init: v1.0.0

gmath/primes.go

@@ -0,0 +1,48 @@
+package gmath
+
+import (
+	"crypto/rand"
+	"math/big"
+
+	"xdx.jelly/xgcl/grand"
+)
+
+const MRConst = 10
+
+// IsPrimeMR tests if n is prime by the Miller-Rabin prime testing method.
+func IsPrimeMR(n *big.Int) bool {
+	return n.ProbablyPrime(MRConst)
+}
+
+// MillerRabin tests if n is prime by the Miller-Rabin prime testing method.
+func MillerRabin(n *big.Int) bool {
+	// n = 2^s * r
+	n1 := new(big.Int)
+	n1.Sub(n, BigInt1)
+	r := new(big.Int).Set(n1)
+	s := 0
+	for r.Bit(0) == 0 {
+		s++
+		r = r.Rsh(r, 1)
+	}
+
+	for i := 0; i < MRConst; i++ {
+		a, _ := rand.Int(grand.Reader, n1)
+
+		//a = a^r mod n
+		a.Exp(a, r, n)
+		if a.Cmp(BigInt1) != 0 && a.Cmp(n1) != 0 {
+			for j := 1; j < s && a.Cmp(n1) != 0; j++ {
+				a.Mul(a, a)
+				a.Mod(a, n)
+				if a.Cmp(BigInt1) == 0 {
+					return false
+				}
+			}
+			if a.Cmp(n1) != 0 {
+				return false
+			}
+		}
+	}
+	return true
+}