docs updated

shamirsecretsharing/README.md

@@ -0,0 +1,48 @@
+## Shamir Secret Sharing
+- https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing
+
+- [x] create secret sharing from number of secrets needed, number of shares, random point p, secret to share
+- [x] Lagrange Interpolation to restore the secret from the shares
+
+#### Usage
+```go
+// define secret to share
+k := 123456789
+
+// define random prime
+p, err := rand.Prime(rand.Reader, bits/2)
+if err!=nil {
+	fmt.Println(err)
+}
+
+// define how many shares want to generate
+nShares := big.NewInt(int64(6))
+
+// define how many shares are needed to recover the secret
+nNeededShares := big.NewInt(int64(3))
+
+// create the shares
+shares, err := Create(
+	nNeededShares,
+	nShares,
+	p,
+	big.NewInt(int64(k)))
+assert.Nil(t, err)
+if err!=nil {
+	fmt.Println(err)
+}
+
+// select shares to use
+var sharesToUse [][]*big.Int
+sharesToUse = append(sharesToUse, shares[2])
+sharesToUse = append(sharesToUse, shares[1])
+sharesToUse = append(sharesToUse, shares[0])
+
+// recover the secret using Lagrange Interpolation
+secr := LagrangeInterpolation(sharesToUse, p)
+
+// check that the restored secret matches the original secret
+if !bytes.Equal(k.Bytes(), secr.Bytes()) {
+	fmt.Println("reconstructed secret not correspond to original secret")
+}
+```

shamirsecretsharing/shamirsecretsharing_test.go

@@ -15,10 +15,10 @@ func TestCreate(t *testing.T) {
 	p, err := rand.Prime(rand.Reader, bits/2)
 	assert.Nil(t, err)
 
-	nNeededSecrets := big.NewInt(int64(3))
 	nShares := big.NewInt(int64(6))
+	nNeededShares := big.NewInt(int64(3))
 	shares, err := Create(
-		nNeededSecrets,
+		nNeededShares,
 		nShares,
 		p,
 		k)