BigMontgomery.hpp

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    Copyright (c) 2009-2010 Christopher A. Taylor.  All rights reserved.

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/*
    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