move crt solver

internal/lib/lib.go

@@ -36,3 +36,43 @@ func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
 
 	return repetend, nil
 }
+
+func CRTSolution(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
+	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
+	m1 := new(big.Int)
+	m2 := new(big.Int)
+	tmp := new(big.Int)
+	tmp.GCD(m1, m2, n1, n2)
+
+	// x = a1*m2*n2 + a2*m1*n1
+	x := new(big.Int).Set(a1)
+	x.Mul(x, m2)
+	x.Mul(x, n2)
+
+	tmp.Set(a2)
+	tmp.Mul(tmp, m1)
+	tmp.Mul(tmp, n1)
+
+	x.Add(x, tmp)
+
+	N := new(big.Int).Set(n1)
+	N.Mul(N, n2)
+
+	x.Mod(x, N)
+
+	return x, N
+}
+
+func ArePairwiseCoprime(moduli []*big.Int) bool {
+	z := new(big.Int)
+	for i, a := range moduli {
+		for _, b := range moduli[i+1:] {
+			z.GCD(nil, nil, a, b)
+			if z.Cmp(big.NewInt(1)) != 0 {
+				return false
+			}
+		}
+	}
+
+	return true
+}