1#ifndef CRYPTOPP_MODARITH_H 2#define CRYPTOPP_MODARITH_H 3 4// implementations are in integer.cpp 5 6#include "cryptlib.h" 7#include "misc.h" 8#include "integer.h" 9#include "algebra.h" 10 11NAMESPACE_BEGIN(CryptoPP) 12 13CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>; 14CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>; 15CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>; 16 17//! ring of congruence classes modulo n 18/*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */ 19class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer> 20{ 21public: 22 23 typedef int RandomizationParameter; 24 typedef Integer Element; 25 26 ModularArithmetic(const Integer &modulus = Integer::One()) 27 : m_modulus(modulus), m_result((word)0, modulus.reg.size()) {} 28 29 ModularArithmetic(const ModularArithmetic &ma) 30 : m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {} 31 32 ModularArithmetic(BufferedTransformation &bt); // construct from BER encoded parameters 33 34 virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);} 35 36 void DEREncode(BufferedTransformation &bt) const; 37 38 void DEREncodeElement(BufferedTransformation &out, const Element &a) const; 39 void BERDecodeElement(BufferedTransformation &in, Element &a) const; 40 41 const Integer& GetModulus() const {return m_modulus;} 42 void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());} 43 44 virtual bool IsMontgomeryRepresentation() const {return false;} 45 46 virtual Integer ConvertIn(const Integer &a) const 47 {return a%m_modulus;} 48 49 virtual Integer ConvertOut(const Integer &a) const 50 {return a;} 51 52 const Integer& Half(const Integer &a) const; 53 54 bool Equal(const Integer &a, const Integer &b) const 55 {return a==b;} 56 57 const Integer& Identity() const 58 {return Integer::Zero();} 59 60 const Integer& Add(const Integer &a, const Integer &b) const; 61 62 Integer& Accumulate(Integer &a, const Integer &b) const; 63 64 const Integer& Inverse(const Integer &a) const; 65 66 const Integer& Subtract(const Integer &a, const Integer &b) const; 67 68 Integer& Reduce(Integer &a, const Integer &b) const; 69 70 const Integer& Double(const Integer &a) const 71 {return Add(a, a);} 72 73 const Integer& MultiplicativeIdentity() const 74 {return Integer::One();} 75 76 const Integer& Multiply(const Integer &a, const Integer &b) const 77 {return m_result1 = a*b%m_modulus;} 78 79 const Integer& Square(const Integer &a) const 80 {return m_result1 = a.Squared()%m_modulus;} 81 82 bool IsUnit(const Integer &a) const 83 {return Integer::Gcd(a, m_modulus).IsUnit();} 84 85 const Integer& MultiplicativeInverse(const Integer &a) const 86 {return m_result1 = a.InverseMod(m_modulus);} 87 88 const Integer& Divide(const Integer &a, const Integer &b) const 89 {return Multiply(a, MultiplicativeInverse(b));} 90 91 Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const; 92 93 void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const; 94 95 unsigned int MaxElementBitLength() const 96 {return (m_modulus-1).BitCount();} 97 98 unsigned int MaxElementByteLength() const 99 {return (m_modulus-1).ByteCount();} 100 101 Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const 102 // left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct 103 { 104 return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 ) ) ; 105 } 106 107 bool operator==(const ModularArithmetic &rhs) const 108 {return m_modulus == rhs.m_modulus;} 109 110 static const RandomizationParameter DefaultRandomizationParameter ; 111 112protected: 113 Integer m_modulus; 114 mutable Integer m_result, m_result1; 115 116}; 117 118// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ; 119 120//! do modular arithmetics in Montgomery representation for increased speed 121/*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */ 122class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic 123{ 124public: 125 MontgomeryRepresentation(const Integer &modulus); // modulus must be odd 126 127 virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);} 128 129 bool IsMontgomeryRepresentation() const {return true;} 130 131 Integer ConvertIn(const Integer &a) const 132 {return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;} 133 134 Integer ConvertOut(const Integer &a) const; 135 136 const Integer& MultiplicativeIdentity() const 137 {return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;} 138 139 const Integer& Multiply(const Integer &a, const Integer &b) const; 140 141 const Integer& Square(const Integer &a) const; 142 143 const Integer& MultiplicativeInverse(const Integer &a) const; 144 145 Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const 146 {return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);} 147 148 void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const 149 {AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);} 150 151private: 152 Integer m_u; 153 mutable IntegerSecBlock m_workspace; 154}; 155 156NAMESPACE_END 157 158#endif 159