reg_p3+112]
+ mov rcx, [reg_p3+120]
+ sub r8, rax
+ sbb r8, [reg_p1+64]
+ sbb r9, [reg_p1+72]
+ sbb r10, [reg_p1+80]
+ sbb r11, [reg_p1+88]
+ sbb r12, [reg_p1+96]
+ sbb r13, [reg_p1+104]
+ sbb r14, [reg_p1+112]
+ sbb rcx, [reg_p1+120]
+ sub r8, [reg_p2+64]
+ sbb r9, [reg_p2+72]
+ sbb r10, [reg_p2+80]
+ sbb r11, [reg_p2+88]
+ sbb r12, [reg_p2+96]
+ sbb r13, [reg_p2+104]
+ sbb r14, [reg_p2+112]
+ sbb rcx, [reg_p2+120]
+ mov [reg_p3+64], r8
+ mov [reg_p3+72], r9
+ mov [reg_p3+80], r10
+ mov [reg_p3+88], r11
+ mov [reg_p3+96], r12
+ mov [reg_p3+104], r13
+ mov [reg_p3+112], r14
+ mov [reg_p3+120], rcx
+
+ pop r14
+ pop r13
+ pop r12
+ ret
diff --git a/third_party/sidh/src/ARM64/fp_arm64.c b/third_party/sidh/src/ARM64/fp_arm64.c
new file mode 100644
index 000000000..3a99cfc19
--- /dev/null
+++ b/third_party/sidh/src/ARM64/fp_arm64.c
@@ -0,0 +1,92 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: modular arithmetic optimized for 64-bit ARMv8 platforms for P503
+*********************************************************************************************/
+
+#include "../internal.h"
+#include "../P503_internal.h"
+
+// Global constants
+extern const struct params_t kP503Params;
+
+inline void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular addition, c = a+b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+
+ fpadd503_asm(a, b, c);
+}
+
+
+inline void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular subtraction, c = a-b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+
+ fpsub503_asm(a, b, c);
+}
+
+
+inline void fpneg503(digit_t* a)
+{ // Modular negation, a = -a mod p503.
+ // Input/output: a in [0, 2*p503-1]
+ unsigned int i, borrow = 0;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, ((digit_t*)kP503Params.primeX2)[i], a[i], borrow, a[i]);
+ }
+}
+
+
+void fpdiv2_503(const digit_t* a, digit_t* c)
+{ // Modular division by two, c = a/2 mod p503.
+ // Input : a in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ unsigned int i, carry = 0;
+ digit_t mask;
+
+ mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p521
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(carry, a[i], ((digit_t*)kP503Params.prime)[i] & mask, carry, c[i]);
+ }
+
+ mp_shiftr1(c, NWORDS_FIELD);
+}
+
+
+void fpcorrection503(digit_t* a)
+{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
+ unsigned int i, borrow = 0;
+ digit_t mask;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, a[i], ((digit_t*)kP503Params.prime)[i], borrow, a[i]);
+ }
+ mask = 0 - (digit_t)borrow;
+
+ borrow = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(borrow, a[i], ((digit_t*)kP503Params.prime)[i] & mask, borrow, a[i]);
+ }
+}
+
+
+void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
+{ // Multiprecision multiply, c = a*b, where lng(a) = lng(b) = nwords.
+
+ UNREFERENCED_PARAMETER(nwords);
+
+ mul503_asm(a, b, c);
+}
+
+
+
+void rdc_mont(const digit_t* ma, digit_t* mc)
+{ // Montgomery reduction exploiting special form of the prime.
+ // mc = ma*R^-1 mod p503x2, where R = 2^512.
+ // If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
+ // ma is assumed to be in Montgomery representation.
+
+ rdc503_asm(ma, mc);
+}
diff --git a/third_party/sidh/src/ARM64/fp_arm64_asm.S b/third_party/sidh/src/ARM64/fp_arm64_asm.S
new file mode 100644
index 000000000..7f96452c2
--- /dev/null
+++ b/third_party/sidh/src/ARM64/fp_arm64_asm.S
@@ -0,0 +1,826 @@
+//*******************************************************************************************
+// SIDH: an efficient supersingular isogeny cryptography library
+//
+// Abstract: field arithmetic in 64-bit ARMv8 assembly for P503 on Linux
+//*******************************************************************************************
+
+// p503 + 1
+p503p1:
+#define P503P1_0 0xAC00000000000000
+#define P503P1_1 0x13085BDA2211E7A0
+#define P503P1_2 0x1B9BF6C87B7E7DAF
+#define P503P1_3 0x6045C6BDDA77A4D0
+#define P503P1_4 0x004066F541811E1E
+
+// 2 * p503
+p503x2:
+#define P503x2_0 0xFFFFFFFFFFFFFFFE
+#define P503x2_1 0xFFFFFFFFFFFFFFFF
+#define P503x2_2 0x57FFFFFFFFFFFFFF
+#define P503x2_3 0x2610B7B44423CF41
+#define P503x2_4 0x3737ED90F6FCFB5E
+#define P503x2_5 0xC08B8D7BB4EF49A0
+#define P503x2_6 0x0080CDEA83023C3C
+
+#define P503P1_NZ_S8_0 0x85BDA2211E7A0AC
+#define P503P1_NZ_S8_1 0x9BF6C87B7E7DAF13
+#define P503P1_NZ_S8_2 0x45C6BDDA77A4D01B
+#define P503P1_NZ_S8_3 0x4066F541811E1E60
+
+
+.text
+//***********************************************************************
+// Field addition
+// Operation: c [x2] = a [x0] + b [x1]
+//***********************************************************************
+.global fpadd503_asm
+fpadd503_asm:
+ ldp x3, x4, [x0,#0]
+ ldp x5, x6, [x0,#16]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+
+ // Add a + b
+ adds x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x13
+ adcs x6, x6, x14
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+ adcs x7, x7, x15
+ adcs x8, x8, x16
+ adcs x9, x9, x17
+ adc x10, x10, x18
+
+ // Subtract 2xp503
+ ldr x11, =P503x2_0
+ ldr x12, =P503x2_1
+ ldr x13, =P503x2_2
+ ldr x14, =P503x2_3
+ subs x3, x3, x11
+ sbcs x4, x4, x12
+ sbcs x5, x5, x12
+ sbcs x6, x6, x13
+ sbcs x7, x7, x14
+ ldr x15, =P503x2_4
+ ldr x16, =P503x2_5
+ ldr x17, =P503x2_6
+ sbcs x8, x8, x15
+ sbcs x9, x9, x16
+ sbcs x10, x10, x17
+ sbc x18, xzr, xzr
+
+ // Add 2xp503 anded with the mask in x18
+ and x11, x11, x18
+ and x12, x12, x18
+ and x13, x13, x18
+ and x14, x14, x18
+ and x15, x15, x18
+ and x16, x16, x18
+ and x17, x17, x18
+
+ adds x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x12
+ adcs x6, x6, x13
+ adcs x7, x7, x14
+ adcs x8, x8, x15
+ adcs x9, x9, x16
+ adc x10, x10, x17
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+ ret
+
+
+//***********************************************************************
+// Field subtraction
+// Operation: c [x2] = a [x0] - b [x1]
+//***********************************************************************
+.global fpsub503_asm
+fpsub503_asm:
+ ldp x3, x4, [x0,#0]
+ ldp x5, x6, [x0,#16]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+
+ // Subtract a - b
+ subs x3, x3, x11
+ sbcs x4, x4, x12
+ sbcs x5, x5, x13
+ sbcs x6, x6, x14
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+ sbcs x7, x7, x15
+ sbcs x8, x8, x16
+ sbcs x9, x9, x17
+ sbcs x10, x10, x18
+ sbc x18, xzr, xzr
+
+ // Add 2xp503 anded with the mask in x18
+ ldr x11, =P503x2_0
+ ldr x12, =P503x2_1
+ ldr x13, =P503x2_2
+ ldr x14, =P503x2_3
+ and x11, x11, x18
+ and x12, x12, x18
+ and x13, x13, x18
+ and x14, x14, x18
+ ldr x15, =P503x2_4
+ ldr x16, =P503x2_5
+ ldr x17, =P503x2_6
+ and x15, x15, x18
+ and x16, x16, x18
+ and x17, x17, x18
+
+ adds x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x12
+ adcs x6, x6, x13
+ adcs x7, x7, x14
+ adcs x8, x8, x15
+ adcs x9, x9, x16
+ adc x10, x10, x17
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+ ret
+
+
+//////////////////////////////////////////// MACRO
+.macro MUL128_COMBA_CUT A0, A1, B0, B1, C0, C1, C2, C3, T0
+ mul \A0, \A1, \B0
+ umulh \B0, \A1, \B0
+ adds \C1, \C1, \C3
+ adc \C2, \C2, xzr
+
+ mul \T0, \A1, \B1
+ umulh \B1, \A1, \B1
+ adds \C1, \C1, \A0
+ adcs \C2, \C2, \B0
+ adc \C3, xzr, xzr
+
+ adds \C2, \C2, \T0
+ adc \C3, \C3, \B1
+.endm
+
+
+//////////////////////////////////////////// MACRO
+.macro MUL256_KARATSUBA_COMBA M,A0,A1,A2,A3,B0,B1,B2,B3,C0,C1,C2,C3,C4,C5,C6,C7,T0,T1
+
+ // A0-A1 <- AH + AL, T0 <- mask
+ adds \A0, \A0, \A2
+ adcs \A1, \A1, \A3
+ adc \T0, xzr, xzr
+
+ // C6, T1 <- BH + BL, C7 <- mask
+ adds \C6, \B0, \B2
+ adcs \T1, \B1, \B3
+ adc \C7, xzr, xzr
+
+ // C0-C1 <- masked (BH + BL)
+ sub \C2, xzr, \T0
+ sub \C3, xzr, \C7
+ and \C0, \C6, \C2
+ and \C1, \T1, \C2
+
+ // C4-C5 <- masked (AH + AL), T0 <- combined carry
+ and \C4, \A0, \C3
+ and \C5, \A1, \C3
+ mul \C2, \A0, \C6
+ mul \C3, \A0, \T1
+ and \T0, \T0, \C7
+
+ // C0-C1, T0 <- (AH+AL) x (BH+BL), part 1
+ adds \C0, \C4, \C0
+ umulh \C4, \A0, \T1
+ adcs \C1, \C5, \C1
+ umulh \C5, \A0, \C6
+ adc \T0, \T0, xzr
+
+ // C2-C5 <- (AH+AL) x (BH+BL), low part
+ MUL128_COMBA_CUT \A0, \A1, \C6, \T1, \C2, \C3, \C4, \C5, \C7
+ ldp \A0, \A1, [\M,#0]
+
+ // C2-C5, T0 <- (AH+AL) x (BH+BL), final part
+ adds \C4, \C0, \C4
+ umulh \C7, \A0, \B0
+ umulh \T1, \A0, \B1
+ adcs \C5, \C1, \C5
+ mul \C0, \A0, \B0
+ mul \C1, \A0, \B1
+ adc \T0, \T0, xzr
+
+ // C0-C1, T1, C7 <- AL x BL
+ MUL128_COMBA_CUT \A0, \A1, \B0, \B1, \C0, \C1, \T1, \C7, \C6
+
+ // C2-C5, T0 <- (AH+AL) x (BH+BL) - ALxBL
+ mul \A0, \A2, \B2
+ umulh \B0, \A2, \B2
+ subs \C2, \C2, \C0
+ sbcs \C3, \C3, \C1
+ sbcs \C4, \C4, \T1
+ mul \A1, \A2, \B3
+ umulh \C6, \A2, \B3
+ sbcs \C5, \C5, \C7
+ sbc \T0, \T0, xzr
+
+ // A0, A1, C6, B0 <- AH x BH
+ MUL128_COMBA_CUT \A2, \A3, \B2, \B3, \A0, \A1, \C6, \B0, \B1
+
+ // C2-C5, T0 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH
+ subs \C2, \C2, \A0
+ sbcs \C3, \C3, \A1
+ sbcs \C4, \C4, \C6
+ sbcs \C5, \C5, \B0
+ sbc \T0, \T0, xzr
+
+ adds \C2, \C2, \T1
+ adcs \C3, \C3, \C7
+ adcs \C4, \C4, \A0
+ adcs \C5, \C5, \A1
+ adcs \C6, \T0, \C6
+ adc \C7, \B0, xzr
+.endm
+
+
+//***********************************************************************************
+// 512-bit integer multiplication using Karatsuba (two levels), Comba (lower level)
+// Operation: c [x2] = a [x0] * b [x1]
+//***********************************************************************************
+.global mul503_asm
+mul503_asm:
+ sub sp, sp, #96
+ stp x19, x20, [sp,#0]
+ stp x21, x22, [sp,#16]
+ stp x23, x24, [sp,#32]
+ stp x25, x26, [sp,#48]
+ stp x27, x28, [sp,#64]
+ str x29, [sp, #80]
+
+ ldp x3, x4, [x0]
+ ldp x5, x6, [x0,#16]
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+
+ // x26-x29 <- AH + AL, x7 <- mask
+ adds x26, x3, x7
+ adcs x27, x4, x8
+ adcs x28, x5, x9
+ adcs x29, x6, x10
+ adc x7, xzr, xzr
+
+ // x11-x14 <- BH + BL, x8 <- mask
+ adds x11, x11, x15
+ adcs x12, x12, x16
+ adcs x13, x13, x17
+ adcs x14, x14, x18
+ adc x8, xzr, xzr
+
+ // x15-x18 <- masked (BH + BL)
+ sub x9, xzr, x7
+ sub x10, xzr, x8
+ and x15, x11, x9
+ and x16, x12, x9
+ and x17, x13, x9
+ and x18, x14, x9
+
+ // x19-x22 <- masked (AH + AL), x7 <- combined carry
+ and x19, x26, x10
+ and x20, x27, x10
+ and x21, x28, x10
+ and x22, x29, x10
+ and x7, x7, x8
+
+ // x15-x18, x7 <- masked (AH+AL) + masked (BH+BL), step 1
+ adds x15, x15, x19
+ adcs x16, x16, x20
+ adcs x17, x17, x21
+ adcs x18, x18, x22
+ adc x7, x7, xzr
+
+ // x8-x10,x19-x23 <- (AH+AL) x (BH+BL), low part
+ stp x26, x27, [x2,#0]
+ MUL256_KARATSUBA_COMBA x2, x26, x27, x28, x29, x11, x12, x13, x14, x8, x9, x10, x19, x20, x21, x22, x23, x24, x25
+
+ // x15-x18, x7 <- (AH+AL) x (BH+BL), final step
+ adds x15, x15, x20
+ adcs x16, x16, x21
+ adcs x17, x17, x22
+ adcs x18, x18, x23
+ adc x7, x7, xzr
+
+ // x20-x27 <- AL x BL
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+ MUL256_KARATSUBA_COMBA x0, x3, x4, x5, x6, x11, x12, x13, x14, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29
+
+ // x13-x14, x3-x5 <- (AH+AL) x (BH+BL) - ALxBL
+ subs x8, x8, x20
+ sbcs x9, x9, x21
+ sbcs x10, x10, x22
+ sbcs x19, x19, x23
+ sbcs x15, x15, x24
+ sbcs x16, x16, x25
+ sbcs x17, x17, x26
+ sbcs x18, x18, x27
+ sbc x7, x7, xzr
+
+ stp x20, x21, [x2]
+ stp x22, x23, [x2,#16]
+
+ ldp x3, x4, [x0,#32]
+ ldp x5, x6, [x0,#48]
+ ldp x11, x12, [x1,#32]
+ ldp x13, x14, [x1,#48]
+
+ adds x8, x8, x24
+ adcs x9, x9, x25
+ adcs x10, x10, x26
+ adcs x19, x19, x27
+ adc x1, xzr, xzr
+
+ // x20-x27 <- AH x BH
+ add x0, x0, #32
+ MUL256_KARATSUBA_COMBA x0, x3, x4, x5, x6, x11, x12, x13, x14, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29
+ neg x1, x1
+
+ // x13-x14, x3-x5 <- (AH+AL) x (BH+BL) - ALxBL - AHxBH
+ subs x8, x8, x20
+ sbcs x9, x9, x21
+ sbcs x10, x10, x22
+ sbcs x19, x19, x23
+ sbcs x15, x15, x24
+ sbcs x16, x16, x25
+ sbcs x17, x17, x26
+ sbcs x18, x18, x27
+ sbc x7, x7, xzr
+
+ stp x8, x9, [x2,#32]
+ stp x10, x19, [x2,#48]
+
+ adds x1, x1, #1
+ adcs x15, x15, x20
+ adcs x16, x16, x21
+ adcs x17, x17, x22
+ adcs x18, x18, x23
+ adcs x24, x7, x24
+ adcs x25, x25, xzr
+ adcs x26, x26, xzr
+ adc x27, x27, xzr
+
+ stp x15, x16, [x2,#64]
+ stp x17, x18, [x2,#80]
+ stp x24, x25, [x2,#96]
+ stp x26, x27, [x2,#112]
+
+ ldp x19, x20, [sp,#0]
+ ldp x21, x22, [sp,#16]
+ ldp x23, x24, [sp,#32]
+ ldp x25, x26, [sp,#48]
+ ldp x27, x28, [sp,#64]
+ ldr x29, [sp,#80]
+ add sp, sp, #96
+ ret
+
+
+//////////////////////////////////////////// MACRO
+.macro MUL128x256_COMBA_CUT A0, A1, B0, B1, B2, B3, C0, C1, C2, C3, C4, C5, T0, T1, T2, T3
+ mul \T0, \A1, \B0
+ umulh \T1, \A1, \B0
+ adds \C1, \C1, \C3
+ adc \C2, \C2, xzr
+
+ mul \T2, \A0, \B2
+ umulh \T3, \A0, \B2
+ adds \C1, \C1, \T0
+ adcs \C2, \C2, \T1
+ adc \C3, xzr, xzr
+
+ mul \T0, \A1, \B1
+ umulh \T1, \A1, \B1
+ adds \C2, \C2, \T2
+ adcs \C3, \C3, \T3
+ adc \C4, xzr, xzr
+
+ mul \T2, \A0, \B3
+ umulh \T3, \A0, \B3
+ adds \C2, \C2, \T0
+ adcs \C3, \C3, \T1
+ adc \C4, \C4, xzr
+
+ mul \T0, \A1, \B2
+ umulh \T1, \A1, \B2
+ adds \C3, \C3, \T2
+ adcs \C4, \C4, \T3
+ adc \C5, xzr, xzr
+
+ mul \T2, \A1, \B3
+ umulh \T3, \A1, \B3
+ adds \C3, \C3, \T0
+ adcs \C4, \C4, \T1
+ adc \C5, \C5, xzr
+ adds \C4, \C4, \T2
+ adc \C5, \C5, \T3
+.endm
+
+
+//**************************************************************************************
+// Montgomery reduction
+// Based on method described in Faz-Hernandez et al. https://eprint.iacr.org/2017/1015
+// Operation: mc [x1] = ma [x0]
+// NOTE: ma=mc is not allowed
+//**************************************************************************************
+.global rdc503_asm
+rdc503_asm:
+ sub sp, sp, #96
+ stp x19, x20, [sp]
+ stp x21, x22, [sp, #16]
+ stp x23, x24, [sp, #32]
+ stp x25, x26, [sp, #48]
+ stp x27, x28, [sp, #64]
+ stp x29, x30, [sp, #80]
+
+ ldp x2, x3, [x0,#0] // a[0-1]
+
+ // Load the prime constant
+ ldr x24, =P503P1_NZ_S8_0
+ ldr x25, =P503P1_NZ_S8_1
+ ldr x26, =P503P1_NZ_S8_2
+ ldr x27, =P503P1_NZ_S8_3
+
+ // a[0-1] x p503p1_nz_s8 --> result: x4:x9
+ mul x4, x2, x24 // a[0] x p503p1_nz_s8[0]
+ umulh x7, x2, x24
+ mul x5, x2, x25 // a[0] x p503p1_nz_s8[1]
+ umulh x6, x2, x25
+ MUL128x256_COMBA_CUT x2, x3, x24, x25, x26, x27, x4, x5, x6, x7, x8, x9, x28, x29, x30, x10
+
+ ldp x3, x11, [x0,#16] // a[2]
+ ldp x12, x13, [x0,#32]
+ ldp x14, x15, [x0,#48]
+
+ orr x10, xzr, x9, lsr #8
+ lsl x9, x9, #56
+ orr x9, x9, x8, lsr #8
+ lsl x8, x8, #56
+ orr x8, x8, x7, lsr #8
+ lsl x7, x7, #56
+ orr x7, x7, x6, lsr #8
+ lsl x6, x6, #56
+ orr x6, x6, x5, lsr #8
+ lsl x5, x5, #56
+ orr x5, x5, x4, lsr #8
+ lsl x4, x4, #56
+
+ adds x11, x4, x11 // a[3]
+ adcs x12, x5, x12 // a[4]
+ adcs x13, x6, x13
+ adcs x14, x7, x14
+ adcs x15, x8, x15
+ ldp x16, x17, [x0,#64]
+ ldp x18, x19, [x0,#80]
+ mul x4, x3, x24 // a[2] x p503p1_nz_s8[0]
+ umulh x7, x3, x24
+ adcs x16, x9, x16
+ adcs x17, x10, x17
+ adcs x18, xzr, x18
+ adcs x19, xzr, x19
+ ldp x20, x21, [x0,#96]
+ ldp x22, x23, [x0,#112]
+ mul x5, x3, x25 // a[2] x p503p1_nz_s8[1]
+ umulh x6, x3, x25
+ adcs x20, xzr, x20
+ adcs x21, xzr, x21
+ adcs x22, xzr, x22
+ adc x23, xzr, x23
+
+ // a[2-3] x p503p1_nz_s8 --> result: x4:x9
+ MUL128x256_COMBA_CUT x3, x11, x24, x25, x26, x27, x4, x5, x6, x7, x8, x9, x28, x29, x30, x10
+
+ orr x10, xzr, x9, lsr #8
+ lsl x9, x9, #56
+ orr x9, x9, x8, lsr #8
+ lsl x8, x8, #56
+ orr x8, x8, x7, lsr #8
+ lsl x7, x7, #56
+ orr x7, x7, x6, lsr #8
+ lsl x6, x6, #56
+ orr x6, x6, x5, lsr #8
+ lsl x5, x5, #56
+ orr x5, x5, x4, lsr #8
+ lsl x4, x4, #56
+
+ adds x13, x4, x13 // a[5]
+ adcs x14, x5, x14 // a[6]
+ adcs x15, x6, x15
+ adcs x16, x7, x16
+ mul x4, x12, x24 // a[4] x p503p1_nz_s8[0]
+ umulh x7, x12, x24
+ adcs x17, x8, x17
+ adcs x18, x9, x18
+ adcs x19, x10, x19
+ adcs x20, xzr, x20
+ mul x5, x12, x25 // a[4] x p503p1_nz_s8[1]
+ umulh x6, x12, x25
+ adcs x21, xzr, x21
+ adcs x22, xzr, x22
+ adc x23, xzr, x23
+
+ // a[4-5] x p503p1_nz_s8 --> result: x4:x9
+ MUL128x256_COMBA_CUT x12, x13, x24, x25, x26, x27, x4, x5, x6, x7, x8, x9, x28, x29, x30, x10
+
+ orr x10, xzr, x9, lsr #8
+ lsl x9, x9, #56
+ orr x9, x9, x8, lsr #8
+ lsl x8, x8, #56
+ orr x8, x8, x7, lsr #8
+ lsl x7, x7, #56
+ orr x7, x7, x6, lsr #8
+ lsl x6, x6, #56
+ orr x6, x6, x5, lsr #8
+ lsl x5, x5, #56
+ orr x5, x5, x4, lsr #8
+ lsl x4, x4, #56
+
+ adds x15, x4, x15 // a[7]
+ adcs x16, x5, x16 // a[8]
+ adcs x17, x6, x17
+ adcs x18, x7, x18
+ mul x4, x14, x24 // a[6] x p503p1_nz_s8[0]
+ umulh x7, x14, x24
+ adcs x19, x8, x19
+ adcs x20, x9, x20
+ adcs x21, x10, x21
+ mul x5, x14, x25 // a[6] x p503p1_nz_s8[1]
+ umulh x6, x14, x25
+ adcs x22, xzr, x22
+ adc x23, xzr, x23
+
+ // a[6-7] x p503p1_nz_s8 --> result: x4:x9
+ MUL128x256_COMBA_CUT x14, x15, x24, x25, x26, x27, x4, x5, x6, x7, x8, x9, x28, x29, x30, x10
+
+ orr x10, xzr, x9, lsr #8
+ lsl x9, x9, #56
+ orr x9, x9, x8, lsr #8
+ lsl x8, x8, #56
+ orr x8, x8, x7, lsr #8
+ lsl x7, x7, #56
+ orr x7, x7, x6, lsr #8
+ lsl x6, x6, #56
+ orr x6, x6, x5, lsr #8
+ lsl x5, x5, #56
+ orr x5, x5, x4, lsr #8
+ lsl x4, x4, #56
+
+ adds x17, x4, x17
+ adcs x18, x5, x18
+ adcs x19, x6, x19
+ adcs x20, x7, x20
+ stp x16, x17, [x1,#0] // Final result
+ stp x18, x19, [x1,#16]
+ adcs x21, x8, x21
+ adcs x22, x9, x22
+ adc x23, x10, x23
+ stp x20, x21, [x1,#32]
+ stp x22, x23, [x1,#48]
+
+ ldp x19, x20, [sp]
+ ldp x21, x22, [sp, #16]
+ ldp x23, x24, [sp, #32]
+ ldp x25, x26, [sp, #48]
+ ldp x27, x28, [sp, #64]
+ ldp x29, x30, [sp, #80]
+ add sp, sp, #96
+ ret
+
+
+//***********************************************************************
+// 503-bit multiprecision addition
+// Operation: c [x2] = a [x0] + b [x1]
+//***********************************************************************
+.global mp_add503_asm
+mp_add503_asm:
+ ldp x3, x4, [x0,#0]
+ ldp x5, x6, [x0,#16]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+
+ adds x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x13
+ adcs x6, x6, x14
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+ adcs x7, x7, x15
+ adcs x8, x8, x16
+ adcs x9, x9, x17
+ adc x10, x10, x18
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+ ret
+
+
+//***********************************************************************
+// 2x503-bit multiprecision addition
+// Operation: c [x2] = a [x0] + b [x1]
+//***********************************************************************
+.global mp_add503x2_asm
+mp_add503x2_asm:
+ ldp x3, x4, [x0,#0]
+ ldp x5, x6, [x0,#16]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+ adds x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x13
+ adcs x6, x6, x14
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+ adcs x7, x7, x15
+ adcs x8, x8, x16
+ adcs x9, x9, x17
+ adcs x10, x10, x18
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+
+ ldp x3, x4, [x0,#64]
+ ldp x5, x6, [x0,#80]
+ ldp x11, x12, [x1,#64]
+ ldp x13, x14, [x1,#80]
+ adcs x3, x3, x11
+ adcs x4, x4, x12
+ adcs x5, x5, x13
+ adcs x6, x6, x14
+ ldp x7, x8, [x0,#96]
+ ldp x9, x10, [x0,#112]
+ ldp x15, x16, [x1,#96]
+ ldp x17, x18, [x1,#112]
+ adcs x7, x7, x15
+ adcs x8, x8, x16
+ adcs x9, x9, x17
+ adc x10, x10, x18
+
+ stp x3, x4, [x2,#64]
+ stp x5, x6, [x2,#80]
+ stp x7, x8, [x2,#96]
+ stp x9, x10, [x2,#112]
+ ret
+
+
+//***********************************************************************
+// 2x503-bit multiprecision subtraction
+// Operation: c [x2] = a [x0] - b [x1]. Returns borrow mask
+//***********************************************************************
+.global mp_sub503x2_asm
+mp_sub503x2_asm:
+ ldp x3, x4, [x0,#0]
+ ldp x5, x6, [x0,#16]
+ ldp x11, x12, [x1,#0]
+ ldp x13, x14, [x1,#16]
+ subs x3, x3, x11
+ sbcs x4, x4, x12
+ sbcs x5, x5, x13
+ sbcs x6, x6, x14
+ ldp x7, x8, [x0,#32]
+ ldp x9, x10, [x0,#48]
+ ldp x15, x16, [x1,#32]
+ ldp x17, x18, [x1,#48]
+ sbcs x7, x7, x15
+ sbcs x8, x8, x16
+ sbcs x9, x9, x17
+ sbcs x10, x10, x18
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+
+ ldp x3, x4, [x0,#64]
+ ldp x5, x6, [x0,#80]
+ ldp x11, x12, [x1,#64]
+ ldp x13, x14, [x1,#80]
+ sbcs x3, x3, x11
+ sbcs x4, x4, x12
+ sbcs x5, x5, x13
+ sbcs x6, x6, x14
+ ldp x7, x8, [x0,#96]
+ ldp x9, x10, [x0,#112]
+ ldp x15, x16, [x1,#96]
+ ldp x17, x18, [x1,#112]
+ sbcs x7, x7, x15
+ sbcs x8, x8, x16
+ sbcs x9, x9, x17
+ sbcs x10, x10, x18
+ sbc x0, xzr, xzr
+
+ stp x3, x4, [x2,#64]
+ stp x5, x6, [x2,#80]
+ stp x7, x8, [x2,#96]
+ stp x9, x10, [x2,#112]
+ ret
+
+
+//***********************************************************************
+// Double 2x503-bit multiprecision subtraction
+// Operation: c [x2] = c [x2] - a [x0] - b [x1]
+//***********************************************************************
+.global mp_dblsub503x2_asm
+mp_dblsub503x2_asm:
+ sub sp, sp, #32
+ stp x27, x28, [sp, #0]
+ stp x29, x30, [sp, #16]
+ ldp x3, x4, [x2,#0]
+ ldp x5, x6, [x2,#16]
+ ldp x7, x8, [x2,#32]
+ ldp x9, x10, [x2,#48]
+ ldp x11, x12, [x2,#64]
+ ldp x13, x14, [x2,#80]
+ ldp x15, x16, [x2,#96]
+ ldp x17, x18, [x2,#112]
+
+ ldp x27, x28, [x0,#0]
+ ldp x29, x30, [x0,#16]
+ subs x3, x3, x27
+ sbcs x4, x4, x28
+ sbcs x5, x5, x29
+ sbcs x6, x6, x30
+ ldp x27, x28, [x0,#32]
+ ldp x29, x30, [x0,#48]
+ sbcs x7, x7, x27
+ sbcs x8, x8, x28
+ sbcs x9, x9, x29
+ sbcs x10, x10, x30
+ ldp x27, x28, [x0,#64]
+ ldp x29, x30, [x0,#80]
+ sbcs x11, x11, x27
+ sbcs x12, x12, x28
+ sbcs x13, x13, x29
+ sbcs x14, x14, x30
+ ldp x27, x28, [x0,#96]
+ ldp x29, x30, [x0,#112]
+ sbcs x15, x15, x27
+ sbcs x16, x16, x28
+ sbcs x17, x17, x29
+ sbc x18, x18, x30
+
+ ldp x27, x28, [x1,#0]
+ ldp x29, x30, [x1,#16]
+ subs x3, x3, x27
+ sbcs x4, x4, x28
+ sbcs x5, x5, x29
+ sbcs x6, x6, x30
+ ldp x27, x28, [x1,#32]
+ ldp x29, x30, [x1,#48]
+ sbcs x7, x7, x27
+ sbcs x8, x8, x28
+ sbcs x9, x9, x29
+ sbcs x10, x10, x30
+ ldp x27, x28, [x1,#64]
+ ldp x29, x30, [x1,#80]
+ sbcs x11, x11, x27
+ sbcs x12, x12, x28
+ sbcs x13, x13, x29
+ sbcs x14, x14, x30
+ ldp x27, x28, [x1,#96]
+ ldp x29, x30, [x1,#112]
+ sbcs x15, x15, x27
+ sbcs x16, x16, x28
+ sbcs x17, x17, x29
+ sbc x18, x18, x30
+
+ stp x3, x4, [x2,#0]
+ stp x5, x6, [x2,#16]
+ stp x7, x8, [x2,#32]
+ stp x9, x10, [x2,#48]
+ stp x11, x12, [x2,#64]
+ stp x13, x14, [x2,#80]
+ stp x15, x16, [x2,#96]
+ stp x17, x18, [x2,#112]
+
+ ldp x27, x28, [sp, #0]
+ ldp x29, x30, [sp, #16]
+ add sp, sp, #32
+ ret
diff --git a/third_party/sidh/src/P503.c b/third_party/sidh/src/P503.c
new file mode 100644
index 000000000..fab51a38b
--- /dev/null
+++ b/third_party/sidh/src/P503.c
@@ -0,0 +1,99 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: supersingular isogeny parameters and generation of functions for P503
+*********************************************************************************************/
+
+#include "sidh/def_p503.h"
+#include "sidh/P503_api.h"
+#include "P503_internal.h"
+
+// Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:
+// --------------------------------------------------------------------------------------------------
+// Elements over GF(p) and Z_order are encoded with the least significant octet (and digit) located at the leftmost position (i.e., little endian format).
+// Elements (a+b*i) over GF(p^2), where a and b are defined over GF(p), are encoded as {a, b}, with a in the least significant position.
+// Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position.
+// Internally, the number of digits used to represent all these elements is obtained by approximating the number of bits to the immediately greater multiple of 32.
+// For example, a 503-bit field element is represented with Ceil(503 / 64) = 8 64-bit digits or Ceil(503 / 32) = 16 32-bit digits.
+
+//
+// Curve isogeny system "SIDHp503". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p503^2), where A=0, B=1, C=1 and p503 = 2^250*3^159-1
+//
+
+const struct params_t kP503Params = {
+ .prime = {
+ 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF,
+ 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E
+ },
+
+ .primeP1 = {
+ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000,
+ 0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E
+ },
+ .primeX2 = {
+ 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF,
+ 0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C
+ },
+ .Alice_order = {
+ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0400000000000000
+ },
+ .Bob_order = {
+ 0xC216F6888479E82B, 0xE6FDB21EDF9F6BC4, 0x1171AF769DE93406, 0x1019BD5060478798
+ },
+ .A_gen = {
+ 0xE7EF4AA786D855AF, 0xED5758F03EB34D3B, 0x09AE172535A86AA9, 0x237B9CC07D622723,
+ 0xE3A284CBA4E7932D, 0x27481D9176C5E63F, 0x6A323FF55C6E71BF, 0x002ECC31A6FB8773, // XPA0
+ 0x64D02E4E90A620B8, 0xDAB8128537D4B9F1, 0x4BADF77B8A228F98, 0x0F5DBDF9D1FB7D1B,
+ 0xBEC4DB288E1A0DCC, 0xE76A8665E80675DB, 0x6D6F252E12929463, 0x003188BD1463FACC, // XPA1
+ 0xB79D41025DE85D56, 0x0B867DA9DF169686, 0x740E5368021C827D, 0x20615D72157BF25C,
+ 0xFF1590013C9B9F5B, 0xC884DCADE8C16CEA, 0xEBD05E53BF724E01, 0x0032FEF8FDA5748C, // XQA0
+ 0x12E2E849AA0A8006, 0x41CF47008635A1E8, 0x9CD720A70798AED7, 0x42A820B42FCF04CF,
+ 0x7BF9BAD32AAE88B1, 0xF619127A54090BBE, 0x1CB10D8F56408EAA, 0x001D6B54C3C0EDEB, // XRA0
+ 0x34DB54931CBAAC36, 0x420A18CB8DD5F0C4, 0x32008C1A48C0F44D, 0x3B3BA772B1CFD44D,
+ 0xA74B058FDAF13515, 0x095FC9CA7EEC17B4, 0x448E829D28F120F8, 0x00261EC3ED16A489 // XRA1
+ },
+ .B_gen = {
+ 0x7EDE37F4FA0BC727, 0xF7F8EC5C8598941C, 0xD15519B516B5F5C8, 0xF6D5AC9B87A36282,
+ 0x7B19F105B30E952E, 0x13BD8B2025B4EBEE, 0x7B96D27F4EC579A2, 0x00140850CAB7E5DE, // XPB0
+ 0x7764909DAE7B7B2D, 0x578ABB16284911AB, 0x76E2BFD146A6BF4D, 0x4824044B23AA02F0,
+ 0x1105048912A321F3, 0xB8A2E482CF0F10C1, 0x42FF7D0BE2152085, 0x0018E599C5223352, // XPB1
+ 0x4256C520FB388820, 0x744FD7C3BAAF0A13, 0x4B6A2DDDB12CBCB8, 0xE46826E27F427DF8,
+ 0xFE4A663CD505A61B, 0xD6B3A1BAF025C695, 0x7C3BB62B8FCC00BD, 0x003AFDDE4A35746C, // XQB0
+ 0x75601CD1E6C0DFCB, 0x1A9007239B58F93E, 0xC1F1BE80C62107AC, 0x7F513B898F29FF08,
+ 0xEA0BEDFF43E1F7B2, 0x2C6D94018CBAE6D0, 0x3A430D31BCD84672, 0x000D26892ECCFE83, // XRB0
+ 0x1119D62AEA3007A1, 0xE3702AA4E04BAE1B, 0x9AB96F7D59F990E7, 0xF58440E8B43319C0,
+ 0xAF8134BEE1489775, 0xE7F7774E905192AA, 0xF54AE09308E98039, 0x001EF7A041A86112 // XRB1
+ },
+ .Montgomery_R2 = {
+ 0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC,
+ 0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771
+ },
+ .Montgomery_one = {
+ 0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000,
+ 0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953
+ },
+ .Montgomery_Rprime = {
+ 0x0C2615CA3C5BAA99, 0x5A4FF3072AB6AA6A, 0xA6AFD4B039AD6AA2, 0x010DA06A26DD05CB
+ },
+ .Montgomery_rprime = {
+ 0x49C8A87190C0697D, 0x2EB7968EA0F0A558, 0x944257B696777FA2, 0xBAA4DDCD6139D2B3
+ },
+ .Border_div3 = {
+ 0xEB5CFCD82C28A2B9, 0x4CFF3B5F9FDFCE96, 0xB07B3A7CDF4DBC02, 0x055DE9C5756D2D32
+ },
+ .strat_Alice = {
+ 61, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1,
+ 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1,
+ 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 29, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1,
+ 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2,
+ 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1
+ },
+ .strat_Bob = {
+ 71, 38, 21, 13, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 4, 2, 1, 1, 2, 1,
+ 1, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 17, 9,
+ 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1,
+ 1, 4, 2, 1, 1, 2, 1, 1, 33, 17, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1,
+ 2, 1, 1, 8, 4, 2, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 1, 2,
+ 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1
+ }
+};
diff --git a/third_party/sidh/src/P503_internal.h b/third_party/sidh/src/P503_internal.h
new file mode 100644
index 000000000..67aed146c
--- /dev/null
+++ b/third_party/sidh/src/P503_internal.h
@@ -0,0 +1,279 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: internal header file for P503
+*********************************************************************************************/
+
+#ifndef P503_INTERNAL_H__
+#define P503_INTERNAL_H__
+
+#include <stdbool.h>
+#include "sidh/def_p503.h"
+
+// Macro definitions
+#define NBITS_TO_NBYTES(nbits) (((nbits)+7)/8) // Conversion macro from number of bits to number of bytes
+#define NBITS_TO_NWORDS(nbits) (((nbits)+(sizeof(digit_t)*8)-1)/(sizeof(digit_t)*8)) // Conversion macro from number of bits to number of computer words
+#define NBYTES_TO_NWORDS(nbytes) (((nbytes)+sizeof(digit_t)-1)/sizeof(digit_t)) // Conversion macro from number of bytes to number of computer words
+
+// Macro to avoid compiler warnings when detecting unreferenced parameters
+#define UNREFERENCED_PARAMETER(PAR) ((void)(PAR))
+
+// SIDH Basic, internally used, constants
+#define MAXBITS_FIELD 512
+#define MAXWORDS_FIELD ((MAXBITS_FIELD+RADIX-1)/RADIX) // Max. number of words to represent field elements
+#define MAXBITS_ORDER NBITS_ORDER
+#define MAXWORDS_ORDER ((MAXBITS_ORDER+RADIX-1)/RADIX) // Max. number of words to represent elements in [1, oA-1] or [1, oB].
+#define ALICE 0
+#define BOB 1
+#define OALICE_BITS 250
+#define OBOB_BITS 253
+#define OBOB_EXPON 159
+// Fixed parameters for isogeny tree computation
+#define MAX_INT_POINTS_ALICE 7
+#define MAX_INT_POINTS_BOB 8
+#define FP2_ENCODED_BYTES 2*((NBITS_FIELD + 7) / 8)
+
+// Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions
+#define fpcopy fpcopy503
+#define fpzero fpzero503
+#define fpadd fpadd503
+#define fpsub fpsub503
+#define fpneg fpneg503
+#define fpdiv2 fpdiv2_503
+#define fpcorrection fpcorrection503
+#define fpmul_mont fpmul503_mont
+#define fpsqr_mont fpsqr503_mont
+#define fpinv_mont fpinv503_mont
+#define fpinv_chain_mont fpinv503_chain_mont
+#define fpinv_mont_bingcd fpinv503_mont_bingcd
+#define fp2copy fp2copy503
+#define fp2zero fp2zero503
+#define fp2add fp2add503
+#define fp2sub fp2sub503
+#define fp2neg fp2neg503
+#define fp2div2 fp2div2_503
+#define fp2correction fp2correction503
+#define fp2mul_mont fp2mul503_mont
+#define fp2sqr_mont fp2sqr503_mont
+#define fp2inv_mont fp2inv503_mont
+#define fp2inv_mont_bingcd fp2inv503_mont_bingcd
+#define fpequal_non_constant_time fpequal503_non_constant_time
+#define cswap_asm cswap503_asm
+#define mp_add_asm mp_add503_asm
+#define mp_subx2_asm mp_sub503x2_asm
+#define mp_dblsubx2_asm mp_dblsub503x2_asm
+#define crypto_kem_keypair crypto_kem_keypair_SIKEp503
+#define crypto_kem_enc crypto_kem_enc_SIKEp503
+#define crypto_kem_dec crypto_kem_dec_SIKEp503
+#define random_mod_order_A random_mod_order_A_SIDHp503
+#define random_mod_order_B random_mod_order_B_SIDHp503
+#define EphemeralKeyGeneration_A EphemeralKeyGeneration_A_SIDHp503
+#define EphemeralKeyGeneration_B EphemeralKeyGeneration_B_SIDHp503
+#define EphemeralSecretAgreement_A EphemeralSecretAgreement_A_SIDHp503
+#define EphemeralSecretAgreement_B EphemeralSecretAgreement_B_SIDHp503
+
+// SIDH's basic element definitions and point representations
+
+typedef digit_t felm_t[NWORDS_FIELD]; // Datatype for representing 503-bit field elements (512-bit max.)
+typedef digit_t dfelm_t[2*NWORDS_FIELD]; // Datatype for representing double-precision 2x503-bit field elements (512-bit max.)
+
+/* An element in F_{p^2}, is composed of two coefficients
+ from F_p, * i.e. Fp2 element = c0 + c1*i in F_{p^2}
+ */
+typedef struct {
+ felm_t c0;
+ felm_t c1;
+} fp2;
+
+// Our F_{p^2} element type is a pointer to the struct.
+typedef fp2 f2elm_t[1];
+
+typedef struct { f2elm_t X; f2elm_t Z; } point_proj; // Point representation in projective XZ Montgomery coordinates.
+typedef point_proj point_proj_t[1];
+
+/* Old GCC 4.9 (jessie) doesn't implement {0} initialization properly,
+ which violates C11 as described in 6.7.9, 21 (similarily C99, 6.7.8).
+ Defines below are used to work around the bug, and provide a way
+ to initialize f2elem_t and point_proj_t structs.
+ Bug has been fixed in GCC6 (debian stretch).
+*/
+#define F2ELM_INIT {{ {0}, {0} }}
+#define POINT_PROJ_INIT {{ F2ELM_INIT, F2ELM_INIT }}
+
+/**************** Function prototypes ****************/
+/************* Multiprecision functions **************/
+
+// Copy wordsize digits, c = a, where lng(a) = nwords
+void copy_words(const digit_t* a, digit_t* c, const unsigned int nwords);
+
+// Multiprecision addition, c = a+b, where lng(a) = lng(b) = nwords. Returns the carry bit
+unsigned int mp_add(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
+
+// 503-bit multiprecision addition, c = a+b
+void mp_add503(const digit_t* a, const digit_t* b, digit_t* c);
+void mp_add503_asm(const digit_t* a, const digit_t* b, digit_t* c);
+void cswap503_asm(point_proj_t x, point_proj_t y, const digit_t option);
+
+// Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit
+unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
+digit_t mp_sub503x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
+
+// Double 2x503-bit multiprecision subtraction, c = c-a-b, where c > a and c > b
+void mp_dblsub503x2_asm(const digit_t* a, const digit_t* b, digit_t* c);
+
+// Multiprecision left shift
+void mp_shiftleft(digit_t* x, unsigned int shift, const unsigned int nwords);
+
+// Multiprecision right shift by one
+void mp_shiftr1(digit_t* x, const unsigned int nwords);
+
+// Multiprecision left right shift by one
+void mp_shiftl1(digit_t* x, const unsigned int nwords);
+
+// Digit multiplication, digit * digit -> 2-digit result
+void digit_x_digit(const digit_t a, const digit_t b, digit_t* c);
+
+// Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
+void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords);
+
+/************ Field arithmetic functions *************/
+
+// Copy of a field element, c = a
+void fpcopy503(const digit_t* a, digit_t* c);
+
+// Zeroing a field element, a = 0
+void fpzero503(digit_t* a);
+
+// Non constant-time comparison of two field elements. If a = b return TRUE, otherwise, return FALSE
+bool fpequal503_non_constant_time(const digit_t* a, const digit_t* b);
+
+// Modular addition, c = a+b mod p503
+extern void fpadd503(const digit_t* a, const digit_t* b, digit_t* c);
+extern void fpadd503_asm(const digit_t* a, const digit_t* b, digit_t* c);
+
+// Modular subtraction, c = a-b mod p503
+extern void fpsub503(const digit_t* a, const digit_t* b, digit_t* c);
+extern void fpsub503_asm(const digit_t* a, const digit_t* b, digit_t* c);
+
+// Modular negation, a = -a mod p503
+extern void fpneg503(digit_t* a);
+
+// Modular division by two, c = a/2 mod p503.
+void fpdiv2_503(const digit_t* a, digit_t* c);
+
+// Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
+void fpcorrection503(digit_t* a);
+
+// 503-bit Montgomery reduction, c = a mod p
+void rdc_mont(const digit_t* a, digit_t* c);
+
+// Field multiplication using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768
+void fpmul503_mont(const digit_t* a, const digit_t* b, digit_t* c);
+void mul503_asm(const digit_t* a, const digit_t* b, digit_t* c);
+void rdc503_asm(const digit_t* ma, digit_t* mc);
+
+// Field squaring using Montgomery arithmetic, c = a*b*R^-1 mod p503, where R=2^768
+void fpsqr503_mont(const digit_t* ma, digit_t* mc);
+
+// Conversion to Montgomery representation
+void to_mont(const digit_t* a, digit_t* mc);
+
+// Conversion from Montgomery representation to standard representation
+void from_mont(const digit_t* ma, digit_t* c);
+
+// Field inversion, a = a^-1 in GF(p503)
+void fpinv503_mont(digit_t* a);
+
+// Field inversion, a = a^-1 in GF(p503) using the binary GCD
+void fpinv503_mont_bingcd(digit_t* a);
+
+// Chain to compute (p503-3)/4 using Montgomery arithmetic
+void fpinv503_chain_mont(digit_t* a);
+
+/************ GF(p^2) arithmetic functions *************/
+
+// Copy of a GF(p503^2) element, c = a
+void fp2copy503(const f2elm_t a, f2elm_t c);
+
+// Zeroing a GF(p503^2) element, a = 0
+void fp2zero503(f2elm_t a);
+
+// GF(p503^2) negation, a = -a in GF(p503^2)
+void fp2neg503(f2elm_t a);
+
+// GF(p503^2) addition, c = a+b in GF(p503^2)
+extern void fp2add503(const f2elm_t a, const f2elm_t b, f2elm_t c);
+
+// GF(p503^2) subtraction, c = a-b in GF(p503^2)
+extern void fp2sub503(const f2elm_t a, const f2elm_t b, f2elm_t c);
+
+// GF(p503^2) division by two, c = a/2 in GF(p503^2)
+void fp2div2_503(const f2elm_t a, f2elm_t c);
+
+// Modular correction, a = a in GF(p503^2)
+void fp2correction503(f2elm_t a);
+
+// GF(p503^2) squaring using Montgomery arithmetic, c = a^2 in GF(p503^2)
+void fp2sqr503_mont(const f2elm_t a, f2elm_t c);
+
+// GF(p503^2) multiplication using Montgomery arithmetic, c = a*b in GF(p503^2)
+void fp2mul503_mont(const f2elm_t a, const f2elm_t b, f2elm_t c);
+
+// Conversion of a GF(p503^2) element to Montgomery representation
+void to_fp2mont(const f2elm_t a, f2elm_t mc);
+
+// Conversion of a GF(p503^2) element from Montgomery representation to standard representation
+void from_fp2mont(const f2elm_t ma, f2elm_t c);
+
+// GF(p503^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2)
+void fp2inv503_mont(f2elm_t a);
+
+// GF(p503^2) inversion, a = (a0-i*a1)/(a0^2+a1^2), GF(p503) inversion done using the binary GCD
+void fp2inv503_mont_bingcd(f2elm_t a);
+
+// n-way Montgomery inversion
+void mont_n_way_inv(const f2elm_t* vec, const int n, f2elm_t* out);
+
+/************ Elliptic curve and isogeny functions *************/
+
+// Computes the j-invariant of a Montgomery curve with projective constant.
+void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv);
+
+// Simultaneous doubling and differential addition.
+void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t xPQ, const f2elm_t A24);
+
+// Doubling of a Montgomery point in projective coordinates (X:Z).
+void xDBL(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24);
+
+// Computes [2^e](X:Z) on Montgomery curve with projective constant via e repeated doublings.
+void xDBLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24, const int e);
+
+// Differential addition.
+void xADD(point_proj_t P, const point_proj_t Q, const f2elm_t xPQ);
+
+// Computes the corresponding 4-isogeny of a projective Montgomery point (X4:Z4) of order 4.
+void get_4_isog(const point_proj_t P, f2elm_t A24plus, f2elm_t C24, f2elm_t* coeff);
+
+// Evaluates the isogeny at the point (X:Z) in the domain of the isogeny.
+void eval_4_isog(point_proj_t P, f2elm_t* coeff);
+
+// Tripling of a Montgomery point in projective coordinates (X:Z).
+void xTPL(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus);
+
+// Computes [3^e](X:Z) on Montgomery curve with projective constant via e repeated triplings.
+void xTPLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus, const int e);
+
+// Computes the corresponding 3-isogeny of a projective Montgomery point (X3:Z3) of order 3.
+void get_3_isog(const point_proj_t P, f2elm_t A24minus, f2elm_t A24plus, f2elm_t* coeff);
+
+// Computes the 3-isogeny R=phi(X:Z), given projective point (X3:Z3) of order 3 on a Montgomery curve and a point P with coefficients given in coeff.
+void eval_3_isog(point_proj_t Q, f2elm_t* coeff);
+
+// 3-way simultaneous inversion
+void inv_3_way(f2elm_t z1, f2elm_t z2, f2elm_t z3);
+
+// Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A.
+void get_A(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A);
+
+
+#endif
diff --git a/third_party/sidh/src/ec_isogeny.c b/third_party/sidh/src/ec_isogeny.c
new file mode 100644
index 000000000..c512c5831
--- /dev/null
+++ b/third_party/sidh/src/ec_isogeny.c
@@ -0,0 +1,270 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: elliptic curve and isogeny functions
+*********************************************************************************************/
+#include "sidh/def_p503.h"
+#include "P503_internal.h"
+
+extern const struct params_t kP503Params;
+
+void xDBL(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24)
+{ // Doubling of a Montgomery point in projective coordinates (X:Z).
+ // Input: projective Montgomery x-coordinates P = (X1:Z1), where x1=X1/Z1 and Montgomery curve constants A+2C and 4C.
+ // Output: projective Montgomery x-coordinates Q = 2*P = (X2:Z2).
+ f2elm_t t0, t1;
+
+ fp2sub(P->X, P->Z, t0); // t0 = X1-Z1
+ fp2add(P->X, P->Z, t1); // t1 = X1+Z1
+ fp2sqr_mont(t0, t0); // t0 = (X1-Z1)^2
+ fp2sqr_mont(t1, t1); // t1 = (X1+Z1)^2
+ fp2mul_mont(C24, t0, Q->Z); // Z2 = C24*(X1-Z1)^2
+ fp2mul_mont(t1, Q->Z, Q->X); // X2 = C24*(X1-Z1)^2*(X1+Z1)^2
+ fp2sub(t1, t0, t1); // t1 = (X1+Z1)^2-(X1-Z1)^2
+ fp2mul_mont(A24plus, t1, t0); // t0 = A24plus*[(X1+Z1)^2-(X1-Z1)^2]
+ fp2add(Q->Z, t0, Q->Z); // Z2 = A24plus*[(X1+Z1)^2-(X1-Z1)^2] + C24*(X1-Z1)^2
+ fp2mul_mont(Q->Z, t1, Q->Z); // Z2 = [A24plus*[(X1+Z1)^2-(X1-Z1)^2] + C24*(X1-Z1)^2]*[(X1+Z1)^2-(X1-Z1)^2]
+}
+
+
+void xDBLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24, const int e)
+{ // Computes [2^e](X:Z) on Montgomery curve with projective constant via e repeated doublings.
+ // Input: projective Montgomery x-coordinates P = (XP:ZP), such that xP=XP/ZP and Montgomery curve constants A+2C and 4C.
+ // Output: projective Montgomery x-coordinates Q <- (2^e)*P.
+ int i;
+
+ copy_words((digit_t*)P, (digit_t*)Q, 2*2*NWORDS_FIELD);
+
+ for (i = 0; i < e; i++) {
+ xDBL(Q, Q, A24plus, C24);
+ }
+}
+
+
+void get_4_isog(const point_proj_t P, f2elm_t A24plus, f2elm_t C24, f2elm_t* coeff)
+{ // Computes the corresponding 4-isogeny of a projective Montgomery point (X4:Z4) of order 4.
+ // Input: projective point of order four P = (X4:Z4).
+ // Output: the 4-isogenous Montgomery curve with projective coefficients A+2C/4C and the 3 coefficients
+ // that are used to evaluate the isogeny at a point in eval_4_isog().
+
+ fp2sub(P->X, P->Z, coeff[1]); // coeff[1] = X4-Z4
+ fp2add(P->X, P->Z, coeff[2]); // coeff[2] = X4+Z4
+ fp2sqr_mont(P->Z, coeff[0]); // coeff[0] = Z4^2
+ fp2add(coeff[0], coeff[0], coeff[0]); // coeff[0] = 2*Z4^2
+ fp2sqr_mont(coeff[0], C24); // C24 = 4*Z4^4
+ fp2add(coeff[0], coeff[0], coeff[0]); // coeff[0] = 4*Z4^2
+ fp2sqr_mont(P->X, A24plus); // A24plus = X4^2
+ fp2add(A24plus, A24plus, A24plus); // A24plus = 2*X4^2
+ fp2sqr_mont(A24plus, A24plus); // A24plus = 4*X4^4
+}
+
+
+void eval_4_isog(point_proj_t P, f2elm_t* coeff)
+{ // Evaluates the isogeny at the point (X:Z) in the domain of the isogeny, given a 4-isogeny phi defined
+ // by the 3 coefficients in coeff (computed in the function get_4_isog()).
+ // Inputs: the coefficients defining the isogeny, and the projective point P = (X:Z).
+ // Output: the projective point P = phi(P) = (X:Z) in the codomain.
+ f2elm_t t0, t1;
+
+ fp2add(P->X, P->Z, t0); // t0 = X+Z
+ fp2sub(P->X, P->Z, t1); // t1 = X-Z
+ fp2mul_mont(t0, coeff[1], P->X); // X = (X+Z)*coeff[1]
+ fp2mul_mont(t1, coeff[2], P->Z); // Z = (X-Z)*coeff[2]
+ fp2mul_mont(t0, t1, t0); // t0 = (X+Z)*(X-Z)
+ fp2mul_mont(t0, coeff[0], t0); // t0 = coeff[0]*(X+Z)*(X-Z)
+ fp2add(P->X, P->Z, t1); // t1 = (X-Z)*coeff[2] + (X+Z)*coeff[1]
+ fp2sub(P->X, P->Z, P->Z); // Z = (X-Z)*coeff[2] - (X+Z)*coeff[1]
+ fp2sqr_mont(t1, t1); // t1 = [(X-Z)*coeff[2] + (X+Z)*coeff[1]]^2
+ fp2sqr_mont(P->Z, P->Z); // Z = [(X-Z)*coeff[2] - (X+Z)*coeff[1]]^2
+ fp2add(t1, t0, P->X); // X = coeff[0]*(X+Z)*(X-Z) + [(X-Z)*coeff[2] + (X+Z)*coeff[1]]^2
+ fp2sub(P->Z, t0, t0); // t0 = [(X-Z)*coeff[2] - (X+Z)*coeff[1]]^2 - coeff[0]*(X+Z)*(X-Z)
+ fp2mul_mont(P->X, t1, P->X); // Xfinal
+ fp2mul_mont(P->Z, t0, P->Z); // Zfinal
+}
+
+
+void xTPL(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus)
+{ // Tripling of a Montgomery point in projective coordinates (X:Z).
+ // Input: projective Montgomery x-coordinates P = (X:Z), where x=X/Z and Montgomery curve constants A24plus = A+2C and A24minus = A-2C.
+ // Output: projective Montgomery x-coordinates Q = 3*P = (X3:Z3).
+ f2elm_t t0, t1, t2, t3, t4, t5, t6;
+
+ fp2sub(P->X, P->Z, t0); // t0 = X-Z
+ fp2sqr_mont(t0, t2); // t2 = (X-Z)^2
+ fp2add(P->X, P->Z, t1); // t1 = X+Z
+ fp2sqr_mont(t1, t3); // t3 = (X+Z)^2
+ fp2add(t0, t1, t4); // t4 = 2*X
+ fp2sub(t1, t0, t0); // t0 = 2*Z
+ fp2sqr_mont(t4, t1); // t1 = 4*X^2
+ fp2sub(t1, t3, t1); // t1 = 4*X^2 - (X+Z)^2
+ fp2sub(t1, t2, t1); // t1 = 4*X^2 - (X+Z)^2 - (X-Z)^2
+ fp2mul_mont(t3, A24plus, t5); // t5 = A24plus*(X+Z)^2
+ fp2mul_mont(t3, t5, t3); // t3 = A24plus*(X+Z)^3
+ fp2mul_mont(A24minus, t2, t6); // t6 = A24minus*(X-Z)^2
+ fp2mul_mont(t2, t6, t2); // t2 = A24minus*(X-Z)^3
+ fp2sub(t2, t3, t3); // t3 = A24minus*(X-Z)^3 - coeff*(X+Z)^3
+ fp2sub(t5, t6, t2); // t2 = A24plus*(X+Z)^2 - A24minus*(X-Z)^2
+ fp2mul_mont(t1, t2, t1); // t1 = [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2]
+ fp2add(t3, t1, t2); // t2 = [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2] + A24minus*(X-Z)^3 - coeff*(X+Z)^3
+ fp2sqr_mont(t2, t2); // t2 = t2^2
+ fp2mul_mont(t4, t2, Q->X); // X3 = 2*X*t2
+ fp2sub(t3, t1, t1); // t1 = A24minus*(X-Z)^3 - A24plus*(X+Z)^3 - [4*X^2 - (X+Z)^2 - (X-Z)^2]*[A24plus*(X+Z)^2 - A24minus*(X-Z)^2]
+ fp2sqr_mont(t1, t1); // t1 = t1^2
+ fp2mul_mont(t0, t1, Q->Z); // Z3 = 2*Z*t1
+}
+
+
+void xTPLe(const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus, const int e)
+{ // Computes [3^e](X:Z) on Montgomery curve with projective constant via e repeated triplings.
+ // Input: projective Montgomery x-coordinates P = (XP:ZP), such that xP=XP/ZP and Montgomery curve constants A24plus = A+2C and A24minus = A-2C.
+ // Output: projective Montgomery x-coordinates Q <- (3^e)*P.
+ int i;
+
+ copy_words((digit_t*)P, (digit_t*)Q, 2*2*NWORDS_FIELD);
+
+ for (i = 0; i < e; i++) {
+ xTPL(Q, Q, A24minus, A24plus);
+ }
+}
+
+
+void get_3_isog(const point_proj_t P, f2elm_t A24minus, f2elm_t A24plus, f2elm_t* coeff)
+{ // Computes the corresponding 3-isogeny of a projective Montgomery point (X3:Z3) of order 3.
+ // Input: projective point of order three P = (X3:Z3).
+ // Output: the 3-isogenous Montgomery curve with projective coefficient A/C.
+ f2elm_t t0, t1, t2, t3, t4;
+
+ fp2sub(P->X, P->Z, coeff[0]); // coeff0 = X-Z
+ fp2sqr_mont(coeff[0], t0); // t0 = (X-Z)^2
+ fp2add(P->X, P->Z, coeff[1]); // coeff1 = X+Z
+ fp2sqr_mont(coeff[1], t1); // t1 = (X+Z)^2
+ fp2add(t0, t1, t2); // t2 = (X+Z)^2 + (X-Z)^2
+ fp2add(coeff[0], coeff[1], t3); // t3 = 2*X
+ fp2sqr_mont(t3, t3); // t3 = 4*X^2
+ fp2sub(t3, t2, t3); // t3 = 4*X^2 - (X+Z)^2 - (X-Z)^2
+ fp2add(t1, t3, t2); // t2 = 4*X^2 - (X-Z)^2
+ fp2add(t3, t0, t3); // t3 = 4*X^2 - (X+Z)^2
+ fp2add(t0, t3, t4); // t4 = 4*X^2 - (X+Z)^2 + (X-Z)^2
+ fp2add(t4, t4, t4); // t4 = 2(4*X^2 - (X+Z)^2 + (X-Z)^2)
+ fp2add(t1, t4, t4); // t4 = 8*X^2 - (X+Z)^2 + 2*(X-Z)^2
+ fp2mul_mont(t2, t4, A24minus); // A24minus = [4*X^2 - (X-Z)^2]*[8*X^2 - (X+Z)^2 + 2*(X-Z)^2]
+ fp2add(t1, t2, t4); // t4 = 4*X^2 + (X+Z)^2 - (X-Z)^2
+ fp2add(t4, t4, t4); // t4 = 2(4*X^2 + (X+Z)^2 - (X-Z)^2)
+ fp2add(t0, t4, t4); // t4 = 8*X^2 + 2*(X+Z)^2 - (X-Z)^2
+ fp2mul_mont(t3, t4, t4); // t4 = [4*X^2 - (X+Z)^2]*[8*X^2 + 2*(X+Z)^2 - (X-Z)^2]
+ fp2sub(t4, A24minus, t0); // t0 = [4*X^2 - (X+Z)^2]*[8*X^2 + 2*(X+Z)^2 - (X-Z)^2] - [4*X^2 - (X-Z)^2]*[8*X^2 - (X+Z)^2 + 2*(X-Z)^2]
+ fp2add(A24minus, t0, A24plus); // A24plus = 8*X^2 - (X+Z)^2 + 2*(X-Z)^2
+}
+
+
+void eval_3_isog(point_proj_t Q, f2elm_t* coeff)
+{ // Computes the 3-isogeny R=phi(X:Z), given projective point (X3:Z3) of order 3 on a Montgomery curve and
+ // a point P with 2 coefficients in coeff (computed in the function get_3_isog()).
+ // Inputs: projective points P = (X3:Z3) and Q = (X:Z).
+ // Output: the projective point Q <- phi(Q) = (X3:Z3).
+ f2elm_t t0, t1, t2;
+
+ fp2add(Q->X, Q->Z, t0); // t0 = X+Z
+ fp2sub(Q->X, Q->Z, t1); // t1 = X-Z
+ fp2mul_mont(t0, coeff[0], t0); // t0 = coeff0*(X+Z)
+ fp2mul_mont(t1, coeff[1], t1); // t1 = coeff1*(X-Z)
+ fp2add(t0, t1, t2); // t2 = coeff0*(X+Z) + coeff1*(X-Z)
+ fp2sub(t1, t0, t0); // t0 = coeff1*(X-Z) - coeff0*(X+Z)
+ fp2sqr_mont(t2, t2); // t2 = [coeff0*(X+Z) + coeff1*(X-Z)]^2
+ fp2sqr_mont(t0, t0); // t0 = [coeff1*(X-Z) - coeff0*(X+Z)]^2
+ fp2mul_mont(Q->X, t2, Q->X); // X3final = X*[coeff0*(X+Z) + coeff1*(X-Z)]^2
+ fp2mul_mont(Q->Z, t0, Q->Z); // Z3final = Z*[coeff1*(X-Z) - coeff0*(X+Z)]^2
+}
+
+
+void inv_3_way(f2elm_t z1, f2elm_t z2, f2elm_t z3)
+{ // 3-way simultaneous inversion
+ // Input: z1,z2,z3
+ // Output: 1/z1,1/z2,1/z3 (override inputs).
+ f2elm_t t0, t1, t2, t3;
+
+ fp2mul_mont(z1, z2, t0); // t0 = z1*z2
+ fp2mul_mont(z3, t0, t1); // t1 = z1*z2*z3
+ fp2inv_mont(t1); // t1 = 1/(z1*z2*z3)
+ fp2mul_mont(z3, t1, t2); // t2 = 1/(z1*z2)
+ fp2mul_mont(t2, z2, t3); // t3 = 1/z1
+ fp2mul_mont(t2, z1, z2); // z2 = 1/z2
+ fp2mul_mont(t0, t1, z3); // z3 = 1/z3
+ fp2copy(t3, z1); // z1 = 1/z1
+}
+
+
+void get_A(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A)
+{ // Given the x-coordinates of P, Q, and R, returns the value A corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A.
+ // Input: the x-coordinates xP, xQ, and xR of the points P, Q and R.
+ // Output: the coefficient A corresponding to the curve E_A: y^2=x^3+A*x^2+x.
+ f2elm_t t0, t1, one = F2ELM_INIT;
+
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, one->c0);
+ fp2add(xP, xQ, t1); // t1 = xP+xQ
+ fp2mul_mont(xP, xQ, t0); // t0 = xP*xQ
+ fp2mul_mont(xR, t1, A); // A = xR*t1
+ fp2add(t0, A, A); // A = A+t0
+ fp2mul_mont(t0, xR, t0); // t0 = t0*xR
+ fp2sub(A, one, A); // A = A-1
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2add(t1, xR, t1); // t1 = t1+xR
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2sqr_mont(A, A); // A = A^2
+ fp2inv_mont(t0); // t0 = 1/t0
+ fp2mul_mont(A, t0, A); // A = A*t0
+ fp2sub(A, t1, A); // Afinal = A-t1
+}
+
+
+void j_inv(const f2elm_t A, const f2elm_t C, f2elm_t jinv)
+{ // Computes the j-invariant of a Montgomery curve with projective constant.
+ // Input: A,C in GF(p^2).
+ // Output: j=256*(A^2-3*C^2)^3/(C^4*(A^2-4*C^2)), which is the j-invariant of the Montgomery curve B*y^2=x^3+(A/C)*x^2+x or (equivalently) j-invariant of B'*y^2=C*x^3+A*x^2+C*x.
+ f2elm_t t0, t1;
+
+ fp2sqr_mont(A, jinv); // jinv = A^2
+ fp2sqr_mont(C, t1); // t1 = C^2
+ fp2add(t1, t1, t0); // t0 = t1+t1
+ fp2sub(jinv, t0, t0); // t0 = jinv-t0
+ fp2sub(t0, t1, t0); // t0 = t0-t1
+ fp2sub(t0, t1, jinv); // jinv = t0-t1
+ fp2sqr_mont(t1, t1); // t1 = t1^2
+ fp2mul_mont(jinv, t1, jinv); // jinv = jinv*t1
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2sqr_mont(t0, t1); // t1 = t0^2
+ fp2mul_mont(t0, t1, t0); // t0 = t0*t1
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2add(t0, t0, t0); // t0 = t0+t0
+ fp2inv_mont(jinv); // jinv = 1/jinv
+ fp2mul_mont(jinv, t0, jinv); // jinv = t0*jinv
+}
+
+
+void xDBLADD(point_proj_t P, point_proj_t Q, const f2elm_t xPQ, const f2elm_t A24)
+{ // Simultaneous doubling and differential addition.
+ // Input: projective Montgomery points P=(XP:ZP) and Q=(XQ:ZQ) such that xP=XP/ZP and xQ=XQ/ZQ, affine difference xPQ=x(P-Q) and Montgomery curve constant A24=(A+2)/4.
+ // Output: projective Montgomery points P <- 2*P = (X2P:Z2P) such that x(2P)=X2P/Z2P, and Q <- P+Q = (XQP:ZQP) such that = x(Q+P)=XQP/ZQP.
+ f2elm_t t0, t1, t2;
+
+ fp2add(P->X, P->Z, t0); // t0 = XP+ZP
+ fp2sub(P->X, P->Z, t1); // t1 = XP-ZP
+ fp2sqr_mont(t0, P->X); // XP = (XP+ZP)^2
+ fp2sub(Q->X, Q->Z, t2); // t2 = XQ-ZQ
+ fp2correction(t2);
+ fp2add(Q->X, Q->Z, Q->X); // XQ = XQ+ZQ
+ fp2mul_mont(t0, t2, t0); // t0 = (XP+ZP)*(XQ-ZQ)
+ fp2sqr_mont(t1, P->Z); // ZP = (XP-ZP)^2
+ fp2mul_mont(t1, Q->X, t1); // t1 = (XP-ZP)*(XQ+ZQ)
+ fp2sub(P->X, P->Z, t2); // t2 = (XP+ZP)^2-(XP-ZP)^2
+ fp2mul_mont(P->X, P->Z, P->X); // XP = (XP+ZP)^2*(XP-ZP)^2
+ fp2mul_mont(t2, A24, Q->X); // XQ = A24*[(XP+ZP)^2-(XP-ZP)^2]
+ fp2sub(t0, t1, Q->Z); // ZQ = (XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)
+ fp2add(Q->X, P->Z, P->Z); // ZP = A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2
+ fp2add(t0, t1, Q->X); // XQ = (XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)
+ fp2mul_mont(P->Z, t2, P->Z); // ZP = [A24*[(XP+ZP)^2-(XP-ZP)^2]+(XP-ZP)^2]*[(XP+ZP)^2-(XP-ZP)^2]
+ fp2sqr_mont(Q->Z, Q->Z); // ZQ = [(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2
+ fp2sqr_mont(Q->X, Q->X); // XQ = [(XP+ZP)*(XQ-ZQ)+(XP-ZP)*(XQ+ZQ)]^2
+ fp2mul_mont(Q->Z, xPQ, Q->Z); // ZQ = xPQ*[(XP+ZP)*(XQ-ZQ)-(XP-ZP)*(XQ+ZQ)]^2
+}
diff --git a/third_party/sidh/src/fpx.c b/third_party/sidh/src/fpx.c
new file mode 100644
index 000000000..4f933cbb5
--- /dev/null
+++ b/third_party/sidh/src/fpx.c
@@ -0,0 +1,420 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: core functions over GF(p) and GF(p^2)
+*********************************************************************************************/
+
+#include "sidh/def_p503.h"
+#include "P503_internal.h"
+#include "internal.h"
+
+extern const struct params_t kP503Params;
+
+inline void fpcopy(const felm_t a, felm_t c)
+{ // Copy a field element, c = a.
+ unsigned int i;
+
+ for (i = 0; i < NWORDS_FIELD; i++)
+ c[i] = a[i];
+}
+
+
+inline void fpzero(felm_t a)
+{ // Zero a field element, a = 0.
+ unsigned int i;
+
+ for (i = 0; i < NWORDS_FIELD; i++)
+ a[i] = 0;
+}
+
+
+void to_mont(const felm_t a, felm_t mc)
+{ // Conversion to Montgomery representation,
+ // mc = a*R^2*R^(-1) mod p = a*R mod p, where a in [0, p-1].
+ // The Montgomery constant R^2 mod p is the global value "Montgomery_R2".
+
+ fpmul_mont(a, (digit_t*)&kP503Params.Montgomery_R2, mc);
+}
+
+
+void from_mont(const felm_t ma, felm_t c)
+{ // Conversion from Montgomery representation to standard representation,
+ // c = ma*R^(-1) mod p = a mod p, where ma in [0, p-1].
+ digit_t one[NWORDS_FIELD] = {0};
+
+ one[0] = 1;
+ fpmul_mont(ma, one, c);
+ fpcorrection(c);
+}
+
+
+void copy_words(const digit_t* a, digit_t* c, const unsigned int nwords)
+{ // Copy wordsize digits, c = a, where lng(a) = nwords.
+ unsigned int i;
+
+ for (i = 0; i < nwords; i++) {
+ c[i] = a[i];
+ }
+}
+
+
+void fpmul_mont(const felm_t ma, const felm_t mb, felm_t mc)
+{ // Multiprecision multiplication, c = a*b mod p.
+ dfelm_t temp = {0};
+
+ mp_mul(ma, mb, temp, NWORDS_FIELD);
+ rdc_mont(temp, mc);
+}
+
+
+void fpsqr_mont(const felm_t ma, felm_t mc)
+{ // Multiprecision squaring, c = a^2 mod p.
+ dfelm_t temp = {0};
+
+ mp_mul(ma, ma, temp, NWORDS_FIELD);
+ rdc_mont(temp, mc);
+}
+
+
+void fpinv_mont(felm_t a)
+{ // Field inversion using Montgomery arithmetic, a = a^(-1)*R mod p.
+ felm_t tt;
+
+ fpcopy(a, tt);
+ fpinv_chain_mont(tt);
+ fpsqr_mont(tt, tt);
+ fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, a);
+}
+
+
+void fp2copy(const f2elm_t a, f2elm_t c)
+{ // Copy a GF(p^2) element, c = a.
+ fpcopy(a->c0, c->c0);
+ fpcopy(a->c1, c->c1);
+}
+
+
+void fp2zero(f2elm_t a)
+{ // Zero a GF(p^2) element, a = 0.
+ fpzero(a->c0);
+ fpzero(a->c1);
+}
+
+
+void fp2neg(f2elm_t a)
+{ // GF(p^2) negation, a = -a in GF(p^2).
+ fpneg(a->c0);
+ fpneg(a->c1);
+}
+
+inline void fp2add(const f2elm_t a, const f2elm_t b, f2elm_t c)
+{ // GF(p^2) addition, c = a+b in GF(p^2).
+ fpadd(a->c0, b->c0, c->c0);
+ fpadd(a->c1, b->c1, c->c1);
+}
+
+inline void fp2sub(const f2elm_t a, const f2elm_t b, f2elm_t c)
+{ // GF(p^2) subtraction, c = a-b in GF(p^2).
+ fpsub(a->c0, b->c0, c->c0);
+ fpsub(a->c1, b->c1, c->c1);
+}
+
+
+void fp2div2(const f2elm_t a, f2elm_t c)
+{ // GF(p^2) division by two, c = a/2 in GF(p^2).
+ fpdiv2(a->c0, c->c0);
+ fpdiv2(a->c1, c->c1);
+}
+
+
+void fp2correction(f2elm_t a)
+{ // Modular correction, a = a in GF(p^2).
+ fpcorrection(a->c0);
+ fpcorrection(a->c1);
+}
+
+
+inline static void mp_addfast(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Multiprecision addition, c = a+b.
+#if defined(OPENSSL_NO_ASM)
+ mp_add(a, b, c, NWORDS_FIELD);
+#else
+ mp_add_asm(a, b, c);
+
+#endif
+}
+
+
+void fp2sqr_mont(const f2elm_t a, f2elm_t c)
+{ // GF(p^2) squaring using Montgomery arithmetic, c = a^2 in GF(p^2).
+ // Inputs: a = a0+a1*i, where a0, a1 are in [0, 2*p-1]
+ // Output: c = c0+c1*i, where c0, c1 are in [0, 2*p-1]
+ felm_t t1, t2, t3;
+
+ mp_addfast(a->c0, a->c1, t1); // t1 = a0+a1
+ fpsub(a->c0, a->c1, t2); // t2 = a0-a1
+ mp_addfast(a->c0, a->c0, t3); // t3 = 2a0
+ fpmul_mont(t1, t2, c->c0); // c0 = (a0+a1)(a0-a1)
+ fpmul_mont(t3, a->c1, c->c1); // c1 = 2a0*a1
+}
+
+
+inline unsigned int mp_sub(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
+{ // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = nwords. Returns the borrow bit.
+ unsigned int i, borrow = 0;
+
+ for (i = 0; i < nwords; i++) {
+ SUBC(borrow, a[i], b[i], borrow, c[i]);
+ }
+
+ return borrow;
+}
+
+
+inline static digit_t mp_subfast(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Multiprecision subtraction, c = a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD.
+ // If c < 0 then returns mask = 0xFF..F, else mask = 0x00..0
+#if defined(OPENSSL_NO_ASM)
+
+ return (0 - (digit_t)mp_sub(a, b, c, 2*NWORDS_FIELD));
+
+#else
+
+ return mp_subx2_asm(a, b, c);
+
+#endif
+}
+
+
+inline static void mp_dblsubfast(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Multiprecision subtraction, c = c-a-b, where lng(a) = lng(b) = 2*NWORDS_FIELD.
+ // Inputs should be s.t. c > a and c > b
+#if defined(OPENSSL_NO_ASM)
+
+ mp_sub(c, a, c, 2*NWORDS_FIELD);
+ mp_sub(c, b, c, 2*NWORDS_FIELD);
+
+#else
+
+ mp_dblsubx2_asm(a, b, c);
+
+#endif
+}
+
+
+void fp2mul_mont(const f2elm_t a, const f2elm_t b, f2elm_t c)
+{ // GF(p^2) multiplication using Montgomery arithmetic, c = a*b in GF(p^2).
+ // Inputs: a = a0+a1*i and b = b0+b1*i, where a0, a1, b0, b1 are in [0, 2*p-1]
+ // Output: c = c0+c1*i, where c0, c1 are in [0, 2*p-1]
+ felm_t t1, t2;
+ dfelm_t tt1, tt2, tt3;
+ digit_t mask;
+ unsigned int i;
+
+ mp_addfast(a->c0, a->c1, t1); // t1 = a0+a1
+ mp_addfast(b->c0, b->c1, t2); // t2 = b0+b1
+ mp_mul(a->c0, b->c0, tt1, NWORDS_FIELD); // tt1 = a0*b0
+ mp_mul(a->c1, b->c1, tt2, NWORDS_FIELD); // tt2 = a1*b1
+ mp_mul(t1, t2, tt3, NWORDS_FIELD); // tt3 = (a0+a1)*(b0+b1)
+ mp_dblsubfast(tt1, tt2, tt3); // tt3 = (a0+a1)*(b0+b1) - a0*b0 - a1*b1
+ mask = mp_subfast(tt1, tt2, tt1); // tt1 = a0*b0 - a1*b1. If tt1 < 0 then mask = 0xFF..F, else if tt1 >= 0 then mask = 0x00..0
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ t1[i] = ((digit_t*)kP503Params.prime)[i] & mask;
+ }
+
+ rdc_mont(tt3, c->c1); // c[1] = (a0+a1)*(b0+b1) - a0*b0 - a1*b1
+ mp_addfast((digit_t*)&tt1[NWORDS_FIELD], t1, (digit_t*)&tt1[NWORDS_FIELD]);
+ rdc_mont(tt1, c->c0); // c[0] = a0*b0 - a1*b1
+}
+
+
+void fpinv_chain_mont(felm_t a)
+{ // Chain to compute a^(p-3)/4 using Montgomery arithmetic.
+ unsigned int i, j;
+ felm_t t[15], tt;
+
+ // Precomputed table
+ fpsqr_mont(a, tt);
+ fpmul_mont(a, tt, t[0]);
+ for (i = 0; i <= 13; i++) fpmul_mont(t[i], tt, t[i+1]);
+
+ fpcopy(a, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[8], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 6; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[9], tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[0], tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[2], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[8], tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[10], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[0], tt, tt);
+ for (i = 0; i < 6; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[10], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[10], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[5], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[2], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[3], tt, tt);
+ for (i = 0; i < 6; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[5], tt, tt);
+ for (i = 0; i < 12; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[12], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[8], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[12], tt, tt);
+ for (i = 0; i < 6; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[11], tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[5], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[14], tt, tt);
+ for (i = 0; i < 7; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[14], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[5], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[8], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[4], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[6], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[5], tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[7], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(a, tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[0], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[11], tt, tt);
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[13], tt, tt);
+ for (i = 0; i < 8; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[1], tt, tt);
+ for (i = 0; i < 6; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[10], tt, tt);
+ for (j = 0; j < 49; j++) {
+ for (i = 0; i < 5; i++) fpsqr_mont(tt, tt);
+ fpmul_mont(t[14], tt, tt);
+ }
+ fpcopy(tt, a);
+}
+
+
+void fp2inv_mont(f2elm_t a)
+{// GF(p^2) inversion using Montgomery arithmetic, a = (a0-i*a1)/(a0^2+a1^2).
+ f2elm_t t1;
+
+ fpsqr_mont(a->c0, t1->c0); // t10 = a0^2
+ fpsqr_mont(a->c1, t1->c1); // t11 = a1^2
+ fpadd(t1->c0, t1->c1, t1->c0); // t10 = a0^2+a1^2
+ fpinv_mont(t1->c0); // t10 = (a0^2+a1^2)^-1
+ fpneg(a->c1); // a = a0-i*a1
+ fpmul_mont(a->c0, t1->c0, a->c0);
+ fpmul_mont(a->c1, t1->c0, a->c1); // a = (a0-i*a1)*(a0^2+a1^2)^-1
+}
+
+
+void to_fp2mont(const f2elm_t a, f2elm_t mc)
+{ // Conversion of a GF(p^2) element to Montgomery representation,
+ // mc_i = a_i*R^2*R^(-1) = a_i*R in GF(p^2).
+
+ to_mont(a->c0, mc->c0);
+ to_mont(a->c1, mc->c1);
+}
+
+
+void from_fp2mont(const f2elm_t ma, f2elm_t c)
+{ // Conversion of a GF(p^2) element from Montgomery representation to standard representation,
+ // c_i = ma_i*R^(-1) = a_i in GF(p^2).
+
+ from_mont(ma->c0, c->c0);
+ from_mont(ma->c1, c->c1);
+}
+
+
+inline unsigned int mp_add(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
+{ // Multiprecision addition, c = a+b, where lng(a) = lng(b) = nwords. Returns the carry bit.
+ unsigned int i, carry = 0;
+
+ for (i = 0; i < nwords; i++) {
+ ADDC(carry, a[i], b[i], carry, c[i]);
+ }
+
+ return carry;
+}
+
+
+void mp_shiftleft(digit_t* x, unsigned int shift, const unsigned int nwords)
+{
+ unsigned int i, j = 0;
+
+ while (shift > RADIX) {
+ j += 1;
+ shift -= RADIX;
+ }
+
+ for (i = 0; i < nwords-j; i++)
+ x[nwords-1-i] = x[nwords-1-i-j];
+ for (i = nwords-j; i < nwords; i++)
+ x[nwords-1-i] = 0;
+ if (shift != 0) {
+ for (j = nwords-1; j > 0; j--)
+ SHIFTL(x[j], x[j-1], shift, x[j], RADIX);
+ x[0] <<= shift;
+ }
+}
+
+
+void mp_shiftr1(digit_t* x, const unsigned int nwords)
+{ // Multiprecision right shift by one.
+ unsigned int i;
+
+ for (i = 0; i < nwords-1; i++) {
+ SHIFTR(x[i+1], x[i], 1, x[i], RADIX);
+ }
+ x[nwords-1] >>= 1;
+}
+
+
+void mp_shiftl1(digit_t* x, const unsigned int nwords)
+{ // Multiprecision left shift by one.
+ int i;
+
+ for (i = nwords-1; i > 0; i--) {
+ SHIFTL(x[i], x[i-1], 1, x[i], RADIX);
+ }
+ x[0] <<= 1;
+}
diff --git a/third_party/sidh/src/generic/fp_generic.c b/third_party/sidh/src/generic/fp_generic.c
new file mode 100644
index 000000000..325053f1c
--- /dev/null
+++ b/third_party/sidh/src/generic/fp_generic.c
@@ -0,0 +1,222 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: portable modular arithmetic for P503
+*********************************************************************************************/
+
+#include "../internal.h"
+#include "../P503_internal.h"
+
+
+// Global constants
+extern const struct params_t kP503Params;
+
+inline void fpadd503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular addition, c = a+b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ unsigned int i, carry = 0;
+ digit_t mask;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(carry, a[i], b[i], carry, c[i]);
+ }
+
+ carry = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(carry, c[i], ((digit_t*)kP503Params.primeX2)[i], carry, c[i]);
+ }
+ mask = 0 - (digit_t)carry;
+
+ carry = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(carry, c[i], ((digit_t*)kP503Params.primeX2)[i] & mask, carry, c[i]);
+ }
+}
+
+
+inline void fpsub503(const digit_t* a, const digit_t* b, digit_t* c)
+{ // Modular subtraction, c = a-b mod p503.
+ // Inputs: a, b in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ unsigned int i, borrow = 0;
+ digit_t mask;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, a[i], b[i], borrow, c[i]);
+ }
+ mask = 0 - (digit_t)borrow;
+
+ borrow = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(borrow, c[i], ((digit_t*)kP503Params.primeX2)[i] & mask, borrow, c[i]);
+ }
+}
+
+
+inline void fpneg503(digit_t* a)
+{ // Modular negation, a = -a mod p503.
+ // Input/output: a in [0, 2*p503-1]
+ unsigned int i, borrow = 0;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, ((digit_t*)kP503Params.primeX2)[i], a[i], borrow, a[i]);
+ }
+}
+
+
+void fpdiv2_503(const digit_t* a, digit_t* c)
+{ // Modular division by two, c = a/2 mod p503.
+ // Input : a in [0, 2*p503-1]
+ // Output: c in [0, 2*p503-1]
+ unsigned int i, carry = 0;
+ digit_t mask;
+
+ mask = 0 - (digit_t)(a[0] & 1); // If a is odd compute a+p503
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(carry, a[i], ((digit_t*)kP503Params.prime)[i] & mask, carry, c[i]);
+ }
+
+ mp_shiftr1(c, NWORDS_FIELD);
+}
+
+
+void fpcorrection503(digit_t* a)
+{ // Modular correction to reduce field element a in [0, 2*p503-1] to [0, p503-1].
+ unsigned int i, borrow = 0;
+ digit_t mask;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ SUBC(borrow, a[i], ((digit_t*)kP503Params.prime)[i], borrow, a[i]);
+ }
+ mask = 0 - (digit_t)borrow;
+
+ borrow = 0;
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ ADDC(borrow, a[i], ((digit_t*)kP503Params.prime)[i] & mask, borrow, a[i]);
+ }
+}
+
+
+void digit_x_digit(const digit_t a, const digit_t b, digit_t* c)
+{ // Digit multiplication, digit * digit -> 2-digit result
+ register digit_t al, ah, bl, bh, temp;
+ digit_t albl, albh, ahbl, ahbh, res1, res2, res3, carry;
+ digit_t mask_low = (digit_t)(-1) >> (sizeof(digit_t)*4), mask_high = (digit_t)(-1) << (sizeof(digit_t)*4);
+
+ al = a & mask_low; // Low part
+ ah = a >> (sizeof(digit_t) * 4); // High part
+ bl = b & mask_low;
+ bh = b >> (sizeof(digit_t) * 4);
+
+ albl = al*bl;
+ albh = al*bh;
+ ahbl = ah*bl;
+ ahbh = ah*bh;
+ c[0] = albl & mask_low; // C00
+
+ res1 = albl >> (sizeof(digit_t) * 4);
+ res2 = ahbl & mask_low;
+ res3 = albh & mask_low;
+ temp = res1 + res2 + res3;
+ carry = temp >> (sizeof(digit_t) * 4);
+ c[0] ^= temp << (sizeof(digit_t) * 4); // C01
+
+ res1 = ahbl >> (sizeof(digit_t) * 4);
+ res2 = albh >> (sizeof(digit_t) * 4);
+ res3 = ahbh & mask_low;
+ temp = res1 + res2 + res3 + carry;
+ c[1] = temp & mask_low; // C10
+ carry = temp & mask_high;
+ c[1] ^= (ahbh & mask_high) + carry; // C11
+}
+
+
+void mp_mul(const digit_t* a, const digit_t* b, digit_t* c, const unsigned int nwords)
+{ // Multiprecision comba multiply, c = a*b, where lng(a) = lng(b) = nwords.
+ unsigned int i, j;
+ digit_t t = 0, u = 0, v = 0, UV[2];
+ unsigned int carry = 0;
+
+ for (i = 0; i < nwords; i++) {
+ for (j = 0; j <= i; j++) {
+ MUL(a[j], b[i-j], UV+1, UV[0]);
+ ADDC(0, UV[0], v, carry, v);
+ ADDC(carry, UV[1], u, carry, u);
+ t += carry;
+ }
+ c[i] = v;
+ v = u;
+ u = t;
+ t = 0;
+ }
+
+ for (i = nwords; i < 2*nwords-1; i++) {
+ for (j = i-nwords+1; j < nwords; j++) {
+ MUL(a[j], b[i-j], UV+1, UV[0]);
+ ADDC(0, UV[0], v, carry, v);
+ ADDC(carry, UV[1], u, carry, u);
+ t += carry;
+ }
+ c[i] = v;
+ v = u;
+ u = t;
+ t = 0;
+ }
+ c[2*nwords-1] = v;
+}
+
+
+void rdc_mont(const digit_t* ma, digit_t* mc)
+{ // Efficient Montgomery reduction using comba and exploiting the special form of the prime p503.
+ // mc = ma*R^-1 mod p503x2, where R = 2^512.
+ // If ma < 2^512*p503, the output mc is in the range [0, 2*p503-1].
+ // ma is assumed to be in Montgomery representation.
+ unsigned int i, j, carry, count = p503_ZERO_WORDS;
+ digit_t UV[2], t = 0, u = 0, v = 0;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ mc[i] = 0;
+ }
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ for (j = 0; j < i; j++) {
+ if (j < (i-p503_ZERO_WORDS+1)) {
+ MUL(mc[j], ((digit_t*)kP503Params.primeP1)[i-j], UV+1, UV[0]);
+ ADDC(0, UV[0], v, carry, v);
+ ADDC(carry, UV[1], u, carry, u);
+ t += carry;
+ }
+ }
+ ADDC(0, v, ma[i], carry, v);
+ ADDC(carry, u, 0, carry, u);
+ t += carry;
+ mc[i] = v;
+ v = u;
+ u = t;
+ t = 0;
+ }
+
+ for (i = NWORDS_FIELD; i < 2*NWORDS_FIELD-1; i++) {
+ if (count > 0) {
+ count -= 1;
+ }
+ for (j = i-NWORDS_FIELD+1; j < NWORDS_FIELD; j++) {
+ if (j < (NWORDS_FIELD-count)) {
+ MUL(mc[j], ((digit_t*)kP503Params.primeP1)[i-j], UV+1, UV[0]);
+ ADDC(0, UV[0], v, carry, v);
+ ADDC(carry, UV[1], u, carry, u);
+ t += carry;
+ }
+ }
+ ADDC(0, v, ma[i], carry, v);
+ ADDC(carry, u, 0, carry, u);
+ t += carry;
+ mc[i-NWORDS_FIELD] = v;
+ v = u;
+ u = t;
+ t = 0;
+ }
+ ADDC(0, v, ma[2*NWORDS_FIELD-1], carry, v);
+ mc[NWORDS_FIELD-1] = v;
+}
\ No newline at end of file
diff --git a/third_party/sidh/src/internal.h b/third_party/sidh/src/internal.h
new file mode 100644
index 000000000..8a32b465c
--- /dev/null
+++ b/third_party/sidh/src/internal.h
@@ -0,0 +1,96 @@
+#ifndef INTERNAL_H_
+#define INTERNAL_H_
+
+#include "sidh/def_p503.h"
+
+/********************** Macros for platform-dependent operations **********************/
+
+#if defined(OPENSSL_NO_ASM)
+
+/********************** Constant-time unsigned comparisons ***********************/
+
+// The following functions return 1 (TRUE) if condition is true, 0 (FALSE) otherwise
+
+static inline unsigned int is_digit_nonzero_ct(digit_t x)
+{ // Is x != 0?
+ return (unsigned int)((x | (0-x)) >> (RADIX-1));
+}
+
+static inline unsigned int is_digit_zero_ct(digit_t x)
+{ // Is x = 0?
+ return (unsigned int)(1 ^ is_digit_nonzero_ct(x));
+}
+
+static inline unsigned int is_digit_lessthan_ct(digit_t x, digit_t y)
+{ // Is x < y?
+ return (unsigned int)((x ^ ((x ^ y) | ((x - y) ^ y))) >> (RADIX-1));
+}
+
+// Digit multiplication
+#define MUL(multiplier, multiplicand, hi, lo) \
+ digit_x_digit((multiplier), (multiplicand), &(lo));
+
+// Digit addition with carry
+#define ADDC(carryIn, addend1, addend2, carryOut, sumOut) \
+ { digit_t tempReg = (addend1) + (digit_t)(carryIn); \
+ (sumOut) = (addend2) + tempReg; \
+ (carryOut) = (is_digit_lessthan_ct(tempReg, (digit_t)(carryIn)) | is_digit_lessthan_ct((sumOut), tempReg)); }
+
+// Digit subtraction with borrow
+#define SUBC(borrowIn, minuend, subtrahend, borrowOut, differenceOut) \
+ { digit_t tempReg = (minuend) - (subtrahend); \
+ unsigned int borrowReg = (is_digit_lessthan_ct((minuend), (subtrahend)) | ((borrowIn) & is_digit_zero_ct(tempReg))); \
+ (differenceOut) = tempReg - (digit_t)(borrowIn); \
+ (borrowOut) = borrowReg; }
+
+// Shift right with flexible datatype
+#define SHIFTR(highIn, lowIn, shift, shiftOut, DigitSize) \
+ (shiftOut) = ((lowIn) >> (shift)) ^ ((highIn) << (DigitSize - (shift)));
+
+// Shift left with flexible datatype
+#define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \
+ (shiftOut) = ((highIn) << (shift)) ^ ((lowIn) >> (DigitSize - (shift)));
+
+// 64x64-bit multiplication
+#define MUL128(multiplier, multiplicand, product) \
+ mp_mul((digit_t*)&(multiplier), (digit_t*)&(multiplicand), (digit_t*)&(product), NWORDS_FIELD/2);
+
+// 128-bit addition, inputs < 2^127
+#define ADD128(addend1, addend2, addition) \
+ mp_add((digit_t*)(addend1), (digit_t*)(addend2), (digit_t*)(addition), NWORDS_FIELD);
+
+// 128-bit addition with output carry
+#define ADC128(addend1, addend2, carry, addition) \
+ (carry) = mp_add((digit_t*)(addend1), (digit_t*)(addend2), (digit_t*)(addition), NWORDS_FIELD);
+
+#else
+
+// Digit multiplication
+#define MUL(multiplier, multiplicand, hi, lo) \
+ { uint128_t tempReg = (uint128_t)(multiplier) * (uint128_t)(multiplicand); \
+ *(hi) = (digit_t)(tempReg >> RADIX); \
+ (lo) = (digit_t)tempReg; }
+
+// Digit addition with carry
+#define ADDC(carryIn, addend1, addend2, carryOut, sumOut) \
+ { uint128_t tempReg = (uint128_t)(addend1) + (uint128_t)(addend2) + (uint128_t)(carryIn); \
+ (carryOut) = (digit_t)(tempReg >> RADIX); \
+ (sumOut) = (digit_t)tempReg; }
+
+// Digit subtraction with borrow
+#define SUBC(borrowIn, minuend, subtrahend, borrowOut, differenceOut) \
+ { uint128_t tempReg = (uint128_t)(minuend) - (uint128_t)(subtrahend) - (uint128_t)(borrowIn); \
+ (borrowOut) = (digit_t)(tempReg >> (sizeof(uint128_t)*8 - 1)); \
+ (differenceOut) = (digit_t)tempReg; }
+
+// Digit shift right
+#define SHIFTR(highIn, lowIn, shift, shiftOut, DigitSize) \
+ (shiftOut) = ((lowIn) >> (shift)) ^ ((highIn) << (RADIX - (shift)));
+
+// Digit shift left
+#define SHIFTL(highIn, lowIn, shift, shiftOut, DigitSize) \
+ (shiftOut) = ((highIn) << (shift)) ^ ((lowIn) >> (RADIX - (shift)));
+
+#endif
+
+#endif // INTERNAL_H_
diff --git a/third_party/sidh/src/sidh.c b/third_party/sidh/src/sidh.c
new file mode 100644
index 000000000..fdbd87e28
--- /dev/null
+++ b/third_party/sidh/src/sidh.c
@@ -0,0 +1,410 @@
+/********************************************************************************************
+* SIDH: an efficient supersingular isogeny cryptography library
+*
+* Abstract: ephemeral supersingular isogeny Diffie-Hellman key exchange (SIDH)
+*********************************************************************************************/
+
+#include "openssl/bn.h"
+#include "openssl/base.h"
+
+#include "sidh/def_p503.h"
+#include "P503_internal.h"
+
+extern const struct params_t kP503Params;
+
+// Returns private key bit size for type A (IsInitiator=true) or B (IsInitiator=false) type.
+static inline size_t PrvKeyBitSz(int IsInitiator) {
+ return IsInitiator?SIDHp503_PRV_A_BITSZ:SIDHp503_PRV_B_BITSZ;
+}
+
+// Swap points.
+// If option = 0 then P <- P and Q <- Q, else if option = 0xFF...FF then P <- Q and Q <- P
+#if !defined(OPENSSL_X86_64) || defined(OPENSSL_NO_ASM)
+static void cswap(point_proj_t P, point_proj_t Q, const digit_t option)
+{
+ digit_t temp;
+ unsigned int i;
+
+ for (i = 0; i < NWORDS_FIELD; i++) {
+ temp = option & (P->X->c0[i] ^ Q->X->c0[i]);
+ P->X->c0[i] = temp ^ P->X->c0[i];
+ Q->X->c0[i] = temp ^ Q->X->c0[i];
+ temp = option & (P->Z->c0[i] ^ Q->Z->c0[i]);
+ P->Z->c0[i] = temp ^ P->Z->c0[i];
+ Q->Z->c0[i] = temp ^ Q->Z->c0[i];
+ temp = option & (P->X->c1[i] ^ Q->X->c1[i]);
+ P->X->c1[i] = temp ^ P->X->c1[i];
+ Q->X->c1[i] = temp ^ Q->X->c1[i];
+ temp = option & (P->Z->c1[i] ^ Q->Z->c1[i]);
+ P->Z->c1[i] = temp ^ P->Z->c1[i];
+ Q->Z->c1[i] = temp ^ Q->Z->c1[i];
+ }
+}
+#endif
+
+// Swap points.
+// If option = 0 then P <- P and Q <- Q, else if option = 0xFF...FF then P <- Q and Q <- P
+static inline void fp2cswap(point_proj_t P, point_proj_t Q, const digit_t option)
+{
+#if defined(OPENSSL_X86_64) && !defined(OPENSSL_NO_ASM)
+ cswap_asm(P, Q, option);
+#else
+ cswap(P, Q, option);
+#endif
+}
+
+static void LADDER3PT(const f2elm_t xP, const f2elm_t xQ, const f2elm_t xPQ, const digit_t* m, const unsigned int AliceOrBob, point_proj_t R, const f2elm_t A)
+{
+ point_proj_t R0 = POINT_PROJ_INIT, R2 = POINT_PROJ_INIT;
+ f2elm_t A24 = F2ELM_INIT;
+ digit_t mask;
+ int i, nbits, bit, swap, prevbit = 0;
+
+ if (AliceOrBob == ALICE) {
+ nbits = OALICE_BITS;
+ } else {
+ nbits = OBOB_BITS;
+ }
+
+ // Initializing constant
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, A24->c0);
+ fp2add(A24, A24, A24);
+ fp2add(A, A24, A24);
+ fp2div2(A24, A24);
+ fp2div2(A24, A24); // A24 = (A+2)/4
+
+ // Initializing points
+ fp2copy(xQ, R0->X);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (digit_t*)R0->Z);
+ fp2copy(xPQ, R2->X);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (digit_t*)R2->Z);
+ fp2copy(xP, R->X);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (digit_t*)R->Z);
+ fpzero((digit_t*)(R->Z)->c1);
+
+ // Main loop
+ for (i = 0; i < nbits; i++) {
+ bit = (m[i >> LOG2RADIX] >> (i & (RADIX-1))) & 1;
+ swap = bit ^ prevbit;
+ prevbit = bit;
+ mask = 0 - (digit_t)swap;
+
+ fp2cswap(R, R2, mask);
+ xDBLADD(R0, R2, R->X, A24);
+ fp2mul_mont(R2->X, R->Z, R2->X);
+ }
+}
+
+// Initialization of basis points
+static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR)
+{
+
+ fpcopy(gen, XP->c0);
+ fpcopy(gen + NWORDS_FIELD, XP->c1);
+ fpcopy(gen + 2*NWORDS_FIELD, XQ->c0);
+ fpzero(XQ->c1);
+ fpcopy(gen + 3*NWORDS_FIELD, XR->c0);
+ fpcopy(gen + 4*NWORDS_FIELD, XR->c1);
+}
+
+// Conversion of GF(p^2) element from Montgomery to standard representation, and encoding by removing leading 0 bytes
+static void fp2_encode(const f2elm_t x, unsigned char *enc)
+{
+ unsigned int i;
+ f2elm_t t;
+
+ from_fp2mont(x, t);
+ for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) {
+ enc[i] = ((unsigned char*)t)[i];
+ enc[i + FP2_ENCODED_BYTES / 2] = ((unsigned char*)t)[i + MAXBITS_FIELD / 8];
+ }
+}
+
+// Parse byte sequence back into GF(p^2) element, and conversion to Montgomery representation
+static void fp2_decode(const unsigned char *enc, f2elm_t x)
+{
+ unsigned int i;
+
+ for (i = 0; i < 2*(MAXBITS_FIELD / 8); i++) ((unsigned char *)x)[i] = 0;
+ for (i = 0; i < FP2_ENCODED_BYTES / 2; i++) {
+ ((unsigned char*)x)[i] = enc[i];
+ ((unsigned char*)x)[i + MAXBITS_FIELD / 8] = enc[i + FP2_ENCODED_BYTES / 2];
+ }
+ to_fp2mont(x, x);
+}
+
+int EphemeralKeyGeneration_A(const unsigned char* PrivateKeyA, unsigned char* PublicKeyA)
+{
+ point_proj_t R, phiP = POINT_PROJ_INIT, phiQ = POINT_PROJ_INIT, phiR = POINT_PROJ_INIT, pts[MAX_INT_POINTS_ALICE];
+ f2elm_t XPA, XQA, XRA, coeff[3], A24plus = F2ELM_INIT, C24 = F2ELM_INIT, A = F2ELM_INIT;
+ unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0;
+
+ // Initialize basis points
+ init_basis((digit_t*)kP503Params.A_gen, XPA, XQA, XRA);
+ init_basis((digit_t*)kP503Params.B_gen, phiP->X, phiQ->X, phiR->X);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiP->Z)->c0);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiQ->Z)->c0);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiR->Z)->c0);
+
+ // Initialize constants
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, A24plus->c0);
+ fp2add(A24plus, A24plus, C24);
+
+ // Retrieve kernel point
+ LADDER3PT(XPA, XQA, XRA, (digit_t*)PrivateKeyA, ALICE, R, A);
+
+ // Traverse tree
+ index = 0;
+ for (row = 1; row < MAX_Alice; row++) {
+ while (index < MAX_Alice-row) {
+ fp2copy(R->X, pts[npts]->X);
+ fp2copy(R->Z, pts[npts]->Z);
+ pts_index[npts++] = index;
+ m = kP503Params.strat_Alice[ii++];
+ xDBLe(R, R, A24plus, C24, (int)(2*m));
+ index += m;
+ }
+ get_4_isog(R, A24plus, C24, coeff);
+
+ for (i = 0; i < npts; i++) {
+ eval_4_isog(pts[i], coeff);
+ }
+ eval_4_isog(phiP, coeff);
+ eval_4_isog(phiQ, coeff);
+ eval_4_isog(phiR, coeff);
+
+ fp2copy(pts[npts-1]->X, R->X);
+ fp2copy(pts[npts-1]->Z, R->Z);
+ index = pts_index[npts-1];
+ npts -= 1;
+ }
+
+ get_4_isog(R, A24plus, C24, coeff);
+ eval_4_isog(phiP, coeff);
+ eval_4_isog(phiQ, coeff);
+ eval_4_isog(phiR, coeff);
+
+ inv_3_way(phiP->Z, phiQ->Z, phiR->Z);
+ fp2mul_mont(phiP->X, phiP->Z, phiP->X);
+ fp2mul_mont(phiQ->X, phiQ->Z, phiQ->X);
+ fp2mul_mont(phiR->X, phiR->Z, phiR->X);
+
+ // Format public key
+ fp2_encode(phiP->X, PublicKeyA);
+ fp2_encode(phiQ->X, PublicKeyA + FP2_ENCODED_BYTES);
+ fp2_encode(phiR->X, PublicKeyA + 2*FP2_ENCODED_BYTES);
+
+ return 0;
+}
+
+
+int EphemeralKeyGeneration_B(const unsigned char* PrivateKeyB, unsigned char* PublicKeyB)
+{
+ point_proj_t R, phiP = POINT_PROJ_INIT, phiQ = POINT_PROJ_INIT, phiR = POINT_PROJ_INIT, pts[MAX_INT_POINTS_BOB];
+ f2elm_t XPB, XQB, XRB, coeff[3], A24plus = F2ELM_INIT, A24minus = F2ELM_INIT, A = F2ELM_INIT;
+ unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
+
+ // Initialize basis points
+ init_basis((digit_t*)kP503Params.B_gen, XPB, XQB, XRB);
+ init_basis((digit_t*)kP503Params.A_gen, phiP->X, phiQ->X, phiR->X);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiP->Z)->c0);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiQ->Z)->c0);
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, (phiR->Z)->c0);
+
+ // Initialize constants
+ fpcopy((digit_t*)&kP503Params.Montgomery_one, A24plus->c0);
+ fp2add(A24plus, A24plus, A24plus);
+ fp2copy(A24plus, A24minus);
+ fp2neg(A24minus);
+
+ // Retrieve kernel point
+ LADDER3PT(XPB, XQB, XRB, (digit_t*)PrivateKeyB, BOB, R, A);
+
+ // Traverse tree
+ index = 0;
+ for (row = 1; row < MAX_Bob; row++) {
+ while (index < MAX_Bob-row) {
+ fp2copy(R->X, pts[npts]->X);
+ fp2copy(R->Z, pts[npts]->Z);
+ pts_index[npts++] = index;
+ m = kP503Params.strat_Bob[ii++];
+ xTPLe(R, R, A24minus, A24plus, (int)m);
+ index += m;
+ }
+ get_3_isog(R, A24minus, A24plus, coeff);
+
+ for (i = 0; i < npts; i++) {
+ eval_3_isog(pts[i], coeff);
+ }
+ eval_3_isog(phiP, coeff);
+ eval_3_isog(phiQ, coeff);
+ eval_3_isog(phiR, coeff);
+
+ fp2copy(pts[npts-1]->X, R->X);
+ fp2copy(pts[npts-1]->Z, R->Z);
+ index = pts_index[npts-1];
+ npts -= 1;
+ }
+
+ get_3_isog(R, A24minus, A24plus, coeff);
+ eval_3_isog(phiP, coeff);
+ eval_3_isog(phiQ, coeff);
+ eval_3_isog(phiR, coeff);
+
+ inv_3_way(phiP->Z, phiQ->Z, phiR->Z);
+ fp2mul_mont(phiP->X, phiP->Z, phiP->X);
+ fp2mul_mont(phiQ->X, phiQ->Z, phiQ->X);
+ fp2mul_mont(phiR->X, phiR->Z, phiR->X);
+
+ // Format public key
+ fp2_encode(phiP->X, PublicKeyB);
+ fp2_encode(phiQ->X, PublicKeyB + FP2_ENCODED_BYTES);
+ fp2_encode(phiR->X, PublicKeyB + 2*FP2_ENCODED_BYTES);
+
+ return 0;
+}
+
+
+int EphemeralSecretAgreement_A(const unsigned char* PrivateKeyA, const unsigned char* PublicKeyB, unsigned char* SharedSecretA)
+{
+ point_proj_t R, pts[MAX_INT_POINTS_ALICE];
+ f2elm_t coeff[3], PKB[3], jinv;
+ f2elm_t A24plus = F2ELM_INIT, C24 = F2ELM_INIT, A = F2ELM_INIT;
+ unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0;
+
+ // Initialize images of Bob's basis
+ fp2_decode(PublicKeyB, PKB[0]);
+ fp2_decode(PublicKeyB + FP2_ENCODED_BYTES, PKB[1]);
+ fp2_decode(PublicKeyB + 2*FP2_ENCODED_BYTES, PKB[2]);
+
+ // Initialize constants
+ get_A(PKB[0], PKB[1], PKB[2], A); // TODO: Can return projective A?
+ fpadd((digit_t*)&kP503Params.Montgomery_one, (digit_t*)&kP503Params.Montgomery_one, C24->c0);
+ fp2add(A, C24, A24plus);
+ fpadd(C24->c0, C24->c0, C24->c0);
+
+ // Retrieve kernel point
+ LADDER3PT(PKB[0], PKB[1], PKB[2], (digit_t*)PrivateKeyA, ALICE, R, A);
+
+ // Traverse tree
+ index = 0;
+ for (row = 1; row < MAX_Alice; row++) {
+ while (index < MAX_Alice-row) {
+ fp2copy(R->X, pts[npts]->X);
+ fp2copy(R->Z, pts[npts]->Z);
+ pts_index[npts++] = index;
+ m = kP503Params.strat_Alice[ii++];
+ xDBLe(R, R, A24plus, C24, (int)(2*m));
+ index += m;
+ }
+ get_4_isog(R, A24plus, C24, coeff);
+
+ for (i = 0; i < npts; i++) {
+ eval_4_isog(pts[i], coeff);
+ }
+
+ fp2copy(pts[npts-1]->X, R->X);
+ fp2copy(pts[npts-1]->Z, R->Z);
+ index = pts_index[npts-1];
+ npts -= 1;
+ }
+
+ get_4_isog(R, A24plus, C24, coeff);
+ fp2div2(C24, C24);
+ fp2sub(A24plus, C24, A24plus);
+ fp2div2(C24, C24);
+ j_inv(A24plus, C24, jinv);
+ fp2_encode(jinv, SharedSecretA); // Format shared secret
+
+ return 0;
+}
+
+int EphemeralSecretAgreement_B(const unsigned char* PrivateKeyB, const unsigned char* PublicKeyA, unsigned char* SharedSecretB)
+{
+ point_proj_t R, pts[MAX_INT_POINTS_BOB];
+ f2elm_t coeff[3], PKB[3], jinv;
+ f2elm_t A24plus = F2ELM_INIT, A24minus = F2ELM_INIT, A = F2ELM_INIT;
+ unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
+
+ // Initialize images of Alice's basis
+ fp2_decode(PublicKeyA, PKB[0]);
+ fp2_decode(PublicKeyA + FP2_ENCODED_BYTES, PKB[1]);
+ fp2_decode(PublicKeyA + 2*FP2_ENCODED_BYTES, PKB[2]);
+
+ // Initialize constants
+ get_A(PKB[0], PKB[1], PKB[2], A); // TODO: Can return projective A?
+ fpadd((digit_t*)&kP503Params.Montgomery_one, (digit_t*)&kP503Params.Montgomery_one, A24minus->c0);
+ fp2add(A, A24minus, A24plus);
+ fp2sub(A, A24minus, A24minus);
+
+ // Retrieve kernel point
+ LADDER3PT(PKB[0], PKB[1], PKB[2], (digit_t*)PrivateKeyB, BOB, R, A);
+
+ // Traverse tree
+ index = 0;
+ for (row = 1; row < MAX_Bob; row++) {
+ while (index < MAX_Bob-row) {
+ fp2copy(R->X, pts[npts]->X);
+ fp2copy(R->Z, pts[npts]->Z);
+ pts_index[npts++] = index;
+ m = kP503Params.strat_Bob[ii++];
+ xTPLe(R, R, A24minus, A24plus, (int)m);
+ index += m;
+ }
+ get_3_isog(R, A24minus, A24plus, coeff);
+
+ for (i = 0; i < npts; i++) {
+ eval_3_isog(pts[i], coeff);
+ }
+
+ fp2copy(pts[npts-1]->X, R->X);
+ fp2copy(pts[npts-1]->Z, R->Z);
+ index = pts_index[npts-1];
+ npts -= 1;
+ }
+
+ get_3_isog(R, A24minus, A24plus, coeff);
+ fp2add(A24plus, A24minus, A);
+ fp2add(A, A, A);
+ fp2sub(A24plus, A24minus, A24plus);
+ j_inv(A, A24plus, jinv);
+ fp2_encode(jinv, SharedSecretB); // Format shared secret
+
+ return 0;
+}
+
+int EphemeralKeyPair_SIDHp503(unsigned char* PrivateKey, unsigned char* PublicKey, int IsInitiator) {
+ int ret = -1;
+
+ BN_CTX *ctx = BN_CTX_new();
+ if (!ctx) {
+ goto end;
+ }
+
+ // Calculate private key for Alice. Needs to be in range [0, 2^0xFA - 1] and < 250 bits
+ BIGNUM *bn_sidh_prv = BN_CTX_get(ctx);
+ if (!bn_sidh_prv) {
+ goto end;
+ }
+
+ if (!BN_rand(bn_sidh_prv, PrvKeyBitSz(IsInitiator), BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY)) {
+ goto end;
+ }
+
+ // Convert to little endian
+ if (!BN_bn2le_padded(PrivateKey, NBITS_TO_NBYTES(PrvKeyBitSz(IsInitiator)), bn_sidh_prv)) {
+ goto end;
+ }
+
+ // Never fails
+ IsInitiator
+ ?(void)EphemeralKeyGeneration_A_SIDHp503(PrivateKey, PublicKey)
+ :(void)EphemeralKeyGeneration_B_SIDHp503(PrivateKey, PublicKey);
+
+ // All good
+ ret = 0;
+
+end:
+ BN_CTX_free(ctx);
+ return ret;
+}
diff --git a/tool/CMakeLists.txt b/tool/CMakeLists.txt
index 7f340171d..6a796cc48 100644
--- a/tool/CMakeLists.txt
+++ b/tool/CMakeLists.txt
@@ -1,4 +1,4 @@
-include_directories(../include)
+include_directories(../include ../third_party/sidh/include)
add_executable(
bssl
diff --git a/tool/speed.cc b/tool/speed.cc
index 2175baa24..4d86441ea 100644
--- a/tool/speed.cc
+++ b/tool/speed.cc
@@ -50,6 +50,10 @@ OPENSSL_MSVC_PRAGMA(warning(pop))
#include "internal.h"
+#include "sidh/def_p503.h"
+#include "sidh/P503_api.h"
+
+
// TimeResults represents the results of benchmarking a function.
struct TimeResults {
// num_calls is the number of function calls done in the time period.
@@ -282,6 +286,78 @@ static bool SpeedRSAKeyGen(const std::string &selected) {
return true;
}
+static bool SpeedSIDHP503KeyGen(bool is_initiator) {
+ uint8_t public_SIDH[SIDHp503_PUB_BYTESZ] = {0};
+ uint8_t private_SIDH[SIDHp503_PRV_KEY_BYTESZ_MAX] = {0};
+ // Key generation function to be benchmarked
+ std::function<int(const unsigned char*, unsigned char*)> keygen =
+ is_initiator?
+ EphemeralKeyGeneration_A_SIDHp503:
+ EphemeralKeyGeneration_B_SIDHp503;
+
+ // Generate private key to be used for public key generation
+ if (EphemeralKeyPair_SIDHp503(private_SIDH, public_SIDH, is_initiator)) {
+ return false;
+ }
+
+ TimeResults results;
+ TimeFunction(&results,
+ [keygen, &private_SIDH, &public_SIDH]() -> bool {
+ // Never fails
+ (void)keygen(private_SIDH, public_SIDH);
+ return true;
+ });
+
+ results.Print(std::string("SIDH/P503 KeyGen ") + std::string(is_initiator?"A":"B"));
+ return true;
+}
+
+static bool SpeedSIDHP503Kex(bool is_initiator) {
+ uint8_t public_SIDH[SIDHp503_PUB_BYTESZ] = {0};
+ uint8_t private_SIDH[SIDHp503_PRV_KEY_BYTESZ_MAX] = {0};
+ uint8_t tmp[SIDHp503_PRV_KEY_BYTESZ_MAX] = {0};
+ uint8_t ss[SIDHp503_SS_BYTESZ] = {0};
+
+ // Key agreement function to be benchmarked
+ std::function<void(const unsigned char*, const unsigned char*, unsigned char*)> kex =
+ is_initiator?
+ EphemeralSecretAgreement_A_SIDHp503:
+ EphemeralSecretAgreement_B_SIDHp503;
+
+ // Generate private key for one side
+ if (EphemeralKeyPair_SIDHp503(private_SIDH, public_SIDH, is_initiator)) {
+ return false;
+ }
+
+ // Generate public key for other side
+ memset(public_SIDH, 0, sizeof(public_SIDH));
+ if (EphemeralKeyPair_SIDHp503(tmp, public_SIDH, !is_initiator)) {
+ return false;
+ }
+
+ TimeResults results;
+ TimeFunction(&results,
+ [kex, &private_SIDH, &public_SIDH, &ss]() -> bool {
+ // Never fails
+ (void)kex(private_SIDH, public_SIDH, ss);
+ return true;
+ });
+
+ results.Print(std::string("SIDH/P503 KEX ") + std::string(is_initiator?"A":"B"));
+ return true;
+}
+
+static bool SpeedSIDHP503(const std::string &selected) {
+ if (!selected.empty() && selected.find("SIDH") == std::string::npos) {
+ return true;
+ }
+ return
+ SpeedSIDHP503KeyGen(true) &&
+ SpeedSIDHP503KeyGen(false) &&
+ SpeedSIDHP503Kex(true) &&
+ SpeedSIDHP503Kex(false);
+}
+
static uint8_t *align(uint8_t *in, unsigned alignment) {
return reinterpret_cast<uint8_t *>(
(reinterpret_cast<uintptr_t>(in) + alignment) &
@@ -815,6 +891,7 @@ bool Speed(const std::vector<std::string> &args) {
!SpeedECDH(selected) ||
!SpeedECDSA(selected) ||
!Speed25519(selected) ||
+ !SpeedSIDHP503(selected) ||
!SpeedSPAKE2(selected) ||
!SpeedScrypt(selected) ||
!SpeedRSAKeyGen(selected)) {
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