modarith.h
#ifndef CRYPTOPP_MODARITH_H
#define CRYPTOPP_MODARITH_H
// implementations are in integer.cpp
#include "cryptlib.h"
#include "misc.h"
#include "integer.h"
#include "algebra.h"
NAMESPACE_BEGIN(CryptoPP)
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
//! ring of congruence classes modulo n
/*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */
class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
{
public:
typedef int RandomizationParameter;
typedef Integer Element;
ModularArithmetic(const Integer &modulus = Integer::One())
: m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
ModularArithmetic(const ModularArithmetic &ma)
: m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}
ModularArithmetic(BufferedTransformation &bt); // construct from BER encoded parameters
virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
void DEREncode(BufferedTransformation &bt) const;
void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
void BERDecodeElement(BufferedTransformation &in, Element &a) const;
const Integer& GetModulus() const {return m_modulus;}
void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
virtual bool IsMontgomeryRepresentation() const {return false;}
virtual Integer ConvertIn(const Integer &a) const
{return a%m_modulus;}
virtual Integer ConvertOut(const Integer &a) const
{return a;}
const Integer& Half(const Integer &a) const;
bool Equal(const Integer &a, const Integer &b) const
{return a==b;}
const Integer& Identity() const
{return Integer::Zero();}
const Integer& Add(const Integer &a, const Integer &b) const;
Integer& Accumulate(Integer &a, const Integer &b) const;
const Integer& Inverse(const Integer &a) const;
const Integer& Subtract(const Integer &a, const Integer &b) const;
Integer& Reduce(Integer &a, const Integer &b) const;
const Integer& Double(const Integer &a) const
{return Add(a, a);}
const Integer& MultiplicativeIdentity() const
{return Integer::One();}
const Integer& Multiply(const Integer &a, const Integer &b) const
{return m_result1 = a*b%m_modulus;}
const Integer& Square(const Integer &a) const
{return m_result1 = a.Squared()%m_modulus;}
bool IsUnit(const Integer &a) const
{return Integer::Gcd(a, m_modulus).IsUnit();}
const Integer& MultiplicativeInverse(const Integer &a) const
{return m_result1 = a.InverseMod(m_modulus);}
const Integer& Divide(const Integer &a, const Integer &b) const
{return Multiply(a, MultiplicativeInverse(b));}
Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
unsigned int MaxElementBitLength() const
{return (m_modulus-1).BitCount();}
unsigned int MaxElementByteLength() const
{return (m_modulus-1).ByteCount();}
Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
{
return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 ) ) ;
}
bool operator==(const ModularArithmetic &rhs) const
{return m_modulus == rhs.m_modulus;}
static const RandomizationParameter DefaultRandomizationParameter ;
protected:
Integer m_modulus;
mutable Integer m_result, m_result1;
};
// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;
//! do modular arithmetics in Montgomery representation for increased speed
/*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */
class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
{
public:
MontgomeryRepresentation(const Integer &modulus); // modulus must be odd
virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
bool IsMontgomeryRepresentation() const {return true;}
Integer ConvertIn(const Integer &a) const
{return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
Integer ConvertOut(const Integer &a) const;
const Integer& MultiplicativeIdentity() const
{return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;}
const Integer& Multiply(const Integer &a, const Integer &b) const;
const Integer& Square(const Integer &a) const;
const Integer& MultiplicativeInverse(const Integer &a) const;
Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
{return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}
void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
{AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
private:
Integer m_u;
mutable IntegerSecBlock m_workspace;
};
NAMESPACE_END
#endif
Integer::One
static const Integer & One()
avoid calling constructors for these frequently used integers
SecBlock::resize
void resize(size_type newSize)
change size and preserve contents
Definition: secblock.h:396
Integer::Gcd
static Integer Gcd(const Integer &a, const Integer &n)
greatest common divisor
SecBlock< word, AllocatorWithCleanup< word, 0 > >
cryptlib.h
AbstractEuclideanDomain
Abstract Euclidean Domain.
Definition: algebra.h:138
Square
Square
Definition: square.h:19
ModularArithmetic
ring of congruence classes modulo n
Definition: modarith.h:19
RandomNumberGenerator
interface for random number generators
Definition: cryptlib.h:668
BufferedTransformation
interface for buffered transformations
Definition: cryptlib.h:770
AbstractRing
Abstract Ring.
Definition: algebra.h:44
Integer::IsUnit
bool IsUnit() const
is 1 or -1
Integer
multiple precision integer and basic arithmetics
Definition: integer.h:26
Integer::Power2
static Integer Power2(size_t e)
return the integer 2**e
AbstractGroup
Abstract Group.
Definition: algebra.h:19
MontgomeryRepresentation
do modular arithmetics in Montgomery representation for increased speed
Definition: modarith.h:122
Integer::InverseMod
Integer InverseMod(const Integer &n) const
calculate multiplicative inverse of *this mod n
integer.h
Integer::Zero
static const Integer & Zero()
avoid calling constructors for these frequently used integers