go-sike/p503/consts.go

package sike

const (
	// Number of uint64 limbs used to store field element
	FP_WORDS = 8
)

// Used internally by this package
// -------------------------------

var p = Fp{
	0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF,
	0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
}

// 2*503
var pX2 = Fp{
	0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF,
	0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C,
}

// p503 + 1
var p1 = Fp{
	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000,
	0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
}

// R^2=(2^512)^2 mod p
var pR2 = Fp{
	0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC,
	0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771,
}

// p503 + 1 left-shifted by 8, assuming little endianness
var p1s8 = Fp{
	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
	0x085BDA2211E7A0AC, 0x9BF6C87B7E7DAF13, 0x45C6BDDA77A4D01B, 0x4066F541811E1E60,
}

// 1/2 * R mod p
var half = Fp2{
	A: Fp{
		0x00000000000001FC, 0x0000000000000000, 0x0000000000000000, 0xB000000000000000,
		0x3B69BB2464785D2A, 0x36824A2AF0FE9896, 0xF5899F427A94F309, 0x0033B15203C83BB8},
}

// 1*R mod p
var one = Fp2{
	A: Fp{
		0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000,
		0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953},
}

// 6*R mod p
var six = Fp2{
	A: Fp{
		0x00000000000017D8, 0x0000000000000000, 0x0000000000000000, 0xE000000000000000,
		0x30B1E6E3A51520FA, 0xB13BC3BF6FFB3992, 0x8045412EEB3E3DED, 0x0069182E2159DBB8},
}

var Params SidhParams

func init() {
	Params = SidhParams{
		// SIDH public key byte size.
		PublicKeySize: 378,
		// SIDH shared secret byte size.
		SharedSecretSize: 126,
		InitCurve: ProjectiveCurveParameters{
			A: six,
			C: one,
		},
		A: DomainParams{
			// The x-coordinate of PA
			Affine_P: Fp2{
				A: Fp{
					0x5D083011589AD893, 0xADFD8D2CB67D0637, 0x330C9AC34FFB6361, 0xF0D47489A2E805A2,
					0x27E2789259C6B8DC, 0x63866A2C121931B9, 0x8D4C65A7137DCF44, 0x003A183AE5967B3F,
				},
				B: Fp{
					0x7E3541B8C96D1519, 0xD3ADAEEC0D61A26C, 0xC0A2219CE7703DD9, 0xFF3E46658FCDBC52,
					0xD5B38DEAE6E196FF, 0x1AAC826364956D58, 0xEC9F4875B9A5F27A, 0x001B0B475AB99843,
				},
			},
			// The x-coordinate of QA
			Affine_Q: Fp2{
				A: Fp{
					0x4D83695107D03BAD, 0x221F3299005E2FCF, 0x78E6AE22F30DECF2, 0x6D982DB5111253E4,
					0x504C80A8AB4526A8, 0xEFD0C3AA210BB024, 0xCB77483501DC6FCF, 0x001052544A96BDF3,
				},
				B: Fp{
					0x0D74FE3402BCAE47, 0xDF5B8CDA832D8AED, 0xB86BCF06E4BD837E, 0x892A2933A0FA1F63,
					0x9F88FC67B6CCB461, 0x822926EA9DDA3AC8, 0xEAC8DDE5855425ED, 0x000618FE6DA37A80,
				},
			},
			// The x-coordinate of RA = PA-QA
			Affine_R: Fp2{
				A: Fp{
					0x6B6F4A4F786CF310, 0xB019D444BDCFDBE3, 0xA14CB06680607834, 0xCB0D5582E7E6E60A,
					0xBA4EE8771667E241, 0xE42A114FCB12E5FF, 0x9A0C074E275BCD98, 0x001871329B28689E,
				},
				B: Fp{
					0x685FA8378513FE76, 0x84E8FC1785E8BDF0, 0x8A380F177CB7C1B7, 0x2227464F4F812C94,
					0x117C94A81A90C279, 0x193D73132FB9FA28, 0x99335336F192C9EB, 0x0006C2FE778A34FD,
				},
			},
			// Max size of secret key for 2-torsion group, corresponds to 2^e2 - 1
			SecretBitLen: 250,
			// SecretBitLen in bytes.
			SecretByteLen: uint((250 + 7) / 8),
			// 2-torsion group computation strategy
			IsogenyStrategy: []uint32{
				0x3D, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
				0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
				0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
				0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
				0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x1D, 0x10, 0x08, 0x04, 0x02, 0x01,
				0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02,
				0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0D, 0x08,
				0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
				0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01},
		},
		B: DomainParams{
			// The x-coordinate of PB
			Affine_P: Fp2{
				A: Fp{
					0xDF630FC5FB2468DB, 0xC30C5541C102040E, 0x3CDC9987B76511FC, 0xF54B5A09353D0CDD,
					0x3ADBA8E00703C42F, 0x8253F9303DDC95D0, 0x62D30778763ABFD7, 0x001CD00FB581CD55,
				},
				B: Fp{
					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
				},
			},
			// The x-coordinate of QB
			Affine_Q: Fp2{
				A: Fp{
					0x2E3457A12B429261, 0x311F94E89627DCF8, 0x5B71C98FD1DB73F6, 0x3671DB7DCFC21541,
					0xB6D1484C9FE0CF4F, 0x19CD110717356E35, 0xF4F9FB00AC9919DF, 0x0035BC124D38A70B,
				},
				B: Fp{
					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
					0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
				},
			},
			// The x-coordinate of RB = PB - QB
			Affine_R: Fp2{
				A: Fp{
					0x2E08BB99413D2952, 0xD3021467CD088D72, 0x21017AF859752245, 0x26314ED8FFD9DE5C,
					0x4AF43C73344B6686, 0xCFA1F91149DF0993, 0xF327A95365587A89, 0x000DBF54E03D3906,
				},
				B: Fp{
					0xFC1FC00CBD0A0CFB, 0x66C29FB284B491A9, 0x7FBED0B26D7F18E0, 0x9C02361066F4C67D,
					0x2D83758DD0B19E6F, 0x0827029DB2CDC1D7, 0x58700A85FAD38A71, 0x0006FA256B614AD2,
				},
			},
			// Size of secret key for 3-torsion group, corresponds to log_2(3^e3) - 1.
			SecretBitLen: 252,
			// SecretBitLen in bytes.
			SecretByteLen: uint((252 + 7) / 8),
			// 3-torsion group computation strategy
			IsogenyStrategy: []uint32{
				0x47, 0x26, 0x15, 0x0D, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
				0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02,
				0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01,
				0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x11, 0x09, 0x05, 0x03, 0x02,
				0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02,
				0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
				0x01, 0x02, 0x01, 0x01, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
				0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04,
				0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
				0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
				0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
				0x01, 0x02, 0x01, 0x01},
		},
		OneFp2:  one,
		HalfFp2: half,
		MsgLen:  24,
		// SIKEp503 provides 128 bit of classical security ([SIKE], 5.1)
		KemSize: 24,
		// ceil(503+7/8)
		Bytelen:        63,
		CiphertextSize: 24 + 378,
	}
}