318 lines
10 KiB
Go
318 lines
10 KiB
Go
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// Copyright (c) 2019, Cloudflare Inc.
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//
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// Permission to use, copy, modify, and/or distribute this software for any
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// purpose with or without fee is hereby granted, provided that the above
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// copyright notice and this permission notice appear in all copies.
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//
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// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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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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// Defines A,C constant for starting curve Cy^2 = x^3 + Ax^2 + x
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InitCurve ProjectiveCurveParameters
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// 2- and 3-torsion group parameter definitions
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A, B DomainParams
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// Precomputed 1/2 in the Fp2 in Montgomery domain
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HalfFp2 Fp2
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// Precomputed identity element in the Fp2 in Montgomery domain
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OneFp2 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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// Size of a ciphertext returned by encapsulation in bytes
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CiphertextSize 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 whether 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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// whether 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 = 7
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)
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// Used internally by this package
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// -------------------------------
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var (
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p = Fp{
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0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFDC1767AE2FFFFFF,
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0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x2341F27177344,
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}
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// 2*p434
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pX2 = Fp{
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0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFB82ECF5C5FFFFFF,
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0xF78CB8F062B15D47, 0xD9F8BFAD038A40AC, 0x4683E4E2EE688,
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}
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// p434 + 1
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p1 = Fp{
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0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0xFDC1767AE3000000,
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0x7BC65C783158AEA3, 0x6CFC5FD681C52056, 0x0002341F27177344,
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}
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// R^2=(2^448)^2 mod p
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R2 = Fp{
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0x28E55B65DCD69B30, 0xACEC7367768798C2, 0xAB27973F8311688D, 0x175CC6AF8D6C7C0B,
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0xABCD92BF2DDE347E, 0x69E16A61C7686D9A, 0x000025A89BCDD12A,
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}
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// 1/2 * R mod p
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half = Fp2{
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A: Fp{
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0x0000000000003A16, 0x0000000000000000, 0x0000000000000000, 0x5C87FA027E000000,
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0x6C00D27DAACFD66A, 0x74992A2A2FBBA086, 0x0000767753DE976D},
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}
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// 1*R mod p
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one = Fp2{
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A: Fp{
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0x000000000000742C, 0x0000000000000000, 0x0000000000000000, 0xB90FF404FC000000,
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0xD801A4FB559FACD4, 0xE93254545F77410C, 0x0000ECEEA7BD2EDA},
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}
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// 6*R mod p
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six = Fp2{
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A: Fp{
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0x000000000002B90A, 0x0000000000000000, 0x0000000000000000, 0x5ADCCB2822000000,
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0x187D24F39F0CAFB4, 0x9D353A4D394145A0, 0x00012559A0403298},
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}
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Params SidhParams
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)
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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: 330,
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// SIDH shared secret byte size.
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SharedSecretSize: 110,
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InitCurve: ProjectiveCurveParameters{
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A: six,
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C: one,
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},
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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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0x05ADF455C5C345BF, 0x91935C5CC767AC2B, 0xAFE4E879951F0257, 0x70E792DC89FA27B1,
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0xF797F526BB48C8CD, 0x2181DB6131AF621F, 0x00000A1C08B1ECC4,
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},
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B: Fp{
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0x74840EB87CDA7788, 0x2971AA0ECF9F9D0B, 0xCB5732BDF41715D5, 0x8CD8E51F7AACFFAA,
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0xA7F424730D7E419F, 0xD671EB919A179E8C, 0x0000FFA26C5A924A,
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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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0xFEC6E64588B7273B, 0xD2A626D74CBBF1C6, 0xF8F58F07A78098C7, 0xE23941F470841B03,
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0x1B63EDA2045538DD, 0x735CFEB0FFD49215, 0x0001C4CB77542876,
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},
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B: Fp{
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0xADB0F733C17FFDD6, 0x6AFFBD037DA0A050, 0x680EC43DB144E02F, 0x1E2E5D5FF524E374,
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0xE2DDA115260E2995, 0xA6E4B552E2EDE508, 0x00018ECCDDF4B53E,
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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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0x01BA4DB518CD6C7D, 0x2CB0251FE3CC0611, 0x259B0C6949A9121B, 0x60E17AC16D2F82AD,
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0x3AA41F1CE175D92D, 0x413FBE6A9B9BC4F3, 0x00022A81D8D55643,
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},
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B: Fp{
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0xB8ADBC70FC82E54A, 0xEF9CDDB0D5FADDED, 0x5820C734C80096A0, 0x7799994BAA96E0E4,
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0x044961599E379AF8, 0xDB2B94FBF09F27E2, 0x0000B87FC716C0C6,
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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: 216,
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// SecretBitLen in bytes.
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SecretByteLen: 27,
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// 2-torsion group computation strategy
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IsogenyStrategy: []uint32{
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0x30, 0x1C, 0x10, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
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0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x0D, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01,
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0x15, 0x0C, 0x07, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x03, 0x02, 0x01, 0x01, 0x01, 0x01, 0x05, 0x03, 0x02, 0x01,
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0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x09, 0x05, 0x03,
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0x02, 0x01, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x01, 0x04,
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0x02, 0x01, 0x01, 0x01, 0x02, 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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0x6E5497556EDD48A3, 0x2A61B501546F1C05, 0xEB919446D049887D, 0x5864A4A69D450C4F,
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0xB883F276A6490D2B, 0x22CC287022D5F5B9, 0x0001BED4772E551F,
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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,
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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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0xFAE2A3F93D8B6B8E, 0x494871F51700FE1C, 0xEF1A94228413C27C, 0x498FF4A4AF60BD62,
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0xB00AD2A708267E8A, 0xF4328294E017837F, 0x000034080181D8AE,
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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,
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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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0x283B34FAFEFDC8E4, 0x9208F44977C3E647, 0x7DEAE962816F4E9A, 0x68A2BA8AA262EC9D,
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0x8176F112EA43F45B, 0x02106D022634F504, 0x00007E8A50F02E37,
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},
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B: Fp{
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0xB378B7C1DA22CCB1, 0x6D089C99AD1D9230, 0xEBE15711813E2369, 0x2B35A68239D48A53,
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0x445F6FD138407C93, 0xBEF93B29A3F6B54B, 0x000173FA910377D3,
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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: 217,
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// SecretBitLen in bytes.
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SecretByteLen: 28,
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// 3-torsion group computation strategy
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IsogenyStrategy: []uint32{
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0x42, 0x21, 0x11, 0x09, 0x05, 0x03, 0x02, 0x01, 0x01, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02,
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0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x10,
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0x08, 0x04, 0x02, 0x01, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x08, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
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0x01, 0x20, 0x10, 0x08, 0x04, 0x03, 0x01, 0x01, 0x01, 0x01,
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0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01,
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0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04, 0x02,
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0x01, 0x01, 0x02, 0x01, 0x01, 0x10, 0x08, 0x04, 0x02, 0x01,
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0x01, 0x02, 0x01, 0x01, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01,
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0x01, 0x08, 0x04, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01, 0x04,
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0x02, 0x01, 0x01, 0x02, 0x01, 0x01},
|
||
|
|
},
|
||
|
|
OneFp2: one,
|
||
|
|
HalfFp2: half,
|
||
|
|
MsgLen: 16,
|
||
|
|
// SIKEp434 provides 128 bit of classical security ([SIKE], 5.1)
|
||
|
|
KemSize: 16,
|
||
|
|
// ceil(434+7/8)
|
||
|
|
Bytelen: 55,
|
||
|
|
CiphertextSize: 16 + 330,
|
||
|
|
}
|
||
|
|
}
|