288 Zeilen
9.7 KiB
Go
288 Zeilen
9.7 KiB
Go
package sike
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// I keep it bool in order to be able to apply logical NOT
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type KeyVariant uint
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// Representation of an element of the base field F_p.
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//
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// No particular meaning is assigned to the representation -- it could represent
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// an element in Montgomery form, or not. Tracking the meaning of the field
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// element is left to higher types.
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type Fp [FP_WORDS]uint64
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// Represents an intermediate product of two elements of the base field F_p.
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type FpX2 [2 * FP_WORDS]uint64
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// Represents an element of the extended field Fp^2 = Fp(x+i)
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type Fp2 struct {
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A Fp
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B Fp
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}
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type DomainParams struct {
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// P, Q and R=P-Q base points
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Affine_P, Affine_Q, Affine_R Fp2
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// Size of a compuatation strategy for x-torsion group
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IsogenyStrategy []uint32
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// Max size of secret key for x-torsion group
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SecretBitLen uint
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// Max size of secret key for x-torsion group
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SecretByteLen uint
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}
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type SidhParams struct {
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Id uint8
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// Bytelen of P
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Bytelen int
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// The public key size, in bytes.
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PublicKeySize int
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// The shared secret size, in bytes.
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SharedSecretSize int
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// 2- and 3-torsion group parameter definitions
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A, B DomainParams
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// Precomputed identity element in the Fp2 in Montgomery domain
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OneFp2 Fp2
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// Precomputed 1/2 in the Fp2 in Montgomery domain
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HalfFp2 Fp2
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// Length of SIKE secret message. Must be one of {24,32,40},
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// depending on size of prime field used (see [SIKE], 1.4 and 5.1)
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MsgLen int
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// Length of SIKE ephemeral KEM key (see [SIKE], 1.4 and 5.1)
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KemSize int
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}
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// Stores curve projective parameters equivalent to A/C. Meaning of the
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// values depends on the context. When working with isogenies over
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// subgroup that are powers of:
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// * three then (A:C) ~ (A+2C:A-2C)
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// * four then (A:C) ~ (A+2C: 4C)
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// See Appendix A of SIKE for more details
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type CurveCoefficientsEquiv struct {
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A Fp2
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C Fp2
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}
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// A point on the projective line P^1(F_{p^2}).
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//
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// This represents a point on the Kummer line of a Montgomery curve. The
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// curve is specified by a ProjectiveCurveParameters struct.
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type ProjectivePoint struct {
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X Fp2
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Z Fp2
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}
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// Base type for public and private key. Used mainly to carry domain
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// parameters.
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type key struct {
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// Domain parameters of the algorithm to be used with a key
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params *SidhParams
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// Flag indicates wether corresponds to 2-, 3-torsion group or SIKE
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keyVariant KeyVariant
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}
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// Defines operations on private key
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type PrivateKey struct {
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key
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// Secret key
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Scalar []byte
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// Used only by KEM
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S []byte
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}
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// Defines operations on public key
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type PublicKey struct {
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key
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affine_xP Fp2
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affine_xQ Fp2
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affine_xQmP Fp2
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}
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// A point on the projective line P^1(F_{p^2}).
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//
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// This is used to work projectively with the curve coefficients.
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type ProjectiveCurveParameters struct {
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A Fp2
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C Fp2
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}
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const (
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// First 2 bits identify SIDH variant third bit indicates
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// wether key is a SIKE variant (set) or SIDH (not set)
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// 001 - SIDH: corresponds to 2-torsion group
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KeyVariant_SIDH_A KeyVariant = 1 << 0
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// 010 - SIDH: corresponds to 3-torsion group
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KeyVariant_SIDH_B = 1 << 1
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// 110 - SIKE
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KeyVariant_SIKE = 1<<2 | KeyVariant_SIDH_B
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// Number of uint64 limbs used to store field element
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FP_WORDS = 8
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)
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// Used internally by this package
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// -------------------------------
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var p503 = Fp{
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0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xABFFFFFFFFFFFFFF,
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0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
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}
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// 2*503
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var p503x2 = Fp{
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0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x57FFFFFFFFFFFFFF,
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0x2610B7B44423CF41, 0x3737ED90F6FCFB5E, 0xC08B8D7BB4EF49A0, 0x0080CDEA83023C3C,
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}
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// p503 + 1
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var p503p1 = Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xAC00000000000000,
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0x13085BDA2211E7A0, 0x1B9BF6C87B7E7DAF, 0x6045C6BDDA77A4D0, 0x004066F541811E1E,
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}
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// R^2=(2^512)^2 mod p
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var p503R2 = Fp{
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0x5289A0CF641D011F, 0x9B88257189FED2B9, 0xA3B365D58DC8F17A, 0x5BC57AB6EFF168EC,
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0x9E51998BD84D4423, 0xBF8999CBAC3B5695, 0x46E9127BCE14CDB6, 0x003F6CFCE8B81771,
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}
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// p503 + 1 left-shifted by 8, assuming little endianness
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var p503p1s8 = Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x085BDA2211E7A0AC, 0x9BF6C87B7E7DAF13, 0x45C6BDDA77A4D01B, 0x4066F541811E1E60,
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}
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// 1*R mod p
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var P503_OneFp2 = Fp2{
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A: Fp{
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0x00000000000003F9, 0x0000000000000000, 0x0000000000000000, 0xB400000000000000,
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0x63CB1A6EA6DED2B4, 0x51689D8D667EB37D, 0x8ACD77C71AB24142, 0x0026FBAEC60F5953},
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}
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// 1/2 * R mod p
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var P503_HalfFp2 = Fp2{
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A: Fp{
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0x00000000000001FC, 0x0000000000000000, 0x0000000000000000, 0xB000000000000000,
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0x3B69BB2464785D2A, 0x36824A2AF0FE9896, 0xF5899F427A94F309, 0x0033B15203C83BB8},
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}
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var Params SidhParams
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func init() {
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Params = SidhParams{
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// SIDH public key byte size.
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PublicKeySize: 378,
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// SIDH shared secret byte size.
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SharedSecretSize: 126,
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A: DomainParams{
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// The x-coordinate of PA
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Affine_P: Fp2{
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A: Fp{
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0xE7EF4AA786D855AF, 0xED5758F03EB34D3B, 0x09AE172535A86AA9, 0x237B9CC07D622723,
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0xE3A284CBA4E7932D, 0x27481D9176C5E63F, 0x6A323FF55C6E71BF, 0x002ECC31A6FB8773,
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},
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B: Fp{
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0x64D02E4E90A620B8, 0xDAB8128537D4B9F1, 0x4BADF77B8A228F98, 0x0F5DBDF9D1FB7D1B,
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0xBEC4DB288E1A0DCC, 0xE76A8665E80675DB, 0x6D6F252E12929463, 0x003188BD1463FACC,
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},
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},
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// The x-coordinate of QA
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Affine_Q: Fp2{
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A: Fp{
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0xB79D41025DE85D56, 0x0B867DA9DF169686, 0x740E5368021C827D, 0x20615D72157BF25C,
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0xFF1590013C9B9F5B, 0xC884DCADE8C16CEA, 0xEBD05E53BF724E01, 0x0032FEF8FDA5748C,
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},
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B: Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 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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Affine_R: Fp2{
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A: Fp{
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0x12E2E849AA0A8006, 0x41CF47008635A1E8, 0x9CD720A70798AED7, 0x42A820B42FCF04CF,
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0x7BF9BAD32AAE88B1, 0xF619127A54090BBE, 0x1CB10D8F56408EAA, 0x001D6B54C3C0EDEB,
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},
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B: Fp{
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0x34DB54931CBAAC36, 0x420A18CB8DD5F0C4, 0x32008C1A48C0F44D, 0x3B3BA772B1CFD44D,
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0xA74B058FDAF13515, 0x095FC9CA7EEC17B4, 0x448E829D28F120F8, 0x00261EC3ED16A489,
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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: 250,
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// SecretBitLen in bytes.
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SecretByteLen: uint((250 + 7) / 8),
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// 2-torsion group computation strategy
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IsogenyStrategy: []uint32{
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0x3D, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
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0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x1D, 0x10, 0x08, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x0D, 0x08,
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0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01},
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},
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B: DomainParams{
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// The x-coordinate of PB
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Affine_P: Fp2{
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A: Fp{
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0x7EDE37F4FA0BC727, 0xF7F8EC5C8598941C, 0xD15519B516B5F5C8, 0xF6D5AC9B87A36282,
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0x7B19F105B30E952E, 0x13BD8B2025B4EBEE, 0x7B96D27F4EC579A2, 0x00140850CAB7E5DE,
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},
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B: Fp{
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0x7764909DAE7B7B2D, 0x578ABB16284911AB, 0x76E2BFD146A6BF4D, 0x4824044B23AA02F0,
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0x1105048912A321F3, 0xB8A2E482CF0F10C1, 0x42FF7D0BE2152085, 0x0018E599C5223352,
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},
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},
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// The x-coordinate of QB
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Affine_Q: Fp2{
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A: Fp{
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0x4256C520FB388820, 0x744FD7C3BAAF0A13, 0x4B6A2DDDB12CBCB8, 0xE46826E27F427DF8,
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0xFE4A663CD505A61B, 0xD6B3A1BAF025C695, 0x7C3BB62B8FCC00BD, 0x003AFDDE4A35746C,
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},
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B: Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000,
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0x0000000000000000, 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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Affine_R: Fp2{
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A: Fp{
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0x75601CD1E6C0DFCB, 0x1A9007239B58F93E, 0xC1F1BE80C62107AC, 0x7F513B898F29FF08,
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0xEA0BEDFF43E1F7B2, 0x2C6D94018CBAE6D0, 0x3A430D31BCD84672, 0x000D26892ECCFE83,
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},
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B: Fp{
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0x1119D62AEA3007A1, 0xE3702AA4E04BAE1B, 0x9AB96F7D59F990E7, 0xF58440E8B43319C0,
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0xAF8134BEE1489775, 0xE7F7774E905192AA, 0xF54AE09308E98039, 0x001EF7A041A86112,
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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: 252,
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// SecretBitLen in bytes.
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SecretByteLen: uint((252 + 7) / 8),
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// 3-torsion group computation strategy
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IsogenyStrategy: []uint32{
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0x47, 0x26, 0x15, 0x0D, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x05, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x01, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x11, 0x09, 0x05, 0x03, 0x02,
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0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04,
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0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01},
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},
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OneFp2: P503_OneFp2,
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HalfFp2: P503_HalfFp2,
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MsgLen: 24,
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// SIKEp503 provides 128 bit of classical security ([SIKE], 5.1)
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KemSize: 16,
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// ceil(503+7/8)
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Bytelen: 63,
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}
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}
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