2020-05-14 01:02:32 +01:00
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package p751
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//go:generate go run ../templates/gen.go P751
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import (
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2020-05-16 21:14:48 +01:00
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"github.com/henrydcase/nobs/dh/sidh/common"
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2020-05-14 01:02:32 +01:00
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"golang.org/x/sys/cpu"
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)
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const (
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// Number of uint64 limbs used to store field element
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FpWords = 12
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)
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var (
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// HasBMI2 signals support for MULX which is in BMI2
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HasBMI2 = cpu.X86.HasBMI2
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// HasADXandBMI2 signals support for ADX and BMI2
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HasADXandBMI2 = cpu.X86.HasBMI2 && cpu.X86.HasADX
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// P751 is a prime used by field Fp751
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P751 = common.Fp{
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0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff,
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0xffffffffffffffff, 0xffffffffffffffff, 0xeeafffffffffffff,
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0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
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0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
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// P751x2 = 2*p751 - 1
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P751x2 = common.Fp{
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0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF,
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0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xDD5FFFFFFFFFFFFF,
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0xC7D92D0A93F0F151, 0xB52B363427EF98ED, 0x109D30CFADD7D0ED,
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0x0AC56A08B964AE90, 0x1C25213F2F75B8CD, 0x0000DFCBAA83EE38}
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// P751p1 = p751 + 1
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P751p1 = common.Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0xeeb0000000000000,
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0xe3ec968549f878a8, 0xda959b1a13f7cc76, 0x084e9867d6ebe876,
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0x8562b5045cb25748, 0x0e12909f97badc66, 0x00006fe5d541f71c}
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// P751R2 = (2^768)^2 mod p
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P751R2 = common.Fp{
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0x233046449DAD4058, 0xDB010161A696452A, 0x5E36941472E3FD8E,
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0xF40BFE2082A2E706, 0x4932CCA8904F8751, 0x1F735F1F1EE7FC81,
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0xA24F4D80C1048E18, 0xB56C383CCDB607C5, 0x441DD47B735F9C90,
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0x5673ED2C6A6AC82A, 0x06C905261132294B, 0x000041AD830F1F35}
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// P751p1Zeros number of 0 digits in the least significant part of P751+1
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P751p1Zeros = 5
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// 1*R mod p
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one = common.Fp2{
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A: common.Fp{
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0x00000000000249ad, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x8310000000000000,
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0x5527b1e4375c6c66, 0x697797bf3f4f24d0, 0xc89db7b2ac5c4e2e,
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0x4ca4b439d2076956, 0x10f7926c7512c7e9, 0x00002d5b24bce5e2},
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}
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// 1/2 * R mod p
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half = common.Fp2{
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A: common.Fp{
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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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}
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// 6*R mod p
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six = common.Fp2{
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A: common.Fp{
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0x00000000000DBA10, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 0x0000000000000000, 0x3500000000000000,
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0x3714FE4EB8399915, 0xC3A2584753EB43F4, 0xA3151D605C520428,
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0xC116CF5232C7C978, 0x49A84D4B8EFAF6AA, 0x0000305731E97514},
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}
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params = common.SidhParams{
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ID: common.Fp751,
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// SIDH public key byte size.
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PublicKeySize: 564,
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// SIDH shared secret byte size.
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SharedSecretSize: 188,
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A: common.DomainParams{
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// The x-coordinate of PA
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AffineP: common.Fp2{
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A: common.Fp{
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0x884F46B74000BAA8, 0xBA52630F939DEC20, 0xC16FB97BA714A04D,
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0x082536745B1AB3DB, 0x1117157F446F9E82, 0xD2F27D621A018490,
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0x6B24AB523D544BCD, 0x9307D6AA2EA85C94, 0xE1A096729528F20F,
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0x896446F868F3255C, 0x2401D996B1BFF8A5, 0x00000EF8786A5C0A,
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},
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B: common.Fp{
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0xAEB78B3B96F59394, 0xAB26681E29C90B74, 0xE520AC30FDC4ACF1,
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0x870AAAE3A4B8111B, 0xF875BDB738D64EFF, 0x50109A7ECD7ED6BC,
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0x4CC64848FF0C56FB, 0xE617CB6C519102C9, 0x9C74B3835921E609,
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0xC91DDAE4A35A7146, 0x7FC82A155C1B9129, 0x0000214FA6B980B3,
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},
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},
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// The x-coordinate of QA
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AffineQ: common.Fp2{
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A: common.Fp{
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0x0F93CC38680A8CA9, 0x762E733822E7FED7, 0xE549F005AC0ADB67,
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0x94A71FDD2C43A4ED, 0xD48645C2B04721C5, 0x432DA1FE4D4CA4DC,
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0xBC99655FAA7A80E8, 0xB2C6D502BCFD4823, 0xEE92F40CA2EC8BDB,
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0x7B074132EFB6D16C, 0x3340B46FA38A7633, 0x0000215749657F6C,
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},
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B: common.Fp{
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0xECFF375BF3079F4C, 0xFBFE74B043E80EF3, 0x17376CBE3C5C7AD1,
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0xC06327A7E29CDBF2, 0x2111649C438BF3D4, 0xC1F9298261BA2E97,
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0x1F9FECE869CFD1C2, 0x01A39B4FC9346D62, 0x147CD1D3E82A3C9F,
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0xDE84E9D249E533EE, 0x1C48A5ADFB7C578D, 0x000061ACA0B82E1D,
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},
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},
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// The x-coordinate of RA = PA-QA
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AffineR: common.Fp2{
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A: common.Fp{
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0x1600C525D41059F1, 0xA596899A0A1D83F7, 0x6BFDEED6D2B23F35,
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0x5C7E707270C23910, 0x276CA1A4E8369411, 0xB193651A602925A0,
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0x243D239F1CA1F04A, 0x543DC6DA457860AD, 0xCDA590F325181DE9,
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0xD3AB7ACFDA80B395, 0x6C97468580FDDF7B, 0x0000352A3E5C4C77,
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},
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B: common.Fp{
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0x9B794F9FD1CC3EE8, 0xDB32E40A9B2FD23E, 0x26192A2542E42B67,
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0xA18E94FCA045BCE7, 0x96DC1BC38E7CDA2D, 0x9A1D91B752487DE2,
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0xCC63763987436DA3, 0x1316717AACCC551D, 0xC4C368A4632AFE72,
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0x4B6EA85C9CCD5710, 0x7A12CAD582C7BC9A, 0x00001C7E240149BF,
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},
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},
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// Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1
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SecretBitLen: 372,
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// SecretBitLen in bytes.
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SecretByteLen: 47,
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// 2-torsion group computation strategy
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IsogenyStrategy: []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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},
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B: common.DomainParams{
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// The x-coordinate of PB
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AffineP: common.Fp2{
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A: common.Fp{
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0x85691AAF4015F88C, 0x7478C5B8C36E9631, 0x7EF2A185DE4DD6E2,
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0x943BBEE46BEB9DC7, 0x1A3EC62798792D22, 0x791BC4B084B31D69,
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0x03DBE6522CEA17C4, 0x04749AA65D665D83, 0x3D52B5C45EF450F3,
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0x0B4219848E36947D, 0xA4CF7070466BDE27, 0x0000334B1FA6D193,
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},
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B: common.Fp{
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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 QB
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AffineQ: common.Fp2{
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A: common.Fp{
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0x8E7CB3FA53211340, 0xD67CE54F7A05EEE0, 0xFDDC2C8BCE46FC38,
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0x08587FAE3110DF1E, 0xD6B8246FA22B058B, 0x4DAC3ACC905A5DBD,
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0x51D0BF2FADCED3E8, 0xE5A2406DF6484425, 0x907F177584F671B8,
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0x4738A2FFCCED051C, 0x2B0067B4177E4853, 0x00002806AC948D3D,
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},
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B: common.Fp{
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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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AffineR: common.Fp2{
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A: common.Fp{
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0xB56457016D1D6D1C, 0x03DECCB38F39C491, 0xDFB910AC8A559452,
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0xA9D0F17D1FF24883, 0x8562BBAF515C248C, 0x249B2A6DDB1CB67D,
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0x3131AF96FB46835C, 0xE10258398480C3E1, 0xEAB5E2B872D4FAB1,
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0xB71E63875FAEB1DF, 0xF8384D4F13757CF6, 0x0000361EC9B09912,
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},
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B: common.Fp{
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0x58C967899ED16EF4, 0x81998376DC622A4B, 0x3D1C1DCFE0B12681,
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0x9347DEBB953E1730, 0x9ABB344D3A82C2D7, 0xE4881BD2820552B2,
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0x0037247923D90266, 0x2E3156EDB157E5A5, 0xF86A46A7506823F7,
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0x8FE5523A7B7F1CFC, 0xFA3CFFA38372F67B, 0x0000692DCE85FFBD,
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},
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},
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// Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1.
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SecretBitLen: 378,
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// SecretBitLen in bytes.
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SecretByteLen: 48,
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// 3-torsion group computation strategy
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IsogenyStrategy: []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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|
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0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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|
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0x0F, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
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|
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x07, 0x04, 0x02, 0x01,
|
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|
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0x01, 0x02, 0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
|
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|
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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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},
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OneFp2: one,
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HalfFp2: half,
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MsgLen: 32,
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// SIKEp751 provides 128 bit of classical security ([SIKE], 5.1)
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KemSize: 32,
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// ceil(751+7/8)
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Bytelen: 94,
|
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CiphertextSize: 32 + 564,
|
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|
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InitCurve: common.ProjectiveCurveParameters{
|
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|
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A: six,
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C: one,
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},
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}
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|
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)
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|
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func init() {
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common.Register(common.Fp751, ¶ms)
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}
|
