63 lines
992 B
Go
63 lines
992 B
Go
package lib
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import (
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"math/big"
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)
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func solveCRT(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
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// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
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m1 := new(big.Int)
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m2 := new(big.Int)
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tmp := new(big.Int)
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tmp.GCD(m1, m2, n1, n2)
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// x = a1*m2*n2 + a2*m1*n1
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x := new(big.Int).Set(a1)
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x.Mul(x, m2)
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x.Mul(x, n2)
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tmp.Set(a2)
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tmp.Mul(tmp, m1)
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tmp.Mul(tmp, n1)
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x.Add(x, tmp)
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N := new(big.Int).Set(n1)
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N.Mul(N, n2)
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x.Mod(x, N)
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return x, N
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}
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func CRTSolution(remainders, moduli []*big.Int) (*big.Int, *big.Int) {
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n1 := new(big.Int)
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a1 := new(big.Int)
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for i, n2 := range moduli {
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a2 := remainders[i]
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if i == 0 {
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a1.Set(a2)
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n1.Set(n2)
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continue
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}
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a1, n1 = solveCRT(a1, n1, a2, n2)
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}
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return a1, n1
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}
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func ArePairwiseCoprime(moduli []*big.Int) bool {
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z := new(big.Int)
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for i, a := range moduli {
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for _, b := range moduli[i+1:] {
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z.GCD(nil, nil, a, b)
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if z.Cmp(big.NewInt(1)) != 0 {
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return false
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}
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}
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}
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return true
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}
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