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SIDH_p751
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SIDH_p751/p751/consts.go

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  1. package p751

  2. 

  3. import . "github.com/cloudflare/sidh/internal/isogeny"

  4. 

  5. const (

  6. 	// SIDH public key byte size

  7. 	P751_PublicKeySize = 564

  8. 	// SIDH shared secret byte size.

  9. 	P751_SharedSecretSize = 188

  10. 	// Max size of secret key for 2-torsion group, corresponds to 2^e2

  11. 	P751_SecretBitLenA = 372

  12. 	// Size of secret key for 3-torsion group, corresponds to floor(log_2(3^e3))

  13. 	P751_SecretBitLenB = 378

  14. 	// P751 bytelen ceil(751/8)

  15. 	P751_Bytelen = 94

  16. 	// Size of a compuatation strategy for 2-torsion group

  17. 	strategySizeA = 185

  18. 	// Size of a compuatation strategy for 3-torsion group

  19. 	strategySizeB = 238

  20. 	// Number of 64-bit limbs used to store Fp element

  21. 	NumWords = 12

  22. )

  23. 

  24. // The x-coordinate of PA

  25. var P751_affine_PA = Fp2Element{

  26. 	A: FpElement{

  27. 		0xC2FC08CEAB50AD8B, 0x1D7D710F55E457B1, 0xE8738D92953DCD6E,

  28. 		0xBAA7EBEE8A3418AA, 0xC9A288345F03F46F, 0xC8D18D167CFE2616,

  29. 		0x02043761F6B1C045, 0xAA1975E13180E7E9, 0x9E13D3FDC6690DE6,

  30. 		0x3A024640A3A3BB4F, 0x4E5AD44E6ACBBDAE, 0x0000544BEB561DAD,

  31. 	},

  32. 	B: FpElement{

  33. 		0xE6CC41D21582E411, 0x07C2ECB7C5DF400A, 0xE8E34B521432AEC4,

  34. 		0x50761E2AB085167D, 0x032CFBCAA6094B3C, 0x6C522F5FDF9DDD71,

  35. 		0x1319217DC3A1887D, 0xDC4FB25803353A86, 0x362C8D7B63A6AB09,

  36. 		0x39DCDFBCE47EA488, 0x4C27C99A2C28D409, 0x00003CB0075527C4,

  37. 	},

  38. }

  39. 

  40. // The x-coordinate of QA

  41. var P751_affine_QA = Fp2Element{

  42. 	A: FpElement{

  43. 		0xD56FE52627914862, 0x1FAD60DC96B5BAEA, 0x01E137D0BF07AB91,

  44. 		0x404D3E9252161964, 0x3C5385E4CD09A337, 0x4476426769E4AF73,

  45. 		0x9790C6DB989DFE33, 0xE06E1C04D2AA8B5E, 0x38C08185EDEA73B9,

  46. 		0xAA41F678A4396CA6, 0x92B9259B2229E9A0, 0x00002F9326818BE0,

  47. 	},

  48. 	B: FpElement{

  49. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  50. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  51. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  52. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  53. 	},

  54. }

  55. 

  56. // The x-coordinate of RA = PA-QA

  57. var P751_affine_RA = Fp2Element{

  58. 	A: FpElement{

  59. 		0x0BB84441DFFD19B3, 0x84B4DEA99B48C18E, 0x692DE648AD313805,

  60. 		0xE6D72761B6DFAEE0, 0x223975C672C3058D, 0xA0FDE0C3CBA26FDC,

  61. 		0xA5326132A922A3CA, 0xCA5E7F5D5EA96FA4, 0x127C7EFE33FFA8C6,

  62. 		0x4749B1567E2A23C4, 0x2B7DF5B4AF413BFA, 0x0000656595B9623C,

  63. 	},

  64. 	B: FpElement{

  65. 		0xED78C17F1EC71BE8, 0xF824D6DF753859B1, 0x33A10839B2A8529F,

  66. 		0xFC03E9E25FDEA796, 0xC4708A8054DF1762, 0x4034F2EC034C6467,

  67. 		0xABFB70FBF06ECC79, 0xDABE96636EC108B7, 0x49CBCFB090605FD3,

  68. 		0x20B89711819A45A7, 0xFB8E1590B2B0F63E, 0x0000556A5F964AB2,

  69. 	},

  70. }

  71. 

  72. // The x-coordinate of PB

  73. var P751_affine_PB = Fp2Element{

  74. 	A: FpElement{

  75. 		0xCFB6D71EF867AB0B, 0x4A5FDD76E9A45C76, 0x38B1EE69194B1F03,

  76. 		0xF6E7B18A7761F3F0, 0xFCF01A486A52C84C, 0xCBE2F63F5AA75466,

  77. 		0x6487BCE837B5E4D6, 0x7747F5A8C622E9B8, 0x4CBFE1E4EE6AEBBA,

  78. 		0x8A8616A13FA91512, 0x53DB980E1579E0A5, 0x000058FEBFF3BE69,

  79. 	},

  80. 	B: FpElement{

  81. 		0xA492034E7C075CC3, 0x677BAF00B04AA430, 0x3AAE0C9A755C94C8,

  82. 		0x1DC4B064E9EBB08B, 0x3684EDD04E826C66, 0x9BAA6CB661F01B22,

  83. 		0x20285A00AD2EFE35, 0xDCE95ABD0497065F, 0x16C7FBB3778E3794,

  84. 		0x26B3AC29CEF25AAF, 0xFB3C28A31A30AC1D, 0x000046ED190624EE,

  85. 	},

  86. }

  87. 

  88. // The x-coordinate of QB

  89. var P751_affine_QB = Fp2Element{

  90. 	A: FpElement{

  91. 		0xF1A8C9ED7B96C4AB, 0x299429DA5178486E, 0xEF4926F20CD5C2F4,

  92. 		0x683B2E2858B4716A, 0xDDA2FBCC3CAC3EEB, 0xEC055F9F3A600460,

  93. 		0xD5A5A17A58C3848B, 0x4652D836F42EAED5, 0x2F2E71ED78B3A3B3,

  94. 		0xA771C057180ADD1D, 0xC780A5D2D835F512, 0x0000114EA3B55AC1,

  95. 	},

  96. 	B: FpElement{

  97. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  98. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  99. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  100. 		0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  101. 	},

  102. }

  103. 

  104. // The x-coordinate of RB = PB - QB

  105. var P751_affine_RB = Fp2Element{

  106. 	A: FpElement{

  107. 		0x1C0D6733769D0F31, 0xF084C3086E2659D1, 0xE23D5DA27BCBD133,

  108. 		0xF38EC9A8D5864025, 0x6426DC781B3B645B, 0x4B24E8E3C9FB03EE,

  109. 		0x6432792F9D2CEA30, 0x7CC8E8B1AE76E857, 0x7F32BFB626BB8963,

  110. 		0xB9F05995B48D7B74, 0x4D71200A7D67E042, 0x0000228457AF0637,

  111. 	},

  112. 	B: FpElement{

  113. 		0x4AE37E7D8F72BD95, 0xDD2D504B3E993488, 0x5D14E7FA1ECB3C3E,

  114. 		0x127610CEB75D6350, 0x255B4B4CAC446B11, 0x9EA12336C1F70CAF,

  115. 		0x79FA68A2147BC2F8, 0x11E895CFDADBBC49, 0xE4B9D3C4D6356C18,

  116. 		0x44B25856A67F951C, 0x5851541F61308D0B, 0x00002FFD994F7E4C,

  117. 	},

  118. }

  119. 

  120. // 2-torsion group computation strategy

  121. var P751_AliceIsogenyStrategy = [strategySizeA]uint32{

  122. 	0x50, 0x30, 0x1B, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,

  123. 	0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07,

  124. 	0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,

  125. 	0x01, 0x01, 0x01, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02,

  126. 	0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03,

  127. 	0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15,

  128. 	0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03,

  129. 	0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01,

  130. 	0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02,

  131. 	0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02,

  132. 	0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x14, 0x0C, 0x07,

  133. 	0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,

  134. 	0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,

  135. 	0x02, 0x01, 0x01, 0x01, 0x08, 0x05, 0x03, 0x02, 0x01, 0x01,

  136. 	0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,

  137. 	0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01,

  138. 	0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,

  139. 	0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,

  140. 	0x01, 0x01, 0x02, 0x01, 0x01}

  141. 

  142. // 3-torsion group computation strategy

  143. var P751_BobIsogenyStrategy = [strategySizeB]uint32{

  144. 	0x70, 0x3F, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,

  145. 	0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08,

  146. 	0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,

  147. 	0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01,

  148. 	0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,

  149. 	0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,

  150. 	0x01, 0x01, 0x02, 0x01, 0x01, 0x1F, 0x10, 0x08, 0x04, 0x02,

  151. 	0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02,

  152. 	0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,

  153. 	0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04,

  154. 	0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,

  155. 	0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,

  156. 	0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x31, 0x1F, 0x10,

  157. 	0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,

  158. 	0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01,

  159. 	0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,

  160. 	0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,

  161. 	0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01,

  162. 	0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,

  163. 	0x15, 0x0C, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,

  164. 	0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x03, 0x02,

  165. 	0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05,

  166. 	0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,

  167. 	0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01}

  168. 

  169. // Used internally by this package. Not consts as Go doesn't allow arrays to be consts

  170. // -------------------------------

  171. 

  172. // p751

  173. var p751 = FpElement{

  174. 	0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff,

  175. 	0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff,

  176. 	0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,

  177. 	0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}

  178. 

  179. // 2*p751

  180. var p751x2 = FpElement{

  181. 	0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,

  182. 	0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,

  183. 	0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED,

  184. 	0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38}

  185. 

  186. // p751 + 1

  187. var p751p1 = FpElement{

  188. 	0x0000000000000000, 0x0000000000000000, 0x0000000000000000,

  189. 	0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000,

  190. 	0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,

  191. 	0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}

  192. 

  193. // R^2 = (2^768)^2 mod p

  194. var p751R2 = FpElement{

  195. 	2535603850726686808, 15780896088201250090, 6788776303855402382,

  196. 	17585428585582356230, 5274503137951975249, 2266259624764636289,

  197. 	11695651972693921304, 13072885652150159301, 4908312795585420432,

  198. 	6229583484603254826, 488927695601805643, 72213483953973}

  199. 

  200. // 1*R mod p

  201. var P751_OneFp2 = Fp2Element{

  202. 	A: FpElement{

  203. 		0x249ad, 0x0, 0x0, 0x0, 0x0, 0x8310000000000000, 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x2d5b24bce5e2},

  204. }

  205. 

  206. // 1/2 * R mod p

  207. var P751_HalfFp2 = Fp2Element{

  208. 	A: FpElement{

  209. 		0x00000000000124D6, 0x0000000000000000, 0x0000000000000000,

  210. 		0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000,

  211. 		0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52,

  212. 		0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F},

  213. }