Initial data commit

Task/Tonelli-Shanks-algorithm/Python/tonelli-shanks-algorithm.py

@@ -0,0 +1,42 @@
+def legendre(a, p):
+    return pow(a, (p - 1) // 2, p)
+
+def tonelli(n, p):
+    assert legendre(n, p) == 1, "not a square (mod p)"
+    q = p - 1
+    s = 0
+    while q % 2 == 0:
+        q //= 2
+        s += 1
+    if s == 1:
+        return pow(n, (p + 1) // 4, p)
+    for z in range(2, p):
+        if p - 1 == legendre(z, p):
+            break
+    c = pow(z, q, p)
+    r = pow(n, (q + 1) // 2, p)
+    t = pow(n, q, p)
+    m = s
+    t2 = 0
+    while (t - 1) % p != 0:
+        t2 = (t * t) % p
+        for i in range(1, m):
+            if (t2 - 1) % p == 0:
+                break
+            t2 = (t2 * t2) % p
+        b = pow(c, 1 << (m - i - 1), p)
+        r = (r * b) % p
+        c = (b * b) % p
+        t = (t * c) % p
+        m = i
+    return r
+
+if __name__ == '__main__':
+    ttest = [(10, 13), (56, 101), (1030, 10009), (44402, 100049),
+	     (665820697, 1000000009), (881398088036, 1000000000039),
+             (41660815127637347468140745042827704103445750172002, 10**50 + 577)]
+    for n, p in ttest:
+        r = tonelli(n, p)
+        assert (r * r - n) % p == 0
+        print("n = %d p = %d" % (n, p))
+        print("\t  roots : %d %d" % (r, p - r))