Add: Shors Algorithm implementation in GO

compression_algorithms/shors/shors.go

@@ -0,0 +1,81 @@
+package main
+
+import (
+	"fmt"
+	"math/rand"
+	"time"
+)
+
+func gcd(m, n int) int {
+	for n != 0 {
+		m, n = n, m%n
+	}
+	return m
+}
+
+func order(a, N int) int {
+	for i := 1; i < N; i++ {
+		if mExpo(a, i, N) == 1 {
+			return i
+		}
+	}
+	return -1
+}
+func mExpo(b, e, m int) int {
+	total := 1
+	b = b % m
+	for e > 0 {
+		if e%2 == 1 {
+			total = (total * b) % m
+		}
+		e = e >> 1
+		b = (b * b) % m
+	}
+	return total
+}
+
+func Shors(N int) (int, int) {
+	rand.Seed(time.Now().UnixNano())
+	a := rand.Intn(N-1) + 1
+	g := gcd(a, N)
+	if g != 1 {
+		return g, N / g
+	}
+
+	if N%2 == 0 {
+		return 2, N / 2
+	}
+
+	o := order(a, N)
+	if o == -1 {
+		return 0, 0
+	}
+
+	if o%2 == 0 {
+		x1 := mExpo(a, o/2, N)
+		if x1 != N-1 {
+			f1 := gcd(a-1, N)
+			f2 := N / f1
+			return f1, f2
+		}
+	}
+	return 0, 0
+}
+
+func main() {
+	N := 12
+	//N:= 16
+	//N:=342
+	//N:= 100
+	fmt.Println("Trying to factorize N:", N)
+
+	for {
+		p, q := Shors(N)
+		if p != 0 && q != 0 {
+			fmt.Printf("Factors of %d: %d and %d\n", N, p, q)
+			break
+		} else {
+			fmt.Println("No factors found, retrying...")
+		}
+	}
+}