Add an implementation of the Shanks-Tonelli algorithm, which is used to

find square roots modulo a prime. Contributed by FlexSecure GmbH

1 files changed, 82 insertions, 0 deletions

diff --git a/src/ressol.cpp b/src/ressol.cpp
new file mode 100644
index 000000000..e0967eae4
--- /dev/null
+++ b/src/ressol.cpp
@@ -0,0 +1,82 @@
+/*************************************************
+* Shanks-Tonnelli (RESSOL) Source File           *
+* (C) 2007-2008 Falko Strenzke, FlexSecure GmbH  *
+* (C) 2008 Jack Lloyd                            *
+*************************************************/
+
+#include <botan/numthry.h>
+#include <botan/reducer.h>
+
+#include <iostream>
+
+namespace Botan {
+
+/*************************************************
+* Shanks-Tonnelli algorithm                      *
+*************************************************/
+BigInt ressol(const BigInt& a, const BigInt& p)
+   {
+   if(a < 0)
+      throw Invalid_Argument("ressol(): a to solve for must be positive");
+   if(p <= 1)
+      throw Invalid_Argument("ressol(): prime must be > 1");
+
+   if(a == 0)
+      return 0;
+   if(p == 2)
+      return a;
+
+   if(jacobi(a, p) != 1) // not a quadratic residue
+      return -1;
+
+   if(p % 4 == 3)
+      return power_mod(a, ((p+1) >> 2), p);
+
+   u32bit s = low_zero_bits(p - 1);
+   BigInt q = p >> s;
+
+   q -= 1;
+   q >>= 1;
+
+   Modular_Reducer mod_p(p);
+
+   BigInt r = power_mod(a, q, p);
+   BigInt n = mod_p.multiply(a, mod_p.square(r));
+   r = mod_p.multiply(r, a);
+
+   if(n == 1)
+      return r;
+
+   // find random non quadratic residue z
+   BigInt z = 2;
+   while(jacobi(z, p) == 1) // while z quadratic residue
+      ++z;
+
+   BigInt c = power_mod(z, (q << 1) + 1, p);
+
+   while(n > 1)
+      {
+      q = n;
+
+      u32bit i = 0;
+      while(q != 1)
+         {
+         q = mod_p.square(q);
+         ++i;
+         }
+      u32bit t = s;
+
+      if(t <= i)
+         return -1;
+
+      c = power_mod(c, BigInt(BigInt::Power2, t-i-1), p);
+      r = mod_p.multiply(r, c);
+      c = mod_p.square(c);
+      n = mod_p.multiply(n, c);
+      s = i;
+      }
+
+   return r;
+   }
+
+}