Schnorr signature implemented. ECC point multiplication with big int. Refactor of the code.

shamirsecretsharing/shamirsecretsharing.go

@@ -0,0 +1,114 @@
+package shamirsecretsharing
+
+import (
+	"crypto/rand"
+	"errors"
+	"math/big"
+)
+
+const (
+	bits = 1024
+)
+
+// t: number of secrets needed
+// n: number of shares
+// p: random point
+// k: secret to share
+// Create calculates the secrets to share from given parameters
+func Create(t, n, p, k *big.Int) (result [][]*big.Int, err error) {
+	if k.Cmp(p) > 0 {
+		return nil, errors.New("Error: need k<p. k: " + k.String() + ", p: " + p.String())
+	}
+	//generate the basePolynomial
+	var basePolynomial []*big.Int
+	basePolynomial = append(basePolynomial, k)
+	for i := 0; i < int(t.Int64())-1; i++ {
+		randPrime, err := rand.Prime(rand.Reader, bits/2)
+		if err != nil {
+			return result, err
+		}
+		basePolynomial = append(basePolynomial, randPrime)
+	}
+
+	//calculate shares, based on the basePolynomial
+	var shares []*big.Int
+	for i := 1; i < int(n.Int64())+1; i++ {
+		var pResultMod *big.Int
+		pResult := big.NewInt(int64(0))
+		for x, polElem := range basePolynomial {
+			if x == 0 {
+				pResult = pResult.Add(pResult, polElem)
+			} else {
+				iBigInt := big.NewInt(int64(i))
+				xBigInt := big.NewInt(int64(x))
+				iPowed := iBigInt.Exp(iBigInt, xBigInt, nil)
+				currElem := iPowed.Mul(iPowed, polElem)
+				pResult = pResult.Add(pResult, currElem)
+				pResultMod = pResult.Mod(pResult, p)
+			}
+		}
+		shares = append(shares, pResultMod)
+	}
+	//put the share together with his p value
+	result = packSharesAndI(shares)
+	return result, nil
+}
+
+func packSharesAndI(sharesString []*big.Int) (r [][]*big.Int) {
+	for i, share := range sharesString {
+		curr := []*big.Int{share, big.NewInt(int64(i + 1))}
+		r = append(r, curr)
+	}
+	return r
+}
+func unpackSharesAndI(sharesPacked [][]*big.Int) ([]*big.Int, []*big.Int) {
+	var shares []*big.Int
+	var i []*big.Int
+	for _, share := range sharesPacked {
+		shares = append(shares, share[0])
+		i = append(i, share[1])
+	}
+	return shares, i
+}
+
+// LagrangeInterpolation calculates the secret from given shares
+func LagrangeInterpolation(sharesGiven [][]*big.Int, p *big.Int) *big.Int {
+	resultN := big.NewInt(int64(0))
+	resultD := big.NewInt(int64(0))
+
+	//unpack shares
+	sharesBigInt, sharesIBigInt := unpackSharesAndI(sharesGiven)
+
+	for i := 0; i < len(sharesBigInt); i++ {
+		lagrangeNumerator := big.NewInt(int64(1))
+		lagrangeDenominator := big.NewInt(int64(1))
+		for j := 0; j < len(sharesBigInt); j++ {
+			if sharesIBigInt[i] != sharesIBigInt[j] {
+				currLagrangeNumerator := sharesIBigInt[j]
+				currLagrangeDenominator := new(big.Int).Sub(sharesIBigInt[j], sharesIBigInt[i])
+				lagrangeNumerator = new(big.Int).Mul(lagrangeNumerator, currLagrangeNumerator)
+				lagrangeDenominator = new(big.Int).Mul(lagrangeDenominator, currLagrangeDenominator)
+			}
+		}
+		numerator := new(big.Int).Mul(sharesBigInt[i], lagrangeNumerator)
+		quo := new(big.Int).Quo(numerator, lagrangeDenominator)
+		if quo.Int64() != 0 {
+			resultN = resultN.Add(resultN, quo)
+		} else {
+			resultNMULlagrangeDenominator := new(big.Int).Mul(resultN, lagrangeDenominator)
+			resultN = new(big.Int).Add(resultNMULlagrangeDenominator, numerator)
+
+			resultD = resultD.Add(resultD, lagrangeDenominator)
+		}
+	}
+
+	var modinvMul *big.Int
+	if resultD.Int64() != 0 {
+		modinv := new(big.Int).ModInverse(resultD, p)
+		modinvMul = new(big.Int).Mul(resultN, modinv)
+	} else {
+		modinvMul = resultN
+	}
+	r := new(big.Int).Mod(modinvMul, p)
+	return r
+}

shamirsecretsharing/shamirsecretsharing_test.go

@@ -0,0 +1,43 @@
+package shamirsecretsharing
+
+import (
+	"crypto/rand"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestCreate(t *testing.T) {
+	k := 123456789
+	p, err := rand.Prime(rand.Reader, bits/2)
+	assert.Nil(t, err)
+
+	nNeededSecrets := big.NewInt(int64(3))
+	nShares := big.NewInt(int64(6))
+	shares, err := Create(
+		nNeededSecrets,
+		nShares,
+		p,
+		big.NewInt(int64(k)))
+	assert.Nil(t, err)
+
+	//generate sharesToUse
+	var sharesToUse [][]*big.Int
+	sharesToUse = append(sharesToUse, shares[2])
+	sharesToUse = append(sharesToUse, shares[1])
+	sharesToUse = append(sharesToUse, shares[0])
+	secr := LagrangeInterpolation(sharesToUse, p)
+
+	// fmt.Print("original secret: ")
+	// fmt.Println(k)
+	// fmt.Print("p: ")
+	// fmt.Println(p)
+	// fmt.Print("shares: ")
+	// fmt.Println(shares)
+	// fmt.Print("secret result: ")
+	// fmt.Println(secr)
+	if int64(k) != secr.Int64() {
+		t.Errorf("reconstructed secret not correspond to original secret")
+	}
+}