2018-09-11 12:02:29 +01:00
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package p751
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import (
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. "github.com/henrydcase/nobs/dh/sidh/internal/isogeny"
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)
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2018-07-23 23:18:38 +01:00
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const (
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// The secret key size, in bytes. Secret key is actually different for
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// torsion group 2 and 3. For 2-torsion group, last byte of secret key
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// is always set to 0.
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P751_SecretKeySize = 48
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// SIDH public key byte size
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P751_PublicKeySize = 564
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// SIDH shared secret byte size.
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P751_SharedSecretSize = 188
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2018-09-11 12:02:29 +01:00
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// Max size of secret key for 2-torsion group, corresponds to e2
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2018-07-23 23:18:38 +01:00
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P751_SecretBitLenA = 372
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2018-09-11 12:02:29 +01:00
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// Size of secret key for 3-torsion group, corresponds to floor(log_2(3^e3))
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P751_SecretBitLenB = 378
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2018-07-23 23:18:38 +01:00
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// Sample rate to obtain a value in [0,3^238]
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P751_SampleRate = 102
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2018-09-11 12:02:29 +01:00
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// P751 bytelen ceil(751/8)
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P751_Bytelen = 94
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2018-07-23 23:18:38 +01:00
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// Size of a compuatation strategy for 2-torsion group
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strategySizeA = 185
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// Size of a compuatation strategy for 3-torsion group
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strategySizeB = 238
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2018-09-11 12:02:29 +01:00
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// Number of 64-bit limbs used to store Fp element
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NumWords = 12
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2018-07-23 23:18:38 +01:00
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)
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// The x-coordinate of PA
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2018-09-11 12:02:29 +01:00
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var P751_affine_PA = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0xC2FC08CEAB50AD8B, 0x1D7D710F55E457B1, 0xE8738D92953DCD6E,
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0xBAA7EBEE8A3418AA, 0xC9A288345F03F46F, 0xC8D18D167CFE2616,
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0x02043761F6B1C045, 0xAA1975E13180E7E9, 0x9E13D3FDC6690DE6,
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0x3A024640A3A3BB4F, 0x4E5AD44E6ACBBDAE, 0x0000544BEB561DAD,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0xE6CC41D21582E411, 0x07C2ECB7C5DF400A, 0xE8E34B521432AEC4,
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0x50761E2AB085167D, 0x032CFBCAA6094B3C, 0x6C522F5FDF9DDD71,
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0x1319217DC3A1887D, 0xDC4FB25803353A86, 0x362C8D7B63A6AB09,
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0x39DCDFBCE47EA488, 0x4C27C99A2C28D409, 0x00003CB0075527C4,
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},
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}
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// The x-coordinate of QA
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2018-09-11 12:02:29 +01:00
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var P751_affine_QA = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0xD56FE52627914862, 0x1FAD60DC96B5BAEA, 0x01E137D0BF07AB91,
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0x404D3E9252161964, 0x3C5385E4CD09A337, 0x4476426769E4AF73,
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0x9790C6DB989DFE33, 0xE06E1C04D2AA8B5E, 0x38C08185EDEA73B9,
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0xAA41F678A4396CA6, 0x92B9259B2229E9A0, 0x00002F9326818BE0,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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},
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}
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// The x-coordinate of RA = PA-QA
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2018-09-11 12:02:29 +01:00
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var P751_affine_RA = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0x0BB84441DFFD19B3, 0x84B4DEA99B48C18E, 0x692DE648AD313805,
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0xE6D72761B6DFAEE0, 0x223975C672C3058D, 0xA0FDE0C3CBA26FDC,
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0xA5326132A922A3CA, 0xCA5E7F5D5EA96FA4, 0x127C7EFE33FFA8C6,
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0x4749B1567E2A23C4, 0x2B7DF5B4AF413BFA, 0x0000656595B9623C,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0xED78C17F1EC71BE8, 0xF824D6DF753859B1, 0x33A10839B2A8529F,
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0xFC03E9E25FDEA796, 0xC4708A8054DF1762, 0x4034F2EC034C6467,
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0xABFB70FBF06ECC79, 0xDABE96636EC108B7, 0x49CBCFB090605FD3,
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0x20B89711819A45A7, 0xFB8E1590B2B0F63E, 0x0000556A5F964AB2,
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},
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}
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// The x-coordinate of PB
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2018-09-11 12:02:29 +01:00
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var P751_affine_PB = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0xCFB6D71EF867AB0B, 0x4A5FDD76E9A45C76, 0x38B1EE69194B1F03,
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0xF6E7B18A7761F3F0, 0xFCF01A486A52C84C, 0xCBE2F63F5AA75466,
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0x6487BCE837B5E4D6, 0x7747F5A8C622E9B8, 0x4CBFE1E4EE6AEBBA,
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0x8A8616A13FA91512, 0x53DB980E1579E0A5, 0x000058FEBFF3BE69,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0xA492034E7C075CC3, 0x677BAF00B04AA430, 0x3AAE0C9A755C94C8,
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0x1DC4B064E9EBB08B, 0x3684EDD04E826C66, 0x9BAA6CB661F01B22,
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0x20285A00AD2EFE35, 0xDCE95ABD0497065F, 0x16C7FBB3778E3794,
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0x26B3AC29CEF25AAF, 0xFB3C28A31A30AC1D, 0x000046ED190624EE,
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},
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}
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// The x-coordinate of QB
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2018-09-11 12:02:29 +01:00
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var P751_affine_QB = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0xF1A8C9ED7B96C4AB, 0x299429DA5178486E, 0xEF4926F20CD5C2F4,
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0x683B2E2858B4716A, 0xDDA2FBCC3CAC3EEB, 0xEC055F9F3A600460,
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0xD5A5A17A58C3848B, 0x4652D836F42EAED5, 0x2F2E71ED78B3A3B3,
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0xA771C057180ADD1D, 0xC780A5D2D835F512, 0x0000114EA3B55AC1,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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},
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}
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// The x-coordinate of RB = PB - QB
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2018-09-11 12:02:29 +01:00
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var P751_affine_RB = Fp2Element{
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A: FpElement{
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2018-07-23 23:18:38 +01:00
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0x1C0D6733769D0F31, 0xF084C3086E2659D1, 0xE23D5DA27BCBD133,
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0xF38EC9A8D5864025, 0x6426DC781B3B645B, 0x4B24E8E3C9FB03EE,
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0x6432792F9D2CEA30, 0x7CC8E8B1AE76E857, 0x7F32BFB626BB8963,
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0xB9F05995B48D7B74, 0x4D71200A7D67E042, 0x0000228457AF0637,
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},
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2018-09-11 12:02:29 +01:00
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B: FpElement{
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2018-07-23 23:18:38 +01:00
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0x4AE37E7D8F72BD95, 0xDD2D504B3E993488, 0x5D14E7FA1ECB3C3E,
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0x127610CEB75D6350, 0x255B4B4CAC446B11, 0x9EA12336C1F70CAF,
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0x79FA68A2147BC2F8, 0x11E895CFDADBBC49, 0xE4B9D3C4D6356C18,
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0x44B25856A67F951C, 0x5851541F61308D0B, 0x00002FFD994F7E4C,
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},
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}
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// 2-torsion group computation strategy
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var P751_AliceIsogenyStrategy = [strategySizeA]uint32{
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0x50, 0x30, 0x1B, 0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,
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0x01, 0x01, 0x01, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03,
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0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x15,
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0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03,
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0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02,
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0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x21, 0x14, 0x0C, 0x07,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01,
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0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x01, 0x08, 0x05, 0x03, 0x02, 0x01, 0x01,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01}
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// 3-torsion group computation strategy
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var P751_BobIsogenyStrategy = [strategySizeB]uint32{
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0x70, 0x3F, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x1F, 0x10, 0x08, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0F, 0x08, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
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0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x31, 0x1F, 0x10,
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0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
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0x15, 0x0C, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x03, 0x02,
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0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05,
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0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,
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0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01}
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2018-09-11 12:02:29 +01:00
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var P751_OneFp2 = Fp2Element{
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A: FpElement{
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0x249ad, 0x0, 0x0, 0x0, 0x0, 0x8310000000000000, 0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e, 0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x2d5b24bce5e2},
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B: FpElement{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},
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}
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var P751_HalfFp2 = Fp2Element{
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A: FpElement{
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0x00000000000124D6, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0xB8E0000000000000,
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0x9C8A2434C0AA7287, 0xA206996CA9A378A3, 0x6876280D41A41B52,
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0xE903B49F175CE04F, 0x0F8511860666D227, 0x00004EA07CFF6E7F},
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B: FpElement{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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}
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// (2^768)^2 mod p
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// This can't be a constant because Go doesn't allow array constants, so try
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// not to modify it.
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var montgomeryRsq = FpElement{
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2535603850726686808, 15780896088201250090, 6788776303855402382,
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17585428585582356230, 5274503137951975249, 2266259624764636289,
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11695651972693921304, 13072885652150159301, 4908312795585420432,
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6229583484603254826, 488927695601805643, 72213483953973}
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