add lagrange interpolation to recover secret, add test

shamirsecretsharing.go

@@ -71,3 +71,45 @@ func unpackSharesAndI(sharesPacked [][]*big.Int) ([]*big.Int, []*big.Int) {
 	}
 	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_test.go

@@ -0,0 +1,47 @@
+package shamirsecretsharing
+
+import (
+	"bytes"
+	"crypto/rand"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestCreate(t *testing.T) {
+	k, ok := new(big.Int).SetString("123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890", 10)
+	assert.True(t, ok)
+
+	p, err := rand.Prime(rand.Reader, bits/2)
+	assert.Nil(t, err)
+
+	nShares := big.NewInt(int64(6))
+	nNeededShares := big.NewInt(int64(3))
+	shares, err := Create(
+		nNeededShares,
+		nShares,
+		p,
+		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("recovered secret result: ")
+	// fmt.Println(secr)
+	if !bytes.Equal(k.Bytes(), secr.Bytes()) {
+		t.Errorf("reconstructed secret not correspond to original secret")
+	}
+	assert.Equal(t, k, secr)
+}