mirror of
https://github.com/henrydcase/nobs.git
synced 2024-11-22 23:28:57 +00:00
375 lines
11 KiB
Go
375 lines
11 KiB
Go
package sidh
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import (
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"errors"
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"io"
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// TODO: This is needed by ExtensionFieldElement struct, which itself
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// depends on implementation of p751.
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. "github.com/henrydcase/nobs/dh/sidh/internal/p751"
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)
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// -----------------------------------------------------------------------------
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// Functions for traversing isogeny trees acoording to strategy. Key type 'A' is
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//
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// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
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// for public key generation.
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func traverseTreePublicKeyA(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint, pub *PublicKey) {
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var points = make([]ProjectivePoint, 0, 8)
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var indices = make([]int, 0, 8)
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var i, sidx int
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cparam := curve.CalcCurveParamsEquiv4()
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phi := NewIsogeny4()
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strat := pub.params.A.IsogenyStrategy
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stratSz := len(strat)
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for j := 1; j <= stratSz; j++ {
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for i <= stratSz-j {
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points = append(points, *xR)
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indices = append(indices, i)
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k := strat[sidx]
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sidx++
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xR.Pow2k(&cparam, xR, 2*k)
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i += int(k)
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}
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cparam = phi.GenerateCurve(xR)
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for k := 0; k < len(points); k++ {
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points[k] = phi.EvaluatePoint(&points[k])
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}
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*phiP = phi.EvaluatePoint(phiP)
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*phiQ = phi.EvaluatePoint(phiQ)
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*phiR = phi.EvaluatePoint(phiR)
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// pop xR from points
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*xR, points = points[len(points)-1], points[:len(points)-1]
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i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
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}
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}
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// Traverses isogeny tree in order to compute xR needed
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// for public key generation.
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func traverseTreeSharedKeyA(curve *ProjectiveCurveParameters, xR *ProjectivePoint, pub *PublicKey) {
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var points = make([]ProjectivePoint, 0, 8)
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var indices = make([]int, 0, 8)
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var i, sidx int
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cparam := curve.CalcCurveParamsEquiv4()
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phi := NewIsogeny4()
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strat := pub.params.A.IsogenyStrategy
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stratSz := len(strat)
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for j := 1; j <= stratSz; j++ {
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for i <= stratSz-j {
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points = append(points, *xR)
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indices = append(indices, i)
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k := strat[sidx]
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sidx++
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xR.Pow2k(&cparam, xR, 2*k)
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i += int(k)
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}
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cparam = phi.GenerateCurve(xR)
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for k := 0; k < len(points); k++ {
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points[k] = phi.EvaluatePoint(&points[k])
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}
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// pop xR from points
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*xR, points = points[len(points)-1], points[:len(points)-1]
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i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
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}
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}
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// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
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// for public key generation.
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func traverseTreePublicKeyB(curve *ProjectiveCurveParameters, xR, phiP, phiQ, phiR *ProjectivePoint, pub *PublicKey) {
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var points = make([]ProjectivePoint, 0, 8)
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var indices = make([]int, 0, 8)
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var i, sidx int
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cparam := curve.CalcCurveParamsEquiv3()
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phi := NewIsogeny3()
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strat := pub.params.B.IsogenyStrategy
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stratSz := len(strat)
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for j := 1; j <= stratSz; j++ {
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for i <= stratSz-j {
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points = append(points, *xR)
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indices = append(indices, i)
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k := strat[sidx]
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sidx++
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xR.Pow3k(&cparam, xR, k)
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i += int(k)
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}
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cparam = phi.GenerateCurve(xR)
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for k := 0; k < len(points); k++ {
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points[k] = phi.EvaluatePoint(&points[k])
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}
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*phiP = phi.EvaluatePoint(phiP)
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*phiQ = phi.EvaluatePoint(phiQ)
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*phiR = phi.EvaluatePoint(phiR)
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// pop xR from points
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*xR, points = points[len(points)-1], points[:len(points)-1]
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i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
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}
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}
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// Traverses isogeny tree in order to compute xR, xP, xQ and xQmP needed
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// for public key generation.
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func traverseTreeSharedKeyB(curve *ProjectiveCurveParameters, xR *ProjectivePoint, pub *PublicKey) {
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var points = make([]ProjectivePoint, 0, 8)
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var indices = make([]int, 0, 8)
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var i, sidx int
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cparam := curve.CalcCurveParamsEquiv3()
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phi := NewIsogeny3()
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strat := pub.params.B.IsogenyStrategy
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stratSz := len(strat)
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for j := 1; j <= stratSz; j++ {
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for i <= stratSz-j {
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points = append(points, *xR)
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indices = append(indices, i)
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k := strat[sidx]
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sidx++
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xR.Pow3k(&cparam, xR, k)
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i += int(k)
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}
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cparam = phi.GenerateCurve(xR)
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for k := 0; k < len(points); k++ {
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points[k] = phi.EvaluatePoint(&points[k])
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}
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// pop xR from points
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*xR, points = points[len(points)-1], points[:len(points)-1]
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i, indices = int(indices[len(indices)-1]), indices[:len(indices)-1]
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}
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}
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// -----------------------------------------------------------------------------
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// Key generation functions
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//
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// Generate a private key for "Alice". Note that because this library does not
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// implement SIDH validation, each keypair must be used for at most one
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// shared secret computation.
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func (prv *PrivateKey) generatePrivateKeyA(rand io.Reader) error {
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_, err := io.ReadFull(rand, prv.Scalar)
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if err != nil {
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return err
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}
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// Bit-twiddle to ensure scalar is in 2*[0,2^371):
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prv.Scalar[prv.params.SecretKeySize-1] = prv.params.A.MaskBytes[0]
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prv.Scalar[prv.params.SecretKeySize-2] &= prv.params.A.MaskBytes[1] // clear high bits, so scalar < 2^372
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prv.Scalar[0] &= prv.params.A.MaskBytes[2] // clear low bit, so scalar is even
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// We actually want scalar in 2*(0,2^371), but the above procedure
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// generates 0 with probability 2^(-371), which isn't worth checking
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// for.
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return nil
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}
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// Generate a private key for "Bob". Note that because this library does not
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// implement SIDH validation, each keypair must be used for at most one
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// shared secret computation.
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func (prv *PrivateKey) generatePrivateKeyB(rand io.Reader) error {
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// Perform rejection sampling to obtain a random value in [0,3^238]:
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var ok uint64
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for i := uint(0); i < prv.params.SampleRate; i++ {
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_, err := io.ReadFull(rand, prv.Scalar)
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if err != nil {
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return err
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}
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// Mask the high bits to obtain a uniform value in [0,2^378):
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// TODO: simply run it in loop, if rand distribution is uniform you surelly get non 0
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// if not - better die, keep looping, hang, whatever, but don't generate secure key
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prv.Scalar[prv.params.SecretKeySize-1] &= prv.params.B.MaskBytes[0]
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// Accept if scalar < 3^238 (this happens w/ prob ~0.5828)
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// TODO this is specific to P751
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ok = checkLessThanThree238(prv.Scalar)
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if ok == 0 {
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break
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}
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}
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// ok is nonzero if all sampleRate trials failed.
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// This happens with probability 0.41719...^102 < 2^(-128), i.e., never
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if ok != 0 {
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// In case this happens user should retry. In practice it is highly
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// improbable (< 2^-128).
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return errors.New("sidh: private key generation failed")
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}
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// Multiply by 3 to get a scalar in 3*[0,3^238):
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multiplyByThree(prv.Scalar)
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// We actually want scalar in 2*(0,2^371), but the above procedure
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// generates 0 with probability 2^(-371), which isn't worth checking
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// for.
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return nil
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}
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// Generate a public key in the 2-torsion group
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func publicKeyGenA(prv *PrivateKey) (pub *PublicKey) {
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var xPA, xQA, xRA ProjectivePoint
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var xPB, xQB, xRB, xR ProjectivePoint
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var invZP, invZQ, invZR ExtensionFieldElement
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var tmp ProjectiveCurveParameters
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var phi = NewIsogeny4()
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pub = NewPublicKey(prv.params.Id, KeyVariant_SIDH_A)
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// Load points for A
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xPA.FromAffine(&prv.params.A.Affine_P)
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xPA.Z.One()
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xQA.FromAffine(&prv.params.A.Affine_Q)
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xQA.Z.One()
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xRA.FromAffine(&prv.params.A.Affine_R)
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xRA.Z.One()
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// Load points for B
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xRB.FromAffine(&prv.params.B.Affine_R)
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xRB.Z.One()
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xQB.FromAffine(&prv.params.B.Affine_Q)
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xQB.Z.One()
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xPB.FromAffine(&prv.params.B.Affine_P)
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xPB.Z.One()
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// Find isogeny kernel
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tmp.A.Zero()
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tmp.C.One()
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xR = RightToLeftLadder(&tmp, &xPA, &xQA, &xRA, prv.params.A.SecretBitLen, prv.Scalar)
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// Reset params object and travers isogeny tree
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tmp.A.Zero()
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tmp.C.One()
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traverseTreePublicKeyA(&tmp, &xR, &xPB, &xQB, &xRB, pub)
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// Secret isogeny
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phi.GenerateCurve(&xR)
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xPA = phi.EvaluatePoint(&xPB)
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xQA = phi.EvaluatePoint(&xQB)
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xRA = phi.EvaluatePoint(&xRB)
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ExtensionFieldBatch3Inv(&xPA.Z, &xQA.Z, &xRA.Z, &invZP, &invZQ, &invZR)
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pub.affine_xP.Mul(&xPA.X, &invZP)
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pub.affine_xQ.Mul(&xQA.X, &invZQ)
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pub.affine_xQmP.Mul(&xRA.X, &invZR)
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return
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}
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// Generate a public key in the 3-torsion group
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func publicKeyGenB(prv *PrivateKey) (pub *PublicKey) {
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var xPB, xQB, xRB, xR ProjectivePoint
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var xPA, xQA, xRA ProjectivePoint
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var invZP, invZQ, invZR ExtensionFieldElement
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var tmp ProjectiveCurveParameters
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var phi = NewIsogeny3()
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pub = NewPublicKey(prv.params.Id, prv.keyVariant)
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// Load points for B
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xRB.FromAffine(&prv.params.B.Affine_R)
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xRB.Z.One()
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xQB.FromAffine(&prv.params.B.Affine_Q)
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xQB.Z.One()
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xPB.FromAffine(&prv.params.B.Affine_P)
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xPB.Z.One()
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// Load points for A
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xPA.FromAffine(&prv.params.A.Affine_P)
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xPA.Z.One()
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xQA.FromAffine(&prv.params.A.Affine_Q)
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xQA.Z.One()
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xRA.FromAffine(&prv.params.A.Affine_R)
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xRA.Z.One()
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tmp.A.Zero()
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tmp.C.One()
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xR = RightToLeftLadder(&tmp, &xPB, &xQB, &xRB, prv.params.B.SecretBitLen, prv.Scalar)
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tmp.A.Zero()
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tmp.C.One()
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traverseTreePublicKeyB(&tmp, &xR, &xPA, &xQA, &xRA, pub)
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phi.GenerateCurve(&xR)
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xPB = phi.EvaluatePoint(&xPA)
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xQB = phi.EvaluatePoint(&xQA)
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xRB = phi.EvaluatePoint(&xRA)
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ExtensionFieldBatch3Inv(&xPB.Z, &xQB.Z, &xRB.Z, &invZP, &invZQ, &invZR)
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pub.affine_xP.Mul(&xPB.X, &invZP)
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pub.affine_xQ.Mul(&xQB.X, &invZQ)
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pub.affine_xQmP.Mul(&xRB.X, &invZR)
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return
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}
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// -----------------------------------------------------------------------------
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// Key agreement functions
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//
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// Establishing shared keys in in 2-torsion group
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func deriveSecretA(prv *PrivateKey, pub *PublicKey) []byte {
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var sharedSecret = make([]byte, pub.params.SharedSecretSize)
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var cparam ProjectiveCurveParameters
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var xP, xQ, xQmP ProjectivePoint
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var xR ProjectivePoint
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var phi = NewIsogeny4()
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// Recover curve coefficients
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cparam.RecoverCoordinateA(&pub.affine_xP, &pub.affine_xQ, &pub.affine_xQmP)
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cparam.C.One()
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// Find kernel of the morphism
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xP.FromAffine(&pub.affine_xP)
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xQ.FromAffine(&pub.affine_xQ)
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xQmP.FromAffine(&pub.affine_xQmP)
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xR = RightToLeftLadder(&cparam, &xP, &xQ, &xQmP, pub.params.A.SecretBitLen, prv.Scalar)
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// Traverse isogeny tree
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traverseTreeSharedKeyA(&cparam, &xR, pub)
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// Calculate j-invariant on isogeneus curve
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c := phi.GenerateCurve(&xR)
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cparam.RecoverCurveCoefficients4(&c)
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cparam.Jinvariant(sharedSecret)
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return sharedSecret
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}
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// Establishing shared keys in in 3-torsion group
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func deriveSecretB(prv *PrivateKey, pub *PublicKey) []byte {
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var sharedSecret = make([]byte, pub.params.SharedSecretSize)
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var xP, xQ, xQmP ProjectivePoint
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var xR ProjectivePoint
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var cparam ProjectiveCurveParameters
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var phi = NewIsogeny3()
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// Recover curve coefficients
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cparam.RecoverCoordinateA(&pub.affine_xP, &pub.affine_xQ, &pub.affine_xQmP)
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cparam.C.One()
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// Find kernel of the morphism
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xP.FromAffine(&pub.affine_xP)
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xQ.FromAffine(&pub.affine_xQ)
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xQmP.FromAffine(&pub.affine_xQmP)
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xR = RightToLeftLadder(&cparam, &xP, &xQ, &xQmP, pub.params.B.SecretBitLen, prv.Scalar)
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// Traverse isogeny tree
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traverseTreeSharedKeyB(&cparam, &xR, pub)
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// Calculate j-invariant on isogeneus curve
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c := phi.GenerateCurve(&xR)
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cparam.RecoverCurveCoefficients3(&c)
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cparam.Jinvariant(sharedSecret)
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return sharedSecret
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}
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