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DependentExtensions/cat/math/BigMontgomery.hpp

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+/*
+	Copyright (c) 2009-2010 Christopher A. Taylor.  All rights reserved.
+
+	Redistribution and use in source and binary forms, with or without
+	modification, are permitted provided that the following conditions are met:
+
+	* Redistributions of source code must retain the above copyright notice,
+	  this list of conditions and the following disclaimer.
+	* Redistributions in binary form must reproduce the above copyright notice,
+	  this list of conditions and the following disclaimer in the documentation
+	  and/or other materials provided with the distribution.
+	* Neither the name of LibCat nor the names of its contributors may be used
+	  to endorse or promote products derived from this software without
+	  specific prior written permission.
+
+	THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+	AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+	IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+	ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+	LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+	CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+	SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+	INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+	CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+	ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+	POSSIBILITY OF SUCH DAMAGE.
+*/
+
+/*
+    Several algorithms based on ideas from the "Handbook of Applied Cryptography"
+    http://www.cacr.math.uwaterloo.ca/hac/
+*/
+
+#ifndef CAT_BIG_MONTGOMERY_HPP
+#define CAT_BIG_MONTGOMERY_HPP
+
+#include <cat/math/BigRTL.hpp>
+#include <cat/rand/IRandom.hpp>
+
+namespace cat {
+
+
+// Performs fast modular arithmetic in the Montgomery Residue Number System
+class BigMontgomery : public BigRTL
+{
+    static const int MON_OVERHEAD = 3 + 4;
+    int mon_regs;
+
+protected:
+	Leg *TempProduct;
+	Leg *TempProductHi;
+    Leg *CachedModulus;
+	Leg mod_inv;
+
+public:
+    BigMontgomery(int regs, int bits);
+
+	// Must call SetModulus() before using this object
+	void SetModulus(const Leg *mod);
+
+public:
+    const Leg *GetModulus() { return CachedModulus; }
+    void CopyModulus(Leg *out);
+
+public:
+	// Convert value in register into RNS, stored in out
+	void MonInput(const Leg *in, Leg *out);
+
+	// Convert value in register from RNS, stored in out
+	void MonOutput(const Leg *in, Leg *out);
+
+	// Note: This will clobber the input product!
+	// Reduce a double-register product to a single register in the RNS
+	void MonReduceProduct(Leg *inout_product, Leg *out);
+
+public:
+	// Inputs and outputs must be in the Montgomery RNS
+    void MonAdd(const Leg *in_a, const Leg *in_b, Leg *out);
+    void MonSubtract(const Leg *in_a, const Leg *in_b, Leg *out);
+    void MonNegate(const Leg *in, Leg *out);
+    void MonDouble(const Leg *in, Leg *out);
+
+public:
+	// Inputs and outputs must be in the Montgomery RNS
+    void MonMultiply(const Leg *in_a, const Leg *in_b, Leg *out);
+    void MonSquare(const Leg *in, Leg *out);
+
+public:
+	// Base must be in the Montgomery RNS.  in_base != out
+	void MonExpMod(const Leg *in_base, const Leg *in_exp, Leg *out);
+
+public:
+	// Input is NOT in the RNS (don't call MonInput)
+	// Probably a prime, certainty = 4^-trials.  20: %99.9999999999 certainty
+	bool IsRabinMillerPrime(IRandom *prng, const Leg *n, int trials = 20);
+};
+
+
+} // namespace cat
+
+#endif // CAT_BIG_MONTGOMERY_HPP