Initial data commit

Task/Tonelli-Shanks-algorithm/Go/tonelli-shanks-algorithm-1.go

@@ -0,0 +1,77 @@
+package main
+
+import "fmt"
+
+// Arguments n, p as described in WP
+// If Legendre symbol != 1, ok return is false.  Otherwise ok return is true,
+// R1 is WP return value R and for convenience R2 is p-R1.
+func ts(n, p int) (R1, R2 int, ok bool) {
+    // a^e mod p
+    powModP := func(a, e int) int {
+        s := 1
+        for ; e > 0; e-- {
+            s = s * a % p
+        }
+        return s
+    }
+    // Legendre symbol, returns 1, 0, or -1 mod p -- that's 1, 0, or p-1.
+    ls := func(a int) int {
+        return powModP(a, (p-1)/2)
+    }
+    // argument validation
+    if ls(n) != 1 {
+        return 0, 0, false
+    }
+    // WP step 1, factor out powers two.
+    // variables Q, S named as at WP.
+    Q := p - 1
+    S := 0
+    for Q&1 == 0 {
+        S++
+        Q >>= 1
+    }
+    // WP step 1, direct solution
+    if S == 1 {
+        R1 = powModP(n, (p+1)/4)
+        return R1, p - R1, true
+    }
+    // WP step 2, select z, assign c
+    z := 2
+    for ; ls(z) != p-1; z++ {
+    }
+    c := powModP(z, Q)
+    // WP step 3, assign R, t, M
+    R := powModP(n, (Q+1)/2)
+    t := powModP(n, Q)
+    M := S
+    // WP step 4, loop
+    for {
+        // WP step 4.1, termination condition
+        if t == 1 {
+            return R, p - R, true
+        }
+        // WP step 4.2, find lowest i...
+        i := 0
+        for z := t; z != 1 && i < M-1; {
+            z = z * z % p
+            i++
+        }
+        // WP step 4.3, using a variable b, assign new values of R, t, c, M
+        b := c
+        for e := M - i - 1; e > 0; e-- {
+            b = b * b % p
+        }
+        R = R * b % p
+        c = b * b % p // more convenient to compute c before t
+        t = t * c % p
+        M = i
+    }
+}
+
+func main() {
+    fmt.Println(ts(10, 13))
+    fmt.Println(ts(56, 101))
+    fmt.Println(ts(1030, 10009))
+    fmt.Println(ts(1032, 10009))
+    fmt.Println(ts(44402, 100049))
+}