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add lagrange interpolation to recover secret, add test

master
arnaucube 5 years ago
parent
commit
ce2ac4707e
2 changed files with 89 additions and 0 deletions
  1. +42
    -0
      shamirsecretsharing.go
  2. +47
    -0
      shamirsecretsharing_test.go

+ 42
- 0
shamirsecretsharing.go

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

+ 47
- 0
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)
}

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