nobs/dh/sidh/p503/consts.go

package p503

import (
	. "github.com/henrydcase/nobs/dh/sidh/internal/isogeny"
)

const (
	// The secret key size, in bytes. Secret key is actually different for
	// torsion group 2 and 3. For 2-torsion group, last byte of secret key
	// is always set to 0.
	P503_SecretKeySize = 32
	// SIDH public key byte size
	P503_PublicKeySize = 378
	// SIDH shared secret byte size.
	P503_SharedSecretSize = 126
	// Max size of secret key for 2-torsion group, corresponds to e2
	P503_SecretBitLenA = 250
	// Size of secret key for 3-torsion group, corresponds to floor(log_2(3^e3))
	P503_SecretBitLenB = 252
	// Sample rate to obtain a value in
	P503_SampleRate = 102
	// Size of a compuatation strategy for 2-torsion group
	strategySizeA = 124
	// Size of a compuatation strategy for 3-torsion group
	strategySizeB = 158
	// ceil(503+7/8)
	P503_Bytelen = 63
	// Number of limbs for a field element
	NumWords = 8
)

// The x-coordinate of PA
var P503_affine_PA = Fp2Element{
	A: FpElement{
		0xE7EF4AA786D855AF, 0xED5758F03EB34D3B, 0x09AE172535A86AA9, 0x237B9CC07D622723,
		0xE3A284CBA4E7932D, 0x27481D9176C5E63F, 0x6A323FF55C6E71BF, 0x002ECC31A6FB8773,
	},
	B: FpElement{
		0x64D02E4E90A620B8, 0xDAB8128537D4B9F1, 0x4BADF77B8A228F98, 0x0F5DBDF9D1FB7D1B,
		0xBEC4DB288E1A0DCC, 0xE76A8665E80675DB, 0x6D6F252E12929463, 0x003188BD1463FACC,
	},
}

// The x-coordinate of QA
var P503_affine_QA = Fp2Element{
	A: FpElement{
		0xB79D41025DE85D56, 0x0B867DA9DF169686, 0x740E5368021C827D, 0x20615D72157BF25C,
		0xFF1590013C9B9F5B, 0xC884DCADE8C16CEA, 0xEBD05E53BF724E01, 0x0032FEF8FDA5748C,
	},
	B: FpElement{
		0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
		0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
	},
}

// The x-coordinate of RA = PA-QA
var P503_affine_RA = Fp2Element{
	A: FpElement{
		0x12E2E849AA0A8006, 0x41CF47008635A1E8, 0x9CD720A70798AED7, 0x42A820B42FCF04CF,
		0x7BF9BAD32AAE88B1, 0xF619127A54090BBE, 0x1CB10D8F56408EAA, 0x001D6B54C3C0EDEB,
	},
	B: FpElement{
		0x34DB54931CBAAC36, 0x420A18CB8DD5F0C4, 0x32008C1A48C0F44D, 0x3B3BA772B1CFD44D,
		0xA74B058FDAF13515, 0x095FC9CA7EEC17B4, 0x448E829D28F120F8, 0x00261EC3ED16A489,
	},
}

// The x-coordinate of PB
var P503_affine_PB = Fp2Element{
	A: FpElement{
		0x7EDE37F4FA0BC727, 0xF7F8EC5C8598941C, 0xD15519B516B5F5C8, 0xF6D5AC9B87A36282,
		0x7B19F105B30E952E, 0x13BD8B2025B4EBEE, 0x7B96D27F4EC579A2, 0x00140850CAB7E5DE,
	},
	B: FpElement{
		0x7764909DAE7B7B2D, 0x578ABB16284911AB, 0x76E2BFD146A6BF4D, 0x4824044B23AA02F0,
		0x1105048912A321F3, 0xB8A2E482CF0F10C1, 0x42FF7D0BE2152085, 0x0018E599C5223352,
	},
}

// The x-coordinate of QB
var P503_affine_QB = Fp2Element{
	A: FpElement{
		0x4256C520FB388820, 0x744FD7C3BAAF0A13, 0x4B6A2DDDB12CBCB8, 0xE46826E27F427DF8,
		0xFE4A663CD505A61B, 0xD6B3A1BAF025C695, 0x7C3BB62B8FCC00BD, 0x003AFDDE4A35746C,
	},
	B: FpElement{
		0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
		0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
	},
}

// The x-coordinate of RB = PB - QB
var P503_affine_RB = Fp2Element{
	A: FpElement{
		0x75601CD1E6C0DFCB, 0x1A9007239B58F93E, 0xC1F1BE80C62107AC, 0x7F513B898F29FF08,
		0xEA0BEDFF43E1F7B2, 0x2C6D94018CBAE6D0, 0x3A430D31BCD84672, 0x000D26892ECCFE83,
	},
	B: FpElement{
		0x1119D62AEA3007A1, 0xE3702AA4E04BAE1B, 0x9AB96F7D59F990E7, 0xF58440E8B43319C0,
		0xAF8134BEE1489775, 0xE7F7774E905192AA, 0xF54AE09308E98039, 0x001EF7A041A86112,
	},
}

// 2-torsion group computation strategy
var P503_AliceIsogenyStrategy = [strategySizeA]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}

// 3-torsion group computation strategy
var P503_BobIsogenyStrategy = [strategySizeB]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}

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

var p503 = FpElement{
	0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF,
	0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
}

// 2*p751
var p503x2 = FpElement{
	0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF,
	0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C,
}

// p503 + 1
var p503p1 = FpElement{
	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000,
	0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
}

// R^2=(2^512)^2 mod p
var p503R2 = FpElement{
	0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC,
	0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771,
}

// 1*R mod p
var P503_OneFp2 = Fp2Element{
	A: FpElement{
		0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000,
		0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953},
}

// 1/2 * R mod p
var P503_HalfFp2 = Fp2Element{
	A: FpElement{
		0x00000000000001FC, 0x0000000000000000, 0x0000000000000000, 0xB000000000000000,
		0x3B69BB2464785D2A, 0x36824A2AF0FE9896, 0xF5899F427A94F309, 0x0033B15203C83BB8},
}