go-sike/p434/types.go

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
	// Defines A,C constant for starting curve Cy^2 = x^3 + Ax^2 + x
	InitCurve ProjectiveCurveParameters
	// 2- and 3-torsion group parameter definitions
	A, B DomainParams
	// Precomputed 1/2 in the Fp2 in Montgomery domain
	HalfFp2 Fp2
	// Precomputed identity element in the Fp2 in Montgomery domain
	OneFp2 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
)