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test-cases.go
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test-cases.go
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package main
import (
"bytes"
"crypto/rand"
"encoding/hex"
"fmt"
"math/big"
"golang.org/x/crypto/curve25519"
)
var (
prng = rand.Reader
n25519x = "1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed"
p *big.Int // Order of prime-order subgroup. (E.g n25519x for X25519)
n *big.Int // Order of composite-order group. n = p * cofactor
cofactor *big.Int
)
func privToPub(a [32]byte) (aGx [32]byte) {
curve25519.ScalarBaseMult(&aGx, &a)
return
}
func newKeyPair() (a, aGx [32]byte) {
prng.Read(a[:])
aGx = privToPub(a)
return
}
func keyPairFromHex(ax string) (a, aG [32]byte) {
ab, _ := hex.DecodeString(ax)
copy(a[:], ab)
a = reverse(a)
aG = privToPub(a)
return
}
func dh(a, bGx [32]byte) (abGx [32]byte) {
curve25519.ScalarMult(&abGx, &a, &bGx)
return
}
func reverse(in [32]byte) (out [32]byte) {
for i, x := range in {
out[len(in)-i-1] = x
}
return
}
func le2bn(le [32]byte) *big.Int {
be := reverse(le)
return big.NewInt(0).SetBytes(be[:])
}
func bn2le(bn *big.Int) [32]byte {
sl := bn.Bytes()
pad := bytes.Repeat([]byte{0}, 32-len(sl))
sl = append(pad, sl...)
be := [32]byte{}
copy(be[:], sl)
return reverse(be)
}
func newDelta() (d [32]byte) {
prng.Read(d[:])
return
}
func clamp(a [32]byte) *big.Int {
out := a
out[0] &= 248
out[31] &= 127
out[31] |= 64
return le2bn(out)
}
func log(label string, x [32]byte) {
fmt.Printf("%-4s %064x\n", label, x)
}
func logn(label string, x *big.Int) {
log(label, bn2le(x))
}
func cswap(c uint, a, b *big.Int) {
if c == 1 {
temp := *a
*a = *b
*b = temp
}
}
func deltaPriv(d, sk [32]byte) [32]byte {
dC := clamp(d)
skC := clamp(sk)
skP := big.NewInt(0)
skP.Mul(dC, skC)
skP.Mod(skP, n)
skN := big.NewInt(0)
skN.Sub(n, skP)
cP := skP.Bit(254)
logn("dC", dC)
logn("skC", skC)
logn("skP", skP)
logn("skN", skN)
logn("cP", big.NewInt(int64(cP)))
cswap(1-cP, skP, skN)
return bn2le(skP)
}
func deltaPub(d, aGx [32]byte) [32]byte {
return dh(d, aGx)
}
func main() {
/* X25519 Constants
----------------
cofactor = 8
p = n25519 = prime order
n = p * cofactor = composite group order.
*/
p, _ = big.NewInt(0).SetString(n25519x, 16)
cofactor = big.NewInt(8)
n = big.NewInt(0)
n.Mul(p, cofactor)
sk0, pk0 := newKeyPair()
d := newDelta()
log("sk0", sk0)
log("pk0", pk0)
log("d", d)
// Apply the delta
sk1 := deltaPriv(d, sk0)
pk1 := deltaPub(d, pk0)
// Check if the homomorphism applies
sk1p := privToPub(sk1)
log("sk1", sk1)
log("pk1", pk1)
log("sk1p", sk1p)
}