65 lines
1.7 KiB
Go
65 lines
1.7 KiB
Go
package paillier
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import (
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"crypto/rand"
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"io"
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"math/big"
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)
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var ZERO = big.NewInt(0)
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var ONE = big.NewInt(1)
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var TWO = big.NewInt(2)
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var FOUR = big.NewInt(4)
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// returns n! = n*(n-1)*(n-2)...3*2*1
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func Factorial(n int) *big.Int {
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ret := big.NewInt(1)
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for i := 1; i <= n; i++ {
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ret = new(big.Int).Mul(ret, big.NewInt(int64(i)))
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}
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return ret
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}
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// Returns 2 primes such that p = 2 * q + 1 and that the length of
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// p is nbits. `p` is called a safe prime
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func GenerateSafePrimes(nbits int, random io.Reader) (p, q *big.Int, err error) {
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for {
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q, err = rand.Prime(random, nbits-1)
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if err != nil {
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return
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}
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p = (new(big.Int)).Mul(q, big.NewInt(2))
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p = p.Add(p, big.NewInt(1))
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if p.ProbablyPrime(50) { //a probability of 2**-100 of not being prime
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return
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}
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}
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}
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// Generate a random element in the group of all the elements in Z/nZ that
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// has a multiplicative inverse.
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func GetRandomNumberInMultiplicativeGroup(n *big.Int, random io.Reader) (*big.Int, error) {
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r, err := rand.Int(random, n)
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if err != nil {
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return nil, err
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}
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zero := big.NewInt(0)
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one := big.NewInt(1)
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if zero.Cmp(r) == 0 || one.Cmp(new(big.Int).GCD(nil, nil, n, r)) != 0 {
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return GetRandomNumberInMultiplicativeGroup(n, random)
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}
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return r, nil
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}
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// Return a random generator of RQn with high probability. THIS METHOD
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// ONLY WORKS IF N IS THE PRODUCT OF TWO SAFE PRIMES! This heuristic is used
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// threshold signature paper in the Victor Shoup
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func GetRandomGeneratorOfTheQuadraticResidue(n *big.Int, rand io.Reader) (*big.Int, error) {
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r, err := GetRandomNumberInMultiplicativeGroup(n, rand)
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if err != nil {
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return nil, err
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}
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return new(big.Int).Mod(new(big.Int).Mul(r, r), n), nil
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}
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