Initial data commit

Task/Tonelli-Shanks-algorithm/Perl/tonelli-shanks-algorithm.pl

@@ -0,0 +1,58 @@
+use bigint;
+use ntheory qw(is_prime powmod kronecker);
+
+sub tonelli_shanks {
+    my($n,$p) = @_;
+    return if kronecker($n,$p) <= 0;
+    my $Q = $p - 1;
+    my $S = 0;
+    $Q >>= 1 and $S++ while 0 == $Q%2;
+    return powmod($n,int(($p+1)/4), $p) if $S == 1;
+
+    my $c;
+    for $n (2..$p) {
+        next if kronecker($n,$p) >= 0;
+        $c = powmod($n, $Q, $p);
+        last;
+    }
+
+    my $R = powmod($n, ($Q+1) >> 1, $p ); # ?
+    my $t = powmod($n, $Q, $p );
+    while (($t-1) % $p) {
+        my $b;
+        my $t2 = $t**2 % $p;
+        for (1 .. $S) {
+            if (0 == ($t2-1)%$p) {
+                $b = powmod($c, 1 << ($S-1-$_), $p);
+                $S = $_;
+                last;
+            }
+            $t2 = $t2**2 % $p;
+        }
+        $R = ($R * $b) % $p;
+        $c = $b**2 % $p;
+        $t = ($t * $c) % $p;
+    }
+    $R;
+}
+
+my @tests = (
+    (10, 13),
+    (56, 101),
+    (1030, 10009),
+    (1032, 10009),
+    (44402, 100049),
+    (665820697, 1000000009),
+    (881398088036, 1000000000039),
+);
+
+while (@tests) {
+    $n = shift @tests;
+    $p = shift @tests;
+    my $t = tonelli_shanks($n, $p);
+    if (!$t or ($t**2 - $n) % $p) {
+        printf "No solution for (%d, %d)\n", $n, $p;
+    } else {
+        printf "Roots of %d are (%d, %d) mod %d\n", $n, $t, $p-$t, $p;
+    }
+}