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sike_ifma/sidh_ref/P751.c

122 строки
11 KiB
Исходник Постоянная ссылка Вина История 

  1. /********************************************************************************************

  2. * Supersingular Isogeny Key Encapsulation Library

  3. *

  4. * Abstract: supersingular isogeny parameters and generation of functions for P751

  5. *********************************************************************************************/  

  6. 

  7. #include "P751_internal.h"

  8. 

  9. 

  10. // Encoding of field elements, elements over Z_order, elements over GF(p^2) and elliptic curve points:

  11. // --------------------------------------------------------------------------------------------------

  12. // 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). 

  13. // 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.

  14. // Elliptic curve points P = (x,y) are encoded as {x, y}, with x in the least significant position. 

  15. // 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.

  16. // For example, a 751-bit field element is represented with Ceil(751 / 64) = 12 64-bit digits or Ceil(751 / 32) = 24 32-bit digits.

  17. 

  18. //

  19. // Curve isogeny system "SIDHp751". Base curve: Montgomery curve By^2 = Cx^3 + Ax^2 + Cx defined over GF(p751^2), where A=0, B=1, C=1 and p751 = 2^372*3^239-1

  20. //

  21.          

  22. const uint64_t p751[NWORDS64_FIELD]              = { 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xEEAFFFFFFFFFFFFF,

  23.                                                      0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C };

  24. const uint64_t p751p1[NWORDS64_FIELD]            = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xEEB0000000000000,

  25.                                                      0xE3EC968549F878A8, 0xDA959B1A13F7CC76, 0x084E9867D6EBE876, 0x8562B5045CB25748, 0x0E12909F97BADC66, 0x00006FE5D541F71C };

  26. const uint64_t p751x2[NWORDS64_FIELD]            = { 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF, 

  27.                                                      0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED, 0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38 }; 

  28. // Order of Alice's subgroup

  29. const uint64_t Alice_order[NWORDS64_ORDER]       = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0010000000000000 }; 

  30. // Order of Bob's subgroup

  31. const uint64_t Bob_order[NWORDS64_ORDER]         = { 0xC968549F878A8EEB, 0x59B1A13F7CC76E3E, 0xE9867D6EBE876DA9, 0x2B5045CB25748084, 0x2909F97BADC66856, 0x06FE5D541F71C0E1 };

  32. // Alice's generator values {XPA0 + XPA1*i, XQA0, XRA0 + XRA1*i} in GF(p751^2), expressed in Montgomery representation

  33. const uint64_t A_gen[5 * NWORDS64_FIELD]         = { 0xC2FC08CEAB50AD8B, 0x1D7D710F55E457B1, 0xE8738D92953DCD6E, 0xBAA7EBEE8A3418AA, 0xC9A288345F03F46F, 0xC8D18D167CFE2616, 

  34.                                                      0x02043761F6B1C045, 0xAA1975E13180E7E9, 0x9E13D3FDC6690DE6, 0x3A024640A3A3BB4F, 0x4E5AD44E6ACBBDAE, 0x0000544BEB561DAD,   // XPA0

  35.                                                      0xE6CC41D21582E411, 0x07C2ECB7C5DF400A, 0xE8E34B521432AEC4, 0x50761E2AB085167D, 0x032CFBCAA6094B3C, 0x6C522F5FDF9DDD71, 

  36.                                                      0x1319217DC3A1887D, 0xDC4FB25803353A86, 0x362C8D7B63A6AB09, 0x39DCDFBCE47EA488, 0x4C27C99A2C28D409, 0x00003CB0075527C4,   // XPA1

  37.                                                      0xD56FE52627914862, 0x1FAD60DC96B5BAEA, 0x01E137D0BF07AB91, 0x404D3E9252161964, 0x3C5385E4CD09A337, 0x4476426769E4AF73, 

  38.                                                      0x9790C6DB989DFE33, 0xE06E1C04D2AA8B5E, 0x38C08185EDEA73B9, 0xAA41F678A4396CA6, 0x92B9259B2229E9A0, 0x00002F9326818BE0,   // XQA0

  39.                                                      0x0BB84441DFFD19B3, 0x84B4DEA99B48C18E, 0x692DE648AD313805, 0xE6D72761B6DFAEE0, 0x223975C672C3058D, 0xA0FDE0C3CBA26FDC, 

  40.                                                      0xA5326132A922A3CA, 0xCA5E7F5D5EA96FA4, 0x127C7EFE33FFA8C6, 0x4749B1567E2A23C4, 0x2B7DF5B4AF413BFA, 0x0000656595B9623C,   // XRA0

  41.                                                      0xED78C17F1EC71BE8, 0xF824D6DF753859B1, 0x33A10839B2A8529F, 0xFC03E9E25FDEA796, 0xC4708A8054DF1762, 0x4034F2EC034C6467, 

  42.                                                      0xABFB70FBF06ECC79, 0xDABE96636EC108B7, 0x49CBCFB090605FD3, 0x20B89711819A45A7, 0xFB8E1590B2B0F63E, 0x0000556A5F964AB2 }; // XRA1

  43. // Bob's generator values {XPB0 + XPB1*i, XQB0, XRB0 + XRB1*i} in GF(p751^2), expressed in Montgomery representation

  44. const uint64_t B_gen[5 * NWORDS64_FIELD]         = { 0xCFB6D71EF867AB0B, 0x4A5FDD76E9A45C76, 0x38B1EE69194B1F03, 0xF6E7B18A7761F3F0, 0xFCF01A486A52C84C, 0xCBE2F63F5AA75466,

  45.                                                      0x6487BCE837B5E4D6, 0x7747F5A8C622E9B8, 0x4CBFE1E4EE6AEBBA, 0x8A8616A13FA91512, 0x53DB980E1579E0A5, 0x000058FEBFF3BE69,   // XPB0

  46.                                                      0xA492034E7C075CC3, 0x677BAF00B04AA430, 0x3AAE0C9A755C94C8, 0x1DC4B064E9EBB08B, 0x3684EDD04E826C66, 0x9BAA6CB661F01B22,

  47.                                                      0x20285A00AD2EFE35, 0xDCE95ABD0497065F, 0x16C7FBB3778E3794, 0x26B3AC29CEF25AAF, 0xFB3C28A31A30AC1D, 0x000046ED190624EE,   // XPB1

  48.                                                      0xF1A8C9ED7B96C4AB, 0x299429DA5178486E, 0xEF4926F20CD5C2F4, 0x683B2E2858B4716A, 0xDDA2FBCC3CAC3EEB, 0xEC055F9F3A600460,

  49.                                                      0xD5A5A17A58C3848B, 0x4652D836F42EAED5, 0x2F2E71ED78B3A3B3, 0xA771C057180ADD1D, 0xC780A5D2D835F512, 0x0000114EA3B55AC1,   // XQB0

  50.                                                      0x1C0D6733769D0F31, 0xF084C3086E2659D1, 0xE23D5DA27BCBD133, 0xF38EC9A8D5864025, 0x6426DC781B3B645B, 0x4B24E8E3C9FB03EE,

  51.                                                      0x6432792F9D2CEA30, 0x7CC8E8B1AE76E857, 0x7F32BFB626BB8963, 0xB9F05995B48D7B74, 0x4D71200A7D67E042, 0x0000228457AF0637,   // XRB0

  52.                                                      0x4AE37E7D8F72BD95, 0xDD2D504B3E993488, 0x5D14E7FA1ECB3C3E, 0x127610CEB75D6350, 0x255B4B4CAC446B11, 0x9EA12336C1F70CAF,

  53.                                                      0x79FA68A2147BC2F8, 0x11E895CFDADBBC49, 0xE4B9D3C4D6356C18, 0x44B25856A67F951C, 0x5851541F61308D0B, 0x00002FFD994F7E4C }; // XRB1

  54. // Montgomery constant Montgomery_R2 = (2^768)^2 mod p751

  55. const uint64_t Montgomery_R2[NWORDS64_FIELD]     = { 0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E, 0xF40BFE2082A2E706, 0x4932CCA8904F8751 ,0x1F735F1F1EE7FC81, 

  56.                                                      0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90, 0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35 };                                                    

  57. // Value one in Montgomery representation 

  58. const uint64_t Montgomery_one[NWORDS64_FIELD]    = { 0x00000000000249ad, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8310000000000000,

  59.                                                      0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2 };     

  60. // Value (2^384)^2 mod 3^239                                                   

  61. const uint64_t Montgomery_Rprime[NWORDS64_ORDER] = { 0x1A55482318541298, 0x070A6370DFA12A03, 0xCB1658E0E3823A40, 0xB3B7384EB5DEF3F9, 0xCBCA952F7006EA33, 0x00569EF8EC94864C };

  62. // Value -(3^239)^-1 mod 2^384 

  63. const uint64_t Montgomery_rprime[NWORDS64_ORDER] = { 0x48062A91D3AB563D, 0x6CE572751303C2F5, 0x5D1319F3F160EC9D, 0xE35554E8C2D5623A, 0xCA29300232BC79A5, 0x8AAD843D646D78C5 };                                           

  64. // Value order_Bob/3 mod p751

  65. const uint64_t Border_div3[NWORDS_ORDER]         = { 0xEDCD718A828384F9, 0x733B35BFD4427A14, 0xF88229CF94D7CF38, 0x63C56C990C7C2AD6, 0xB858A87E8F4222C7, 0x0254C9C6B525EAF5 };

  66. 

  67. 

  68. // Fixed parameters for isogeny tree computation

  69. const unsigned int strat_Alice[MAX_Alice-1] = { 

  70. 80, 48, 27, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 

  71. 1, 3, 2, 1, 1, 1, 1, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 

  72. 1, 1, 2, 1, 1, 1, 21, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 

  73. 1, 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, 

  74. 33, 20, 12, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 2, 1, 

  75. 1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 

  76. 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 };

  77. 

  78. const unsigned int strat_Bob[MAX_Bob-1] = { 

  79. 112, 63, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 

  80. 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, 

  81. 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 31, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 

  82. 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 

  83. 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 49, 31, 16, 8, 4, 2, 

  84. 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, 

  85. 15, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 7, 4, 2, 1, 1, 2, 1, 1, 3, 2, 1, 

  86. 1, 1, 1, 21, 12, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 5, 3, 2, 1, 1, 1, 1, 

  87. 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 1, 2, 1, 1 };

  88. 

  89. // Setting up macro defines and including GF(p), GF(p^2), curve, isogeny and kex functions

  90. 

  91. #define fpcopy                  fpcopy751

  92. #define fpzero                  fpzero751

  93. #define fpadd                   fpadd751

  94. #define fpsub                   fpsub751

  95. #define fpneg                   fpneg751

  96. #define fpdiv2                  fpdiv2_751

  97. #define fpcorrection            fpcorrection751

  98. #define fpmul_mont              fpmul751_mont

  99. #define fpsqr_mont              fpsqr751_mont

  100. #define fpinv_mont              fpinv751_mont

  101. #define fpinv_chain_mont        fpinv751_chain_mont

  102. #define fpinv_mont_bingcd       fpinv751_mont_bingcd

  103. #define fp2copy                 fp2copy751

  104. #define fp2zero                 fp2zero751

  105. #define fp2add                  fp2add751

  106. #define fp2sub                  fp2sub751

  107. #define fp2neg                  fp2neg751

  108. #define fp2div2                 fp2div2_751

  109. #define fp2correction           fp2correction751

  110. #define fp2mul_mont             fp2mul751_mont

  111. #define fp2sqr_mont             fp2sqr751_mont

  112. #define fp2inv_mont             fp2inv751_mont

  113. #define fp2inv_mont_bingcd      fp2inv751_mont_bingcd

  114. #define fpequal_non_constant_time  fpequal751_non_constant_time

  115. #define mp_add_asm              mp_add751_asm

  116. #define mp_addx2_asm            mp_add751x2_asm

  117. #define mp_subx2_asm            mp_sub751x2_asm

  118. 

  119. #include "fpx.c"

  120. #include "ec_isogeny.c"

  121. #include "sidh.c"

  122. #include "sike.c"