schnorr.go

// Schnorr Signature
// Ref. Textbook: Nigel Smart - Cryptography An Introduction 3e, pp. 228-229

package main

import (
	"crypto/rand"
	"crypto/sha256"
	"encoding/hex"
	"fmt"
	"math/big"
)

func main() {
	// Prime Number
	p, _ := new(big.Int).SetString("113256005124119095887362785281379157446404829882999979448622682261851008142579707394232374642751898128900799220373652000701783958989737948170371610619031868024000569000834673195257818439729317108630237021891041144289230787346772418776549397214093418292376184510379483807693634331424008004223721261786568283629", 0)
	q, _ := new(big.Int).SetString("58508050319346346411247266832333505875101282222691606960622102756222717350237", 0)
	// Generator
	g, _ := new(big.Int).SetString("61995837307178551264627902471930418226063720987162275719035943735379849036295356612596402538370130606871549084613181542200476416422180948344921683453084001924786075195620479781873421932856722132237494145265573577037713306883903369443425145319999630695887996282517079193878060590362971381335924171579781687137", 0)

	x, _ := rand.Prime(rand.Reader, 255) // Secret Key 0 < x < q
	y := new(big.Int).Exp(g, x, p)       // Public key y = g^x mod p
	k, _ := rand.Prime(rand.Reader, 255) // Ephemeral key 0 < k < q
	m := big.NewInt(7)                   // Message

	fmt.Println("Secret Key: ", x)
	fmt.Println("Public Key: ", y)

	// Sign, signature is (e, s) for message m
	r := new(big.Int).Exp(g, k, p) // r = g^k mod p

	hashParam := m.String() + r.String() // m||r
	hash := sha256.New()
	hash.Write([]byte(hashParam))
	md := hash.Sum(nil)
	fHash := hex.EncodeToString(md)
	valfHash, _ := new(big.Int).SetString(fHash, 16)

	e := new(big.Int).Mod(valfHash, q)                                    // e = h(m||r) mod q
	s := new(big.Int).Mod(new(big.Int).Add(k, new(big.Int).Mul(x, e)), q) // s = k + x * e mod q

	fmt.Println("fHash: ", fHash)
	fmt.Println("valfHash: ", valfHash.String())
	fmt.Println("r: ", r)
	fmt.Println("e: ", e)
	fmt.Println("s: ", s)

	// Verification
	yPowe := new(big.Int).Exp(y, e, p)                                           // yPowe = y^e mod p
	eInv := new(big.Int).ModInverse(yPowe, p)                                    // eInv = yPowe^-1 mod p
	rV := new(big.Int).Mod(new(big.Int).Mul(new(big.Int).Exp(g, s, p), eInv), p) // r = g^s * y^-e mod p

	fmt.Println("rV: ", rV)

	hashParamV := m.String() + rV.String() // m||rV
	hashV := sha256.New()
	hashV.Write([]byte(hashParamV))
	mdV := hashV.Sum(nil)
	fHashV := hex.EncodeToString(mdV)
	valfHashV, _ := new(big.Int).SetString(fHashV, 16)

	eV := new(big.Int).Mod(valfHashV, q) // eV = h(m||rV) mod q

	fmt.Println("fHashV: ", fHashV)
	fmt.Println("eV: ", eV)

	// Result
	var cmpResult string

	switch eV.Cmp(e) {
	case -1:
		cmpResult = "eV < e"
	case 0:
		cmpResult = "eV = e"
	case 1:
		cmpResult = "eV > e"
	}

	fmt.Println("Verification result: ", cmpResult)
}