Initial data commit

Task/Tonelli-Shanks-algorithm/Go/tonelli-shanks-algorithm-2.go

@@ -0,0 +1,72 @@
+package main
+
+import (
+    "fmt"
+    "math/big"
+)
+
+func ts(n, p big.Int) (R1, R2 big.Int, ok bool) {
+    if big.Jacobi(&n, &p) != 1 {
+        return
+    }
+    var one, Q big.Int
+    one.SetInt64(1)
+    Q.Sub(&p, &one)
+    S := 0
+    for Q.Bit(0) == 0 {
+        S++
+        Q.Rsh(&Q, 1)
+    }
+    if S == 1 {
+        R1.Exp(&n, R1.Rsh(R1.Add(&p, &one), 2), &p)
+        R2.Sub(&p, &R1)
+        return R1, R2, true
+    }
+    var z, c big.Int
+    for z.SetInt64(2); big.Jacobi(&z, &p) != -1; z.Add(&z, &one) {
+    }
+    c.Exp(&z, &Q, &p)
+    var R, t big.Int
+    R.Exp(&n, R.Rsh(R.Add(&Q, &one), 1), &p)
+    t.Exp(&n, &Q, &p)
+    M := S
+    for {
+        if t.Cmp(&one) == 0 {
+            R2.Sub(&p, &R)
+            return R, R2, true
+        }
+        i := 0
+        // reuse z as a scratch variable
+        for z.Set(&t); z.Cmp(&one) != 0 && i < M-1; {
+            z.Mod(z.Mul(&z, &z), &p)
+            i++
+        }
+        // and instead of a new scratch variable b, continue using z
+        z.Set(&c)
+        for e := M - i - 1; e > 0; e-- {
+            z.Mod(z.Mul(&z, &z), &p)
+        }
+        R.Mod(R.Mul(&R, &z), &p)
+        c.Mod(c.Mul(&z, &z), &p)
+        t.Mod(t.Mul(&t, &c), &p)
+        M = i
+    }
+}
+
+func main() {
+    var n, p big.Int
+    n.SetInt64(665820697)
+    p.SetInt64(1000000009)
+    R1, R2, ok := ts(n, p)
+    fmt.Println(&R1, &R2, ok)
+
+    n.SetInt64(881398088036)
+    p.SetInt64(1000000000039)
+    R1, R2, ok = ts(n, p)
+    fmt.Println(&R1, &R2, ok)
+    n.SetString("41660815127637347468140745042827704103445750172002", 10)
+    p.SetString("100000000000000000000000000000000000000000000000577", 10)
+    R1, R2, ok = ts(n, p)
+    fmt.Println(&R1)
+    fmt.Println(&R2)
+}