shamir秘密共享 go语言实现

算法原理参考：shamir 秘密共享

大素数p的选取，这里选取的是128bit大素数
```
 prime, _ := rand.Prime(rand.Reader, 128)
```
Share和Polynomial 结构体定义，Share结构体定义了参与者拥有的秘密(x,y), Polynomial结构体定义了多项式，多项式的「知识」即该多项式的系数，知道多项式的系数，也就知道该多项式
```
type Share struct {x, y *big.Int
}type Polynomial struct {coefficients []*big.Intmodulus      *big.Int
}
```

拉格朗日插值算法实现：对定点shares，计算该多项式在x处的值，对于sss算法，秘密在x=0处，需要注意的是拉格朗日插值算法中有模除，需要转为乘以这个数的逆元

func Lagrange(x, modulus *big.Int, shares ...Share) *big.Int {xs := make([]*big.Int, len(shares))ys := make([]*big.Int, len(shares))for i := range shares {xs[i] = shares[i].xys[i] = shares[i].y}numerators := make([]*big.Int, len(xs))denominators := make([]*big.Int, len(ys))for i := range xs {numerators[i] = cal(xs, x, i)denominators[i] = cal(xs, xs[i], i)}result := big.NewInt(0)for i := range numerators {numerators[i].Mul(numerators[i], ys[i])numerators[i].Mod(numerators[i], modulus)v := (&big.Int{}).Set(numerators[i].Mul(numerators[i], denominators[i].ModInverse(denominators[i],modulus)))result.Add(result, v)}return result.Mod(result, modulus)
}

秘密分发：生成t-1次对多项式，若提供secret，则使用提供的秘密，否则随机生成秘密，随后计算n个参与者的秘密shares

func SecretDistribute(secret, modulus *big.Int, t, n int64) ([]Share, *big.Int) {if t > n {panic("t has to be less than n")}p := NewPolynomial(t, modulus)if secret != nil {p.coefficients[0] = secret}secret = p.coefficients[0]shares := make([]Share, n)for i := int64(0); i < n; i++ {x, _ := rand.Int(rand.Reader, modulus)y := p.valueAt(x)shares[i] = Share{x, y}}return shares, secret
}

验证

func main() {prime := prime128Bit()//secret := big.NewInt(12345678987654321)shares, secret1 := SecretDistribute(nil, prime, 5, 8)respect := Lagrange(big.NewInt(0), prime, shares[0], shares[5], shares[4], shares[1],shares[7])fmt.Println(secret1,respect)
}

完整代码：


package mainimport ("crypto/rand""fmt""math/big"
)type Share struct {x, y *big.Int
}type Polynomial struct {coefficients []*big.Intmodulus      *big.Int
}// Calculate the value of the polynomial at a point
func (p *Polynomial) eval(x *big.Int) *big.Int {length := len(p.coefficients)if length == 0 {return big.NewInt(0)}result := (&big.Int{}).Set(p.coefficients[length-1])for i := length - 1; i > 0; i-- {tmp := big.Int{}tmp.Mul(x, result)result.Add(p.coefficients[i-1], &tmp)result.Mod(result, p.modulus)}return result
}func NewPolynomial(degree int, modulus *big.Int) Polynomial {coefficients := make([]*big.Int, degree+1)for i := 0; i < degree+1; i++ {coefficients[i], _ = rand.Int(rand.Reader, modulus)}return Polynomial{coefficients, modulus}
}func Lagrange(x, modulus *big.Int, shares ...Share) *big.Int {xs := make([]*big.Int, len(shares))ys := make([]*big.Int, len(shares))for i := range shares {xs[i] = shares[i].xys[i] = shares[i].y}numerators := make([]*big.Int, len(xs))denominators := make([]*big.Int, len(ys))for i := range xs {numerators[i] = cal(xs, x, i, modulus)denominators[i] = cal(xs, xs[i], i, modulus)}result := big.NewInt(0)for i := range numerators {numerators[i].Mul(numerators[i], ys[i])numerators[i].Mod(numerators[i], modulus)v := (&big.Int{}).Set(numerators[i].Mul(numerators[i], denominators[i].ModInverse(denominators[i], modulus)))result.Add(result, v)}return result.Mod(result, modulus)
}func cal(xs []*big.Int, x *big.Int, i int, modulus *big.Int) *big.Int {res := big.NewInt(1)for j := 0; j < len(xs); j++ {if j != i {tmp := (&big.Int{}).Sub(x, xs[j])res.Mul(res, tmp)res.Mod(res, modulus)}}return res
}func SecretDistribute(secret, modulus *big.Int, t, n int) ([]Share, *big.Int) {if t > n {panic("t has to be less than n")}p := NewPolynomial(t-1, modulus)if secret != nil {p.coefficients[0] = secret}secret = p.coefficients[0]shares := make([]Share, n)for i := 0; i < n; i++ {x, _ := rand.Int(rand.Reader, modulus)y := p.eval(x)shares[i] = Share{x, y}}return shares, secret
}func main() {prime, _ := rand.Prime(rand.Reader, 128)//secret := big.NewInt(12345678987654321)shares, secret1 := SecretDistribute(nil, prime, 5, 8)respect := Lagrange(big.NewInt(0), prime, shares[0], shares[5], shares[4], shares[1], shares[7])fmt.Println(secret1, respect)
}

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