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boringssl/crypto/curve25519/spake25519.c

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  1. /* Copyright (c) 2016, Google Inc.

  2.  *

  3.  * Permission to use, copy, modify, and/or distribute this software for any

  4.  * purpose with or without fee is hereby granted, provided that the above

  5.  * copyright notice and this permission notice appear in all copies.

  6.  *

  7.  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES

  8.  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF

  9.  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY

  10.  * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES

  11.  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION

  12.  * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN

  13.  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */

  14. 

  15. #include <openssl/curve25519.h>

  16. 

  17. #include <string.h>

  18. 

  19. #include <openssl/bytestring.h>

  20. #include <openssl/mem.h>

  21. #include <openssl/rand.h>

  22. #include <openssl/sha.h>

  23. 

  24. #include "internal.h"

  25. #include "../internal.h"

  26. 

  27. 

  28. // The following precomputation tables are for the following

  29. // points used in the SPAKE2 protocol.

  30. //

  31. // N:

  32. //   x: 49918732221787544735331783592030787422991506689877079631459872391322455579424

  33. //   y: 54629554431565467720832445949441049581317094546788069926228343916274969994000

  34. //   encoded: 10e3df0ae37d8e7a99b5fe74b44672103dbddcbd06af680d71329a11693bc778

  35. //

  36. // M:

  37. //   x: 31406539342727633121250288103050113562375374900226415211311216773867585644232

  38. //   y: 21177308356423958466833845032658859666296341766942662650232962324899758529114

  39. //   encoded: 5ada7e4bf6ddd9adb6626d32131c6b5c51a1e347a3478f53cfcf441b88eed12e

  40. //

  41. // These points and their precomputation tables are generated with the

  42. // following Python code. For a description of the precomputation table,

  43. // see curve25519.c in this directory.

  44. //

  45. // Exact copies of the source code are kept in bug 27296743.

  46. //

  47. // import hashlib

  48. // import ed25519 as E  # http://ed25519.cr.yp.to/python/ed25519.py

  49. //

  50. // SEED_N = 'edwards25519 point generation seed (N)'

  51. // SEED_M = 'edwards25519 point generation seed (M)'

  52. 

  53. /*

  54. def genpoint(seed):

  55.     v = hashlib.sha256(seed).digest()

  56.     it = 1

  57.     while True:

  58.         try:

  59.             x,y = E.decodepoint(v)

  60.         except Exception, e:

  61.             print e

  62.             it += 1

  63.             v = hashlib.sha256(v).digest()

  64.             continue

  65.         print "Found in %d iterations:" % it

  66.         print "  x = %d" % x

  67.         print "  y = %d" % y

  68.         print " Encoded (hex)"

  69.         print E.encodepoint((x,y)).encode('hex')

  70.         return (x,y)

  71. 

  72. def gentable(P):

  73.     t = []

  74.     for i in range(1,16):

  75.         k = (i >> 3 & 1) * (1 << 192) + \

  76.             (i >> 2 & 1) * (1 << 128) + \

  77.             (i >> 1 & 1) * (1 <<  64) + \

  78.             (i      & 1)

  79.         t.append(E.scalarmult(P, k))

  80.     return ''.join(E.encodeint(x) + E.encodeint(y) for (x,y) in t)

  81. 

  82. def printtable(table, name):

  83.     print "static const uint8_t %s[15 * 2 * 32] = {" % name,

  84.     for i in range(15 * 2 * 32):

  85.         if i % 12 == 0:

  86.             print "\n   ",

  87.         print " 0x%02x," % ord(table[i]),

  88.     print "\n};"

  89. 

  90. if __name__ == "__main__":

  91.     print "Searching for N"

  92.     N = genpoint(SEED_N)

  93.     print "Generating precomputation table for N"

  94.     Ntable = gentable(N)

  95.     printtable(Ntable, "kSpakeNSmallPrecomp")

  96. 

  97.     print "Searching for M"

  98.     M = genpoint(SEED_M)

  99.     print "Generating precomputation table for M"

  100.     Mtable = gentable(M)

  101.     printtable(Mtable, "kSpakeMSmallPrecomp")

  102. */

  103. 

  104. static const uint8_t kSpakeNSmallPrecomp[15 * 2 * 32] = {

  105.     0x20, 0x1b, 0xc5, 0xb3, 0x43, 0x17, 0x71, 0x10, 0x44, 0x1e, 0x73, 0xb3,

  106.     0xae, 0x3f, 0xbf, 0x9f, 0xf5, 0x44, 0xc8, 0x13, 0x8f, 0xd1, 0x01, 0xc2,

  107.     0x8a, 0x1a, 0x6d, 0xea, 0x4d, 0x00, 0x5d, 0x6e, 0x10, 0xe3, 0xdf, 0x0a,

  108.     0xe3, 0x7d, 0x8e, 0x7a, 0x99, 0xb5, 0xfe, 0x74, 0xb4, 0x46, 0x72, 0x10,

  109.     0x3d, 0xbd, 0xdc, 0xbd, 0x06, 0xaf, 0x68, 0x0d, 0x71, 0x32, 0x9a, 0x11,

  110.     0x69, 0x3b, 0xc7, 0x78, 0x93, 0xf1, 0x57, 0x97, 0x6e, 0xf0, 0x6e, 0x45,

  111.     0x37, 0x4a, 0xf4, 0x0b, 0x18, 0x51, 0xf5, 0x4f, 0x67, 0x3c, 0xdc, 0xec,

  112.     0x84, 0xed, 0xd0, 0xeb, 0xca, 0xfb, 0xdb, 0xff, 0x7f, 0xeb, 0xa8, 0x23,

  113.     0x68, 0x87, 0x13, 0x64, 0x6a, 0x10, 0xf7, 0x45, 0xe0, 0x0f, 0x32, 0x21,

  114.     0x59, 0x7c, 0x0e, 0x50, 0xad, 0x56, 0xd7, 0x12, 0x69, 0x7b, 0x58, 0xf8,

  115.     0xb9, 0x3b, 0xa5, 0xbb, 0x4d, 0x1b, 0x87, 0x1c, 0x46, 0xa7, 0x17, 0x9d,

  116.     0x6d, 0x84, 0x45, 0xbe, 0x7f, 0x95, 0xd2, 0x34, 0xcd, 0x89, 0x95, 0xc0,

  117.     0xf0, 0xd3, 0xdf, 0x6e, 0x10, 0x4a, 0xe3, 0x7b, 0xce, 0x7f, 0x40, 0x27,

  118.     0xc7, 0x2b, 0xab, 0x66, 0x03, 0x59, 0xb4, 0x7b, 0xc7, 0xc7, 0xf0, 0x39,

  119.     0x9a, 0x33, 0x35, 0xbf, 0xcc, 0x2f, 0xf3, 0x2e, 0x68, 0x9d, 0x53, 0x5c,

  120.     0x88, 0x52, 0xe3, 0x77, 0x90, 0xa1, 0x27, 0x85, 0xc5, 0x74, 0x7f, 0x23,

  121.     0x0e, 0x93, 0x01, 0x3e, 0xe7, 0x2e, 0x2e, 0x95, 0xf3, 0x0d, 0xc2, 0x25,

  122.     0x25, 0x39, 0x39, 0x3d, 0x6e, 0x8e, 0x89, 0xbd, 0xe8, 0xbb, 0x67, 0x5e,

  123.     0x8c, 0x66, 0x8b, 0x63, 0x28, 0x1e, 0x4e, 0x74, 0x85, 0xa8, 0xaf, 0x0f,

  124.     0x12, 0x5d, 0xb6, 0x8a, 0x83, 0x1a, 0x77, 0x76, 0x5e, 0x62, 0x8a, 0xa7,

  125.     0x3c, 0xb8, 0x05, 0x57, 0x2b, 0xaf, 0x36, 0x2e, 0x10, 0x90, 0xb2, 0x39,

  126.     0xb4, 0x3e, 0x75, 0x6d, 0x3a, 0xa8, 0x31, 0x35, 0xc2, 0x1e, 0x8f, 0xc2,

  127.     0x79, 0x89, 0x35, 0x16, 0x26, 0xd1, 0xc7, 0x0b, 0x04, 0x1f, 0x1d, 0xf9,

  128.     0x9c, 0x05, 0xa6, 0x6b, 0xb5, 0x19, 0x5a, 0x24, 0x6d, 0x91, 0xc5, 0x31,

  129.     0xfd, 0xc5, 0xfa, 0xe7, 0xa6, 0xcb, 0x0e, 0x4b, 0x18, 0x0d, 0x94, 0xc7,

  130.     0xee, 0x1d, 0x46, 0x1f, 0x92, 0xb1, 0xb2, 0x4a, 0x2b, 0x43, 0x37, 0xfe,

  131.     0xc2, 0x15, 0x11, 0x89, 0xef, 0x59, 0x73, 0x3c, 0x06, 0x76, 0x78, 0xcb,

  132.     0xa6, 0x0d, 0x79, 0x5f, 0x28, 0x0b, 0x5b, 0x8c, 0x9e, 0xe4, 0xaa, 0x51,

  133.     0x9a, 0x42, 0x6f, 0x11, 0x50, 0x3d, 0x01, 0xd6, 0x21, 0xc0, 0x99, 0x5e,

  134.     0x1a, 0xe8, 0x81, 0x25, 0x80, 0xeb, 0xed, 0x5d, 0x37, 0x47, 0x30, 0x70,

  135.     0xa0, 0x4e, 0x0b, 0x43, 0x17, 0xbe, 0xb6, 0x47, 0xe7, 0x2a, 0x62, 0x9d,

  136.     0x5d, 0xa6, 0xc5, 0x33, 0x62, 0x9d, 0x56, 0x24, 0x9d, 0x1d, 0xb2, 0x13,

  137.     0xbc, 0x17, 0x66, 0x43, 0xd1, 0x68, 0xd5, 0x3b, 0x17, 0x69, 0x17, 0xa6,

  138.     0x06, 0x9e, 0x12, 0xb8, 0x7c, 0xd5, 0xaf, 0x3e, 0x21, 0x1b, 0x31, 0xeb,

  139.     0x0b, 0xa4, 0x98, 0x1c, 0xf2, 0x6a, 0x5e, 0x7c, 0x9b, 0x45, 0x8f, 0xb2,

  140.     0x12, 0x06, 0xd5, 0x8c, 0x1d, 0xb2, 0xa7, 0x57, 0x5f, 0x2f, 0x4f, 0xdb,

  141.     0x52, 0x99, 0x7c, 0x58, 0x01, 0x5f, 0xf2, 0xa5, 0xf6, 0x51, 0x86, 0x21,

  142.     0x2f, 0x5b, 0x8d, 0x6a, 0xae, 0x83, 0x34, 0x6d, 0x58, 0x4b, 0xef, 0xfe,

  143.     0xbf, 0x73, 0x5d, 0xdb, 0xc4, 0x97, 0x2a, 0x85, 0xf3, 0x6c, 0x46, 0x42,

  144.     0xb3, 0x90, 0xc1, 0x57, 0x97, 0x50, 0x35, 0xb1, 0x9d, 0xb7, 0xc7, 0x3c,

  145.     0x85, 0x6d, 0x6c, 0xfd, 0xce, 0xb0, 0xc9, 0xa2, 0x77, 0xee, 0xc3, 0x6b,

  146.     0x0c, 0x37, 0xfa, 0x30, 0x91, 0xd1, 0x2c, 0xb8, 0x5e, 0x7f, 0x81, 0x5f,

  147.     0x87, 0xfd, 0x18, 0x02, 0x5a, 0x30, 0x4e, 0x62, 0xbc, 0x65, 0xc6, 0xce,

  148.     0x1a, 0xcf, 0x2b, 0xaa, 0x56, 0x3e, 0x4d, 0xcf, 0xba, 0x62, 0x5f, 0x9a,

  149.     0xd0, 0x72, 0xff, 0xef, 0x28, 0xbd, 0xbe, 0xd8, 0x57, 0x3d, 0xf5, 0x57,

  150.     0x7d, 0xe9, 0x71, 0x31, 0xec, 0x98, 0x90, 0x94, 0xd9, 0x54, 0xbf, 0x84,

  151.     0x0b, 0xe3, 0x06, 0x47, 0x19, 0x9a, 0x13, 0x1d, 0xef, 0x9d, 0x13, 0xf3,

  152.     0xdb, 0xc3, 0x5c, 0x72, 0x9e, 0xed, 0x24, 0xaa, 0x64, 0xed, 0xe7, 0x0d,

  153.     0xa0, 0x7c, 0x73, 0xba, 0x9b, 0x86, 0xa7, 0x3b, 0x55, 0xab, 0x58, 0x30,

  154.     0xf1, 0x15, 0x81, 0x83, 0x2f, 0xf9, 0x62, 0x84, 0x98, 0x66, 0xf6, 0x55,

  155.     0x21, 0xd8, 0xf2, 0x25, 0x64, 0x71, 0x4b, 0x12, 0x76, 0x59, 0xc5, 0xaa,

  156.     0x93, 0x67, 0xc3, 0x86, 0x25, 0xab, 0x4e, 0x4b, 0xf6, 0xd8, 0x3f, 0x44,

  157.     0x2e, 0x11, 0xe0, 0xbd, 0x6a, 0xf2, 0x5d, 0xf5, 0xf9, 0x53, 0xea, 0xa4,

  158.     0xc8, 0xd9, 0x50, 0x33, 0x81, 0xd9, 0xa8, 0x2d, 0x91, 0x7d, 0x13, 0x2a,

  159.     0x11, 0xcf, 0xde, 0x3f, 0x0a, 0xd2, 0xbc, 0x33, 0xb2, 0x62, 0x53, 0xea,

  160.     0x77, 0x88, 0x43, 0x66, 0x27, 0x43, 0x85, 0xe9, 0x5f, 0x55, 0xf5, 0x2a,

  161.     0x8a, 0xac, 0xdf, 0xff, 0x9b, 0x4c, 0x96, 0x9c, 0xa5, 0x7a, 0xce, 0xd5,

  162.     0x79, 0x18, 0xf1, 0x0b, 0x58, 0x95, 0x7a, 0xe7, 0xd3, 0x74, 0x65, 0x0b,

  163.     0xa4, 0x64, 0x30, 0xe8, 0x5c, 0xfc, 0x55, 0x56, 0xee, 0x14, 0x14, 0xd3,

  164.     0x45, 0x3b, 0xf8, 0xde, 0x05, 0x3e, 0xb9, 0x3c, 0xd7, 0x6a, 0x52, 0x72,

  165.     0x5b, 0x39, 0x09, 0xbe, 0x82, 0x23, 0x10, 0x4a, 0xb7, 0xc3, 0xdc, 0x4c,

  166.     0x5d, 0xc9, 0xf1, 0x14, 0x83, 0xf9, 0x0b, 0x9b, 0xe9, 0x23, 0x84, 0x6a,

  167.     0xc4, 0x08, 0x3d, 0xda, 0x3d, 0x12, 0x95, 0x87, 0x18, 0xa4, 0x7d, 0x3f,

  168.     0x23, 0xde, 0xd4, 0x1e, 0xa8, 0x47, 0xc3, 0x71, 0xdb, 0xf5, 0x03, 0x6c,

  169.     0x57, 0xe7, 0xa4, 0x43, 0x82, 0x33, 0x7b, 0x62, 0x46, 0x7d, 0xf7, 0x10,

  170.     0x69, 0x18, 0x38, 0x27, 0x9a, 0x6f, 0x38, 0xac, 0xfa, 0x92, 0xc5, 0xae,

  171.     0x66, 0xa6, 0x73, 0x95, 0x15, 0x0e, 0x4c, 0x04, 0xb6, 0xfc, 0xf5, 0xc7,

  172.     0x21, 0x3a, 0x99, 0xdb, 0x0e, 0x36, 0xf0, 0x56, 0xbc, 0x75, 0xf9, 0x87,

  173.     0x9b, 0x11, 0x18, 0x92, 0x64, 0x1a, 0xe7, 0xc7, 0xab, 0x5a, 0xc7, 0x26,

  174.     0x7f, 0x13, 0x98, 0x42, 0x52, 0x43, 0xdb, 0xc8, 0x6d, 0x0b, 0xb7, 0x31,

  175.     0x93, 0x24, 0xd6, 0xe8, 0x24, 0x1f, 0x6f, 0x21, 0xa7, 0x8c, 0xeb, 0xdb,

  176.     0x83, 0xb8, 0x89, 0xe3, 0xc1, 0xd7, 0x69, 0x3b, 0x02, 0x6b, 0x54, 0x0f,

  177.     0x84, 0x2f, 0xb5, 0x5c, 0x17, 0x77, 0xbe, 0xe5, 0x61, 0x0d, 0xc5, 0xdf,

  178.     0x3b, 0xcf, 0x3e, 0x93, 0x4f, 0xf5, 0x89, 0xb9, 0x5a, 0xc5, 0x29, 0x31,

  179.     0xc0, 0xc2, 0xff, 0xe5, 0x3f, 0xa6, 0xac, 0x03, 0xca, 0xf5, 0xff, 0xe0,

  180.     0x36, 0xce, 0xf3, 0xe2, 0xb7, 0x9c, 0x02, 0xe9, 0x9e, 0xd2, 0xbc, 0x87,

  181.     0x2f, 0x3d, 0x9a, 0x1d, 0x8f, 0xc5, 0x72, 0xb8, 0xa2, 0x01, 0xd4, 0x68,

  182.     0xb1, 0x84, 0x16, 0x10, 0xf6, 0xf3, 0x52, 0x25, 0xd9, 0xdc, 0x4c, 0xdd,

  183.     0x0f, 0xd6, 0x4a, 0xcf, 0x60, 0x96, 0x7e, 0xcc, 0x42, 0x0f, 0x64, 0x9d,

  184.     0x72, 0x46, 0x04, 0x07, 0xf2, 0x5b, 0xf4, 0x07, 0xd1, 0xf4, 0x59, 0x71,

  185. };

  186. 

  187. static const uint8_t kSpakeMSmallPrecomp[15 * 2 * 32] = {

  188.     0xc8, 0xa6, 0x63, 0xc5, 0x97, 0xf1, 0xee, 0x40, 0xab, 0x62, 0x42, 0xee,

  189.     0x25, 0x6f, 0x32, 0x6c, 0x75, 0x2c, 0xa7, 0xd3, 0xbd, 0x32, 0x3b, 0x1e,

  190.     0x11, 0x9c, 0xbd, 0x04, 0xa9, 0x78, 0x6f, 0x45, 0x5a, 0xda, 0x7e, 0x4b,

  191.     0xf6, 0xdd, 0xd9, 0xad, 0xb6, 0x62, 0x6d, 0x32, 0x13, 0x1c, 0x6b, 0x5c,

  192.     0x51, 0xa1, 0xe3, 0x47, 0xa3, 0x47, 0x8f, 0x53, 0xcf, 0xcf, 0x44, 0x1b,

  193.     0x88, 0xee, 0xd1, 0x2e, 0x03, 0x89, 0xaf, 0xc0, 0x61, 0x2d, 0x9e, 0x35,

  194.     0xeb, 0x0e, 0x03, 0xe0, 0xb7, 0xfb, 0xa5, 0xbc, 0x44, 0xbe, 0x0c, 0x89,

  195.     0x0a, 0x0f, 0xd6, 0x59, 0x47, 0x9e, 0xe6, 0x3d, 0x36, 0x9d, 0xff, 0x44,

  196.     0x5e, 0xac, 0xab, 0xe5, 0x3a, 0xd5, 0xb0, 0x35, 0x9f, 0x6d, 0x7f, 0xba,

  197.     0xc0, 0x85, 0x0e, 0xf4, 0x70, 0x3f, 0x13, 0x90, 0x4c, 0x50, 0x1a, 0xee,

  198.     0xc5, 0xeb, 0x69, 0xfe, 0x98, 0x42, 0x87, 0x1d, 0xce, 0x6c, 0x29, 0xaa,

  199.     0x2b, 0x31, 0xc2, 0x38, 0x7b, 0x6b, 0xee, 0x88, 0x0b, 0xba, 0xce, 0xa8,

  200.     0xca, 0x19, 0x60, 0x1b, 0x16, 0xf1, 0x25, 0x1e, 0xcf, 0x63, 0x66, 0x1e,

  201.     0xbb, 0x63, 0xeb, 0x7d, 0xca, 0xd2, 0xb4, 0x23, 0x5a, 0x01, 0x6f, 0x05,

  202.     0xd1, 0xdc, 0x41, 0x73, 0x75, 0xc0, 0xfd, 0x30, 0x91, 0x52, 0x68, 0x96,

  203.     0x45, 0xb3, 0x66, 0x01, 0x3b, 0x53, 0x89, 0x3c, 0x69, 0xbc, 0x6c, 0x69,

  204.     0xe3, 0x51, 0x8f, 0xe3, 0xd2, 0x84, 0xd5, 0x28, 0x66, 0xb5, 0xe6, 0x06,

  205.     0x09, 0xfe, 0x6d, 0xb0, 0x72, 0x16, 0xe0, 0x8a, 0xce, 0x61, 0x65, 0xa9,

  206.     0x21, 0x32, 0x48, 0xdc, 0x7a, 0x1d, 0xe1, 0x38, 0x7f, 0x8c, 0x75, 0x88,

  207.     0x3d, 0x08, 0xa9, 0x4a, 0x6f, 0x3d, 0x9f, 0x7f, 0x3f, 0xbd, 0x57, 0x6b,

  208.     0x19, 0xce, 0x3f, 0x4a, 0xc9, 0xd3, 0xf9, 0x6e, 0x72, 0x7b, 0x5b, 0x74,

  209.     0xea, 0xbe, 0x9c, 0x7a, 0x6d, 0x9c, 0x40, 0x49, 0xe6, 0xfb, 0x2a, 0x1a,

  210.     0x75, 0x70, 0xe5, 0x4e, 0xed, 0x74, 0xe0, 0x75, 0xac, 0xc0, 0xb1, 0x11,

  211.     0x3e, 0xf2, 0xaf, 0x88, 0x4d, 0x66, 0xb6, 0xf6, 0x15, 0x4f, 0x3c, 0x6c,

  212.     0x77, 0xae, 0x47, 0x51, 0x63, 0x9a, 0xfe, 0xe1, 0xb4, 0x1a, 0x12, 0xdf,

  213.     0xe9, 0x54, 0x8d, 0x3b, 0x30, 0x2a, 0x75, 0xe3, 0xe5, 0x29, 0xb1, 0x4c,

  214.     0xb0, 0x7c, 0x6d, 0xb5, 0xae, 0x85, 0xdb, 0x1e, 0x38, 0x55, 0x96, 0xa5,

  215.     0x5b, 0x9f, 0x15, 0x23, 0x28, 0x36, 0xb8, 0xa2, 0x41, 0xb4, 0xd7, 0x19,

  216.     0x91, 0x8d, 0x26, 0x3e, 0xca, 0x9c, 0x05, 0x7a, 0x2b, 0x60, 0x45, 0x86,

  217.     0x8b, 0xee, 0x64, 0x6f, 0x5c, 0x09, 0x4d, 0x4b, 0x5a, 0x7f, 0xb0, 0xc3,

  218.     0x26, 0x9d, 0x8b, 0xb8, 0x83, 0x69, 0xcf, 0x16, 0x72, 0x62, 0x3e, 0x5e,

  219.     0x53, 0x4f, 0x9c, 0x73, 0x76, 0xfc, 0x19, 0xef, 0xa0, 0x74, 0x3a, 0x11,

  220.     0x1e, 0xd0, 0x4d, 0xb7, 0x87, 0xa1, 0xd6, 0x87, 0x6c, 0x0e, 0x6c, 0x8c,

  221.     0xe9, 0xa0, 0x44, 0xc4, 0x72, 0x3e, 0x73, 0x17, 0x13, 0xd1, 0x4e, 0x3d,

  222.     0x8e, 0x1d, 0x5a, 0x8b, 0x75, 0xcb, 0x59, 0x2c, 0x47, 0x87, 0x15, 0x41,

  223.     0xfe, 0x08, 0xe9, 0xa6, 0x97, 0x17, 0x08, 0x26, 0x6a, 0xb5, 0xbb, 0x73,

  224.     0xaa, 0xb8, 0x5b, 0x65, 0x65, 0x5b, 0x30, 0x9e, 0x62, 0x59, 0x02, 0xf8,

  225.     0xb8, 0x0f, 0x32, 0x10, 0xc1, 0x36, 0x08, 0x52, 0x98, 0x4a, 0x1e, 0xf0,

  226.     0xab, 0x21, 0x5e, 0xde, 0x16, 0x0c, 0xda, 0x09, 0x99, 0x6b, 0x9e, 0xc0,

  227.     0x90, 0xa5, 0x5a, 0xcc, 0xb0, 0xb7, 0xbb, 0xd2, 0x8b, 0x5f, 0xd3, 0x3b,

  228.     0x3e, 0x8c, 0xa5, 0x71, 0x66, 0x06, 0xe3, 0x28, 0xd4, 0xf8, 0x3f, 0xe5,

  229.     0x27, 0xdf, 0xfe, 0x0f, 0x09, 0xb2, 0x8a, 0x09, 0x5a, 0x23, 0x61, 0x0d,

  230.     0x2d, 0xf5, 0x44, 0xf1, 0x5c, 0xf8, 0x82, 0x4e, 0xdc, 0x78, 0x7a, 0xab,

  231.     0xc3, 0x57, 0x91, 0xaf, 0x65, 0x6e, 0x71, 0xf1, 0x44, 0xbf, 0xed, 0x43,

  232.     0x50, 0xb4, 0x67, 0x48, 0xef, 0x5a, 0x10, 0x46, 0x81, 0xb4, 0x0c, 0xc8,

  233.     0x48, 0xed, 0x99, 0x7a, 0x45, 0xa5, 0x92, 0xc3, 0x69, 0xd6, 0xd7, 0x8a,

  234.     0x20, 0x1b, 0xeb, 0x8f, 0xb2, 0xff, 0xec, 0x6d, 0x76, 0x04, 0xf8, 0xc2,

  235.     0x58, 0x9b, 0xf2, 0x20, 0x53, 0xc4, 0x74, 0x91, 0x19, 0xdd, 0x2d, 0x12,

  236.     0x53, 0xc7, 0x6e, 0xd0, 0x02, 0x51, 0x3c, 0xa6, 0x7d, 0x80, 0x75, 0x6b,

  237.     0x1d, 0xdf, 0xf8, 0x6a, 0x52, 0xbb, 0x81, 0xf8, 0x30, 0x45, 0xef, 0x51,

  238.     0x85, 0x36, 0xbe, 0x8e, 0xcf, 0x0b, 0x9a, 0x46, 0xe8, 0x3f, 0x99, 0xfd,

  239.     0xf7, 0xd9, 0x3e, 0x84, 0xe5, 0xe3, 0x37, 0xcf, 0x98, 0x7f, 0xeb, 0x5e,

  240.     0x5a, 0x53, 0x77, 0x1c, 0x20, 0xdc, 0xf1, 0x20, 0x99, 0xec, 0x60, 0x40,

  241.     0x93, 0xef, 0x5c, 0x1c, 0x81, 0xe2, 0xa5, 0xad, 0x2a, 0xc2, 0xdb, 0x6b,

  242.     0xc1, 0x7e, 0x8f, 0xa9, 0x23, 0x5b, 0xd9, 0x0d, 0xfe, 0xa0, 0xac, 0x11,

  243.     0x28, 0xba, 0x8e, 0x92, 0x07, 0x2d, 0x07, 0x40, 0x83, 0x14, 0x4c, 0x35,

  244.     0x8d, 0xd0, 0x11, 0xff, 0x98, 0xdb, 0x00, 0x30, 0x6f, 0x65, 0xb6, 0xa0,

  245.     0x7f, 0x9c, 0x08, 0xb8, 0xce, 0xb3, 0xa8, 0x42, 0xd3, 0x84, 0x45, 0xe1,

  246.     0xe3, 0x8f, 0xa6, 0x89, 0x21, 0xd7, 0x74, 0x02, 0x4d, 0x64, 0xdf, 0x54,

  247.     0x15, 0x9e, 0xba, 0x12, 0x49, 0x09, 0x41, 0xf6, 0x10, 0x24, 0xa1, 0x84,

  248.     0x15, 0xfd, 0x68, 0x6a, 0x57, 0x66, 0xb3, 0x6d, 0x4c, 0xea, 0xbf, 0xbc,

  249.     0x60, 0x3f, 0x52, 0x1c, 0x44, 0x1b, 0xc0, 0x4a, 0x25, 0xe3, 0xd9, 0x4c,

  250.     0x9a, 0x74, 0xad, 0xfc, 0x9e, 0x8d, 0x0b, 0x18, 0x66, 0x24, 0xd1, 0x06,

  251.     0xac, 0x68, 0xc1, 0xae, 0x14, 0xce, 0xb1, 0xf3, 0x86, 0x9f, 0x87, 0x11,

  252.     0xd7, 0x9f, 0x30, 0x92, 0xdb, 0xec, 0x0b, 0x4a, 0xe8, 0xf6, 0x53, 0x36,

  253.     0x68, 0x12, 0x11, 0x5e, 0xe0, 0x34, 0xa4, 0xff, 0x00, 0x0a, 0x26, 0xb8,

  254.     0x62, 0x79, 0x9c, 0x0c, 0xd5, 0xe5, 0xf5, 0x1c, 0x1a, 0x16, 0x84, 0x4d,

  255.     0x8e, 0x5d, 0x31, 0x7e, 0xf7, 0xe2, 0xd3, 0xa1, 0x41, 0x90, 0x61, 0x5d,

  256.     0x04, 0xb2, 0x9a, 0x18, 0x9e, 0x54, 0xfb, 0xd1, 0x61, 0x95, 0x1b, 0x08,

  257.     0xca, 0x7c, 0x49, 0x44, 0x74, 0x1d, 0x2f, 0xca, 0xc4, 0x7a, 0xe1, 0x8b,

  258.     0x2f, 0xbb, 0x96, 0xee, 0x19, 0x8a, 0x5d, 0xfb, 0x3e, 0x82, 0xe7, 0x15,

  259.     0xdb, 0x29, 0x14, 0xee, 0xc9, 0x4d, 0x9a, 0xfb, 0x9f, 0x8a, 0xbb, 0x17,

  260.     0x37, 0x1b, 0x6e, 0x28, 0x6c, 0xf9, 0xff, 0xb5, 0xb5, 0x8b, 0x9d, 0x88,

  261.     0x20, 0x08, 0x10, 0xd7, 0xca, 0x58, 0xf6, 0xe1, 0x32, 0x91, 0x6f, 0x36,

  262.     0xc0, 0xad, 0xc1, 0x57, 0x5d, 0x76, 0x31, 0x43, 0xf3, 0xdd, 0xec, 0xf1,

  263.     0xa9, 0x79, 0xe9, 0xe9, 0x85, 0xd7, 0x91, 0xc7, 0x31, 0x62, 0x3c, 0xd2,

  264.     0x90, 0x2c, 0x9c, 0xa4, 0x56, 0x37, 0x7b, 0xbe, 0x40, 0x58, 0xc0, 0x81,

  265.     0x83, 0x22, 0xe8, 0x13, 0x79, 0x18, 0xdb, 0x3a, 0x1b, 0x31, 0x0d, 0x00,

  266.     0x6c, 0x22, 0x62, 0x75, 0x70, 0xd8, 0x96, 0x59, 0x99, 0x44, 0x79, 0x71,

  267.     0xa6, 0x76, 0x81, 0x28, 0xb2, 0x65, 0xe8, 0x47, 0x14, 0xc6, 0x39, 0x06,

  268. };

  269. 

  270. enum spake2_state_t {

  271.   spake2_state_init = 0,

  272.   spake2_state_msg_generated,

  273.   spake2_state_key_generated,

  274. };

  275. 

  276. struct spake2_ctx_st {

  277.   uint8_t private_key[32];

  278.   uint8_t my_msg[32];

  279.   uint8_t password_scalar[32];

  280.   uint8_t password_hash[SHA512_DIGEST_LENGTH];

  281.   uint8_t *my_name;

  282.   size_t my_name_len;

  283.   uint8_t *their_name;

  284.   size_t their_name_len;

  285.   enum spake2_role_t my_role;

  286.   enum spake2_state_t state;

  287. };

  288. 

  289. SPAKE2_CTX *SPAKE2_CTX_new(enum spake2_role_t my_role,

  290.                            const uint8_t *my_name, size_t my_name_len,

  291.                            const uint8_t *their_name, size_t their_name_len) {

  292.   SPAKE2_CTX *ctx = OPENSSL_malloc(sizeof(SPAKE2_CTX));

  293.   if (ctx == NULL) {

  294.     return NULL;

  295.   }

  296. 

  297.   OPENSSL_memset(ctx, 0, sizeof(SPAKE2_CTX));

  298.   ctx->my_role = my_role;

  299. 

  300.   CBS my_name_cbs, their_name_cbs;

  301.   CBS_init(&my_name_cbs, my_name, my_name_len);

  302.   CBS_init(&their_name_cbs, their_name, their_name_len);

  303.   if (!CBS_stow(&my_name_cbs, &ctx->my_name, &ctx->my_name_len) ||

  304.       !CBS_stow(&their_name_cbs, &ctx->their_name, &ctx->their_name_len)) {

  305.     SPAKE2_CTX_free(ctx);

  306.     return NULL;

  307.   }

  308. 

  309.   return ctx;

  310. }

  311. 

  312. void SPAKE2_CTX_free(SPAKE2_CTX *ctx) {

  313.   if (ctx == NULL) {

  314.     return;

  315.   }

  316. 

  317.   OPENSSL_free(ctx->my_name);

  318.   OPENSSL_free(ctx->their_name);

  319.   OPENSSL_free(ctx);

  320. }

  321. 

  322. // left_shift_3 sets |n| to |n|*8, where |n| is represented in little-endian

  323. // order.

  324. static void left_shift_3(uint8_t n[32]) {

  325.   uint8_t carry = 0;

  326.   unsigned i;

  327. 

  328.   for (i = 0; i < 32; i++) {

  329.     const uint8_t next_carry = n[i] >> 5;

  330.     n[i] = (n[i] << 3) | carry;

  331.     carry = next_carry;

  332.   }

  333. }

  334. 

  335. int SPAKE2_generate_msg(SPAKE2_CTX *ctx, uint8_t *out, size_t *out_len,

  336.                          size_t max_out_len, const uint8_t *password,

  337.                          size_t password_len) {

  338.   if (ctx->state != spake2_state_init) {

  339.     return 0;

  340.   }

  341. 

  342.   if (max_out_len < sizeof(ctx->my_msg)) {

  343.     return 0;

  344.   }

  345. 

  346.   uint8_t private_tmp[64];

  347.   RAND_bytes(private_tmp, sizeof(private_tmp));

  348.   x25519_sc_reduce(private_tmp);

  349.   // Multiply by the cofactor (eight) so that we'll clear it when operating on

  350.   // the peer's point later in the protocol.

  351.   left_shift_3(private_tmp);

  352.   OPENSSL_memcpy(ctx->private_key, private_tmp, sizeof(ctx->private_key));

  353. 

  354.   ge_p3 P;

  355.   x25519_ge_scalarmult_base(&P, ctx->private_key);

  356. 

  357.   // mask = h(password) * <N or M>.

  358.   uint8_t password_tmp[SHA512_DIGEST_LENGTH];

  359.   SHA512(password, password_len, password_tmp);

  360.   OPENSSL_memcpy(ctx->password_hash, password_tmp, sizeof(ctx->password_hash));

  361.   x25519_sc_reduce(password_tmp);

  362.   OPENSSL_memcpy(ctx->password_scalar, password_tmp, sizeof(ctx->password_scalar));

  363. 

  364.   ge_p3 mask;

  365.   x25519_ge_scalarmult_small_precomp(&mask, ctx->password_scalar,

  366.                               ctx->my_role == spake2_role_alice

  367.                                   ? kSpakeMSmallPrecomp

  368.                                   : kSpakeNSmallPrecomp);

  369. 

  370.   // P* = P + mask.

  371.   ge_cached mask_cached;

  372.   x25519_ge_p3_to_cached(&mask_cached, &mask);

  373.   ge_p1p1 Pstar;

  374.   x25519_ge_add(&Pstar, &P, &mask_cached);

  375. 

  376.   // Encode P*

  377.   ge_p2 Pstar_proj;

  378.   x25519_ge_p1p1_to_p2(&Pstar_proj, &Pstar);

  379.   x25519_ge_tobytes(ctx->my_msg, &Pstar_proj);

  380. 

  381.   OPENSSL_memcpy(out, ctx->my_msg, sizeof(ctx->my_msg));

  382.   *out_len = sizeof(ctx->my_msg);

  383.   ctx->state = spake2_state_msg_generated;

  384. 

  385.   return 1;

  386. }

  387. 

  388. static void update_with_length_prefix(SHA512_CTX *sha, const uint8_t *data,

  389.                                       const size_t len) {

  390.   uint8_t len_le[8];

  391.   size_t l = len;

  392.   unsigned i;

  393. 

  394.   for (i = 0; i < 8; i++) {

  395.     len_le[i] = l & 0xff;

  396.     l >>= 8;

  397.   }

  398. 

  399.   SHA512_Update(sha, len_le, sizeof(len_le));

  400.   SHA512_Update(sha, data, len);

  401. }

  402. 

  403. int SPAKE2_process_msg(SPAKE2_CTX *ctx, uint8_t *out_key, size_t *out_key_len,

  404.                        size_t max_out_key_len, const uint8_t *their_msg,

  405.                        size_t their_msg_len) {

  406.   if (ctx->state != spake2_state_msg_generated ||

  407.       their_msg_len != 32) {

  408.     return 0;

  409.   }

  410. 

  411.   ge_p3 Qstar;

  412.   if (0 != x25519_ge_frombytes_vartime(&Qstar, their_msg)) {

  413.     // Point received from peer was not on the curve.

  414.     return 0;

  415.   }

  416. 

  417.   // Unmask peer's value.

  418.   ge_p3 peers_mask;

  419.   x25519_ge_scalarmult_small_precomp(&peers_mask, ctx->password_scalar,

  420.                                     ctx->my_role == spake2_role_alice

  421.                                         ? kSpakeNSmallPrecomp

  422.                                         : kSpakeMSmallPrecomp);

  423. 

  424.   ge_cached peers_mask_cached;

  425.   x25519_ge_p3_to_cached(&peers_mask_cached, &peers_mask);

  426. 

  427.   ge_p1p1 Q_compl;

  428.   ge_p3 Q_ext;

  429.   x25519_ge_sub(&Q_compl, &Qstar, &peers_mask_cached);

  430.   x25519_ge_p1p1_to_p3(&Q_ext, &Q_compl);

  431. 

  432.   ge_p2 dh_shared;

  433.   x25519_ge_scalarmult(&dh_shared, ctx->private_key, &Q_ext);

  434. 

  435.   uint8_t dh_shared_encoded[32];

  436.   x25519_ge_tobytes(dh_shared_encoded, &dh_shared);

  437. 

  438.   SHA512_CTX sha;

  439.   SHA512_Init(&sha);

  440.   if (ctx->my_role == spake2_role_alice) {

  441.     update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len);

  442.     update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len);

  443.     update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg));

  444.     update_with_length_prefix(&sha, their_msg, 32);

  445.   } else {

  446.     update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len);

  447.     update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len);

  448.     update_with_length_prefix(&sha, their_msg, 32);

  449.     update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg));

  450.   }

  451.   update_with_length_prefix(&sha, dh_shared_encoded, sizeof(dh_shared_encoded));

  452.   update_with_length_prefix(&sha, ctx->password_hash,

  453.                             sizeof(ctx->password_hash));

  454. 

  455.   uint8_t key[SHA512_DIGEST_LENGTH];

  456.   SHA512_Final(key, &sha);

  457. 

  458.   size_t to_copy = max_out_key_len;

  459.   if (to_copy > sizeof(key)) {

  460.     to_copy = sizeof(key);

  461.   }

  462.   OPENSSL_memcpy(out_key, key, to_copy);

  463.   *out_key_len = to_copy;

  464.   ctx->state = spake2_state_key_generated;

  465. 

  466.   return 1;

  467. }