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