add Create shares from secret with given parameters

shamirsecretsharing.go

@@ -0,0 +1,73 @@
+package shamirsecretsharing
+
+import (
+	"crypto/rand"
+	"errors"
+	"math/big"
+)
+
+const (
+	// bits = 1024
+	bits = 2048
+)
+
+// Create calculates the secrets to share from given parameters
+// t: number of secrets needed
+// n: number of shares
+// p: random point
+// k: secret to share
+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
+}