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96e5f1d7ae
As identified in: Qian Guo, Thomas Johansson, Alexander Nilsson. A
key-recovery timing attack on post-quantum primitives using the
Fujisaki-Okamoto transformation and its application on FrodoKEM. In
CRYPTO 2020.
Based on
155c24c3df
238 lines
13 KiB
C
238 lines
13 KiB
C
/********************************************************************************************
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* FrodoKEM: Learning with Errors Key Encapsulation
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*
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* Abstract: Key Encapsulation Mechanism (KEM) based on Frodo
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*********************************************************************************************/
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#include <stdint.h>
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#include <string.h>
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#include "fips202.h"
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#include "randombytes.h"
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#include "api.h"
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#include "common.h"
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#include "params.h"
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int PQCLEAN_FRODOKEM1344AES_OPT_crypto_kem_keypair(uint8_t *pk, uint8_t *sk) {
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// FrodoKEM's key generation
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// Outputs: public key pk ( BYTES_SEED_A + (PARAMS_LOGQ*PARAMS_N*PARAMS_NBAR)/8 bytes)
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// secret key sk (CRYPTO_BYTES + BYTES_SEED_A + (PARAMS_LOGQ*PARAMS_N*PARAMS_NBAR)/8 + 2*PARAMS_N*PARAMS_NBAR + BYTES_PKHASH bytes)
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uint8_t *pk_seedA = &pk[0];
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uint8_t *pk_b = &pk[BYTES_SEED_A];
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uint8_t *sk_s = &sk[0];
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uint8_t *sk_pk = &sk[CRYPTO_BYTES];
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uint8_t *sk_S = &sk[CRYPTO_BYTES + CRYPTO_PUBLICKEYBYTES];
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uint8_t *sk_pkh = &sk[CRYPTO_BYTES + CRYPTO_PUBLICKEYBYTES + 2 * PARAMS_N * PARAMS_NBAR];
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uint16_t B[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t S[2 * PARAMS_N * PARAMS_NBAR] = {0}; // contains secret data
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uint16_t *E = &S[PARAMS_N * PARAMS_NBAR]; // contains secret data
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uint8_t randomness[2 * CRYPTO_BYTES + BYTES_SEED_A]; // contains secret data via randomness_s and randomness_seedSE
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uint8_t *randomness_s = &randomness[0]; // contains secret data
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uint8_t *randomness_seedSE = &randomness[CRYPTO_BYTES]; // contains secret data
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uint8_t *randomness_z = &randomness[2 * CRYPTO_BYTES];
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uint8_t shake_input_seedSE[1 + CRYPTO_BYTES]; // contains secret data
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// Generate the secret value s, the seed for S and E, and the seed for the seed for A. Add seed_A to the public key
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randombytes(randomness, CRYPTO_BYTES + CRYPTO_BYTES + BYTES_SEED_A);
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shake(pk_seedA, BYTES_SEED_A, randomness_z, BYTES_SEED_A);
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// Generate S and E, and compute B = A*S + E. Generate A on-the-fly
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shake_input_seedSE[0] = 0x5F;
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memcpy(&shake_input_seedSE[1], randomness_seedSE, CRYPTO_BYTES);
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shake((uint8_t *)S, 2 * PARAMS_N * PARAMS_NBAR * sizeof(uint16_t), shake_input_seedSE, 1 + CRYPTO_BYTES);
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for (size_t i = 0; i < 2 * PARAMS_N * PARAMS_NBAR; i++) {
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S[i] = PQCLEAN_FRODOKEM1344AES_OPT_LE_TO_UINT16(S[i]);
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}
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(S, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(E, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_add_as_plus_e(B, S, E, pk);
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// Encode the second part of the public key
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PQCLEAN_FRODOKEM1344AES_OPT_pack(pk_b, CRYPTO_PUBLICKEYBYTES - BYTES_SEED_A, B, PARAMS_N * PARAMS_NBAR, PARAMS_LOGQ);
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// Add s, pk and S to the secret key
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memcpy(sk_s, randomness_s, CRYPTO_BYTES);
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memcpy(sk_pk, pk, CRYPTO_PUBLICKEYBYTES);
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for (size_t i = 0; i < PARAMS_N * PARAMS_NBAR; i++) {
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S[i] = PQCLEAN_FRODOKEM1344AES_OPT_UINT16_TO_LE(S[i]);
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}
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memcpy(sk_S, S, 2 * PARAMS_N * PARAMS_NBAR);
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// Add H(pk) to the secret key
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shake(sk_pkh, BYTES_PKHASH, pk, CRYPTO_PUBLICKEYBYTES);
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// Cleanup:
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)S, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)E, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(randomness, 2 * CRYPTO_BYTES);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(shake_input_seedSE, 1 + CRYPTO_BYTES);
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return 0;
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}
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int PQCLEAN_FRODOKEM1344AES_OPT_crypto_kem_enc(uint8_t *ct, uint8_t *ss, const uint8_t *pk) {
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// FrodoKEM's key encapsulation
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const uint8_t *pk_seedA = &pk[0];
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const uint8_t *pk_b = &pk[BYTES_SEED_A];
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uint8_t *ct_c1 = &ct[0];
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uint8_t *ct_c2 = &ct[(PARAMS_LOGQ * PARAMS_N * PARAMS_NBAR) / 8];
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uint16_t B[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t V[PARAMS_NBAR * PARAMS_NBAR] = {0}; // contains secret data
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uint16_t C[PARAMS_NBAR * PARAMS_NBAR] = {0};
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uint16_t Bp[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t Sp[(2 * PARAMS_N + PARAMS_NBAR)*PARAMS_NBAR] = {0}; // contains secret data
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uint16_t *Ep = &Sp[PARAMS_N * PARAMS_NBAR]; // contains secret data
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uint16_t *Epp = &Sp[2 * PARAMS_N * PARAMS_NBAR]; // contains secret data
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uint8_t G2in[BYTES_PKHASH + BYTES_MU]; // contains secret data via mu
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uint8_t *pkh = &G2in[0];
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uint8_t *mu = &G2in[BYTES_PKHASH]; // contains secret data
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uint8_t G2out[2 * CRYPTO_BYTES]; // contains secret data
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uint8_t *seedSE = &G2out[0]; // contains secret data
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uint8_t *k = &G2out[CRYPTO_BYTES]; // contains secret data
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uint8_t Fin[CRYPTO_CIPHERTEXTBYTES + CRYPTO_BYTES]; // contains secret data via Fin_k
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uint8_t *Fin_ct = &Fin[0];
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uint8_t *Fin_k = &Fin[CRYPTO_CIPHERTEXTBYTES]; // contains secret data
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uint8_t shake_input_seedSE[1 + CRYPTO_BYTES]; // contains secret data
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// pkh <- G_1(pk), generate random mu, compute (seedSE || k) = G_2(pkh || mu)
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shake(pkh, BYTES_PKHASH, pk, CRYPTO_PUBLICKEYBYTES);
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randombytes(mu, BYTES_MU);
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shake(G2out, CRYPTO_BYTES + CRYPTO_BYTES, G2in, BYTES_PKHASH + BYTES_MU);
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// Generate Sp and Ep, and compute Bp = Sp*A + Ep. Generate A on-the-fly
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shake_input_seedSE[0] = 0x96;
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memcpy(&shake_input_seedSE[1], seedSE, CRYPTO_BYTES);
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shake((uint8_t *)Sp, (2 * PARAMS_N + PARAMS_NBAR) * PARAMS_NBAR * sizeof(uint16_t), shake_input_seedSE, 1 + CRYPTO_BYTES);
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for (size_t i = 0; i < (2 * PARAMS_N + PARAMS_NBAR) * PARAMS_NBAR; i++) {
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Sp[i] = PQCLEAN_FRODOKEM1344AES_OPT_LE_TO_UINT16(Sp[i]);
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}
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Sp, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Ep, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_add_sa_plus_e(Bp, Sp, Ep, pk_seedA);
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PQCLEAN_FRODOKEM1344AES_OPT_pack(ct_c1, (PARAMS_LOGQ * PARAMS_N * PARAMS_NBAR) / 8, Bp, PARAMS_N * PARAMS_NBAR, PARAMS_LOGQ);
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// Generate Epp, and compute V = Sp*B + Epp
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Epp, PARAMS_NBAR * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_unpack(B, PARAMS_N * PARAMS_NBAR, pk_b, CRYPTO_PUBLICKEYBYTES - BYTES_SEED_A, PARAMS_LOGQ);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_add_sb_plus_e(V, B, Sp, Epp);
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// Encode mu, and compute C = V + enc(mu) (mod q)
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PQCLEAN_FRODOKEM1344AES_OPT_key_encode(C, (uint16_t *)mu);
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PQCLEAN_FRODOKEM1344AES_OPT_add(C, V, C);
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PQCLEAN_FRODOKEM1344AES_OPT_pack(ct_c2, (PARAMS_LOGQ * PARAMS_NBAR * PARAMS_NBAR) / 8, C, PARAMS_NBAR * PARAMS_NBAR, PARAMS_LOGQ);
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// Compute ss = F(ct||KK)
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memcpy(Fin_ct, ct, CRYPTO_CIPHERTEXTBYTES);
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memcpy(Fin_k, k, CRYPTO_BYTES);
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shake(ss, CRYPTO_BYTES, Fin, CRYPTO_CIPHERTEXTBYTES + CRYPTO_BYTES);
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// Cleanup:
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)V, PARAMS_NBAR * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Sp, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Ep, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Epp, PARAMS_NBAR * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(mu, BYTES_MU);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(G2out, 2 * CRYPTO_BYTES);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(Fin_k, CRYPTO_BYTES);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(shake_input_seedSE, 1 + CRYPTO_BYTES);
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return 0;
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}
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int PQCLEAN_FRODOKEM1344AES_OPT_crypto_kem_dec(uint8_t *ss, const uint8_t *ct, const uint8_t *sk) {
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// FrodoKEM's key decapsulation
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uint16_t B[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t Bp[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t W[PARAMS_NBAR * PARAMS_NBAR] = {0}; // contains secret data
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uint16_t C[PARAMS_NBAR * PARAMS_NBAR] = {0};
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uint16_t CC[PARAMS_NBAR * PARAMS_NBAR] = {0};
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uint16_t BBp[PARAMS_N * PARAMS_NBAR] = {0};
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uint16_t Sp[(2 * PARAMS_N + PARAMS_NBAR)*PARAMS_NBAR] = {0}; // contains secret data
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uint16_t *Ep = &Sp[PARAMS_N * PARAMS_NBAR]; // contains secret data
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uint16_t *Epp = &Sp[2 * PARAMS_N * PARAMS_NBAR]; // contains secret data
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const uint8_t *ct_c1 = &ct[0];
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const uint8_t *ct_c2 = &ct[(PARAMS_LOGQ * PARAMS_N * PARAMS_NBAR) / 8];
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const uint8_t *sk_s = &sk[0];
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const uint8_t *sk_pk = &sk[CRYPTO_BYTES];
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const uint8_t *sk_S = &sk[CRYPTO_BYTES + CRYPTO_PUBLICKEYBYTES];
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uint16_t S[PARAMS_N * PARAMS_NBAR]; // contains secret data
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const uint8_t *sk_pkh = &sk[CRYPTO_BYTES + CRYPTO_PUBLICKEYBYTES + 2 * PARAMS_N * PARAMS_NBAR];
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const uint8_t *pk_seedA = &sk_pk[0];
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const uint8_t *pk_b = &sk_pk[BYTES_SEED_A];
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uint8_t G2in[BYTES_PKHASH + BYTES_MU]; // contains secret data via muprime
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uint8_t *pkh = &G2in[0];
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uint8_t *muprime = &G2in[BYTES_PKHASH]; // contains secret data
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uint8_t G2out[2 * CRYPTO_BYTES]; // contains secret data
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uint8_t *seedSEprime = &G2out[0]; // contains secret data
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uint8_t *kprime = &G2out[CRYPTO_BYTES]; // contains secret data
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uint8_t Fin[CRYPTO_CIPHERTEXTBYTES + CRYPTO_BYTES]; // contains secret data via Fin_k
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uint8_t *Fin_ct = &Fin[0];
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uint8_t *Fin_k = &Fin[CRYPTO_CIPHERTEXTBYTES]; // contains secret data
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uint8_t shake_input_seedSEprime[1 + CRYPTO_BYTES]; // contains secret data
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for (size_t i = 0; i < PARAMS_N * PARAMS_NBAR; i++) {
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S[i] = sk_S[2 * i] | (sk_S[2 * i + 1] << 8);
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}
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// Compute W = C - Bp*S (mod q), and decode the randomness mu
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PQCLEAN_FRODOKEM1344AES_OPT_unpack(Bp, PARAMS_N * PARAMS_NBAR, ct_c1, (PARAMS_LOGQ * PARAMS_N * PARAMS_NBAR) / 8, PARAMS_LOGQ);
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PQCLEAN_FRODOKEM1344AES_OPT_unpack(C, PARAMS_NBAR * PARAMS_NBAR, ct_c2, (PARAMS_LOGQ * PARAMS_NBAR * PARAMS_NBAR) / 8, PARAMS_LOGQ);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_bs(W, Bp, S);
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PQCLEAN_FRODOKEM1344AES_OPT_sub(W, C, W);
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PQCLEAN_FRODOKEM1344AES_OPT_key_decode((uint16_t *)muprime, W);
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// Generate (seedSE' || k') = G_2(pkh || mu')
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memcpy(pkh, sk_pkh, BYTES_PKHASH);
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shake(G2out, CRYPTO_BYTES + CRYPTO_BYTES, G2in, BYTES_PKHASH + BYTES_MU);
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// Generate Sp and Ep, and compute BBp = Sp*A + Ep. Generate A on-the-fly
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shake_input_seedSEprime[0] = 0x96;
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memcpy(&shake_input_seedSEprime[1], seedSEprime, CRYPTO_BYTES);
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shake((uint8_t *)Sp, (2 * PARAMS_N + PARAMS_NBAR) * PARAMS_NBAR * sizeof(uint16_t), shake_input_seedSEprime, 1 + CRYPTO_BYTES);
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for (size_t i = 0; i < (2 * PARAMS_N + PARAMS_NBAR) * PARAMS_NBAR; i++) {
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Sp[i] = PQCLEAN_FRODOKEM1344AES_OPT_LE_TO_UINT16(Sp[i]);
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}
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Sp, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Ep, PARAMS_N * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_add_sa_plus_e(BBp, Sp, Ep, pk_seedA);
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// Generate Epp, and compute W = Sp*B + Epp
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PQCLEAN_FRODOKEM1344AES_OPT_sample_n(Epp, PARAMS_NBAR * PARAMS_NBAR);
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PQCLEAN_FRODOKEM1344AES_OPT_unpack(B, PARAMS_N * PARAMS_NBAR, pk_b, CRYPTO_PUBLICKEYBYTES - BYTES_SEED_A, PARAMS_LOGQ);
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PQCLEAN_FRODOKEM1344AES_OPT_mul_add_sb_plus_e(W, B, Sp, Epp);
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// Encode mu, and compute CC = W + enc(mu') (mod q)
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PQCLEAN_FRODOKEM1344AES_OPT_key_encode(CC, (uint16_t *)muprime);
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PQCLEAN_FRODOKEM1344AES_OPT_add(CC, W, CC);
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// Prepare input to F
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memcpy(Fin_ct, ct, CRYPTO_CIPHERTEXTBYTES);
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// Reducing BBp modulo q
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for (size_t i = 0; i < PARAMS_N * PARAMS_NBAR; i++) {
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BBp[i] = BBp[i] & ((1 << PARAMS_LOGQ) - 1);
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}
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// If (Bp == BBp & C == CC) then ss = F(ct || k'), else ss = F(ct || s)
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// Needs to avoid branching on secret data as per:
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// Qian Guo, Thomas Johansson, Alexander Nilsson. A key-recovery timing attack on post-quantum
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// primitives using the Fujisaki-Okamoto transformation and its application on FrodoKEM. In CRYPTO 2020.
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int8_t selector = PQCLEAN_FRODOKEM1344AES_OPT_ct_verify(Bp, BBp, PARAMS_N * PARAMS_NBAR) | PQCLEAN_FRODOKEM1344AES_OPT_ct_verify(C, CC, PARAMS_NBAR * PARAMS_NBAR);
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// If (selector == 0) then load k' to do ss = F(ct || k'), else if (selector == -1) load s to do ss = F(ct || s)
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PQCLEAN_FRODOKEM1344AES_OPT_ct_select((uint8_t *)Fin_k, (uint8_t *)kprime, (uint8_t *)sk_s, CRYPTO_BYTES, selector);
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shake(ss, CRYPTO_BYTES, Fin, CRYPTO_CIPHERTEXTBYTES + CRYPTO_BYTES);
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// Cleanup:
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)W, PARAMS_NBAR * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Sp, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)S, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Ep, PARAMS_N * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes((uint8_t *)Epp, PARAMS_NBAR * PARAMS_NBAR * sizeof(uint16_t));
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(muprime, BYTES_MU);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(G2out, 2 * CRYPTO_BYTES);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(Fin_k, CRYPTO_BYTES);
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PQCLEAN_FRODOKEM1344AES_OPT_clear_bytes(shake_input_seedSEprime, 1 + CRYPTO_BYTES);
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return 0;
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}
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