/usr/include/crypto++/algebra.h is in libcrypto++-dev 5.6.1-9.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 | #ifndef CRYPTOPP_ALGEBRA_H
#define CRYPTOPP_ALGEBRA_H
#include "config.h"
NAMESPACE_BEGIN(CryptoPP)
class Integer;
// "const Element&" returned by member functions are references
// to internal data members. Since each object may have only
// one such data member for holding results, the following code
// will produce incorrect results:
// abcd = group.Add(group.Add(a,b), group.Add(c,d));
// But this should be fine:
// abcd = group.Add(a, group.Add(b, group.Add(c,d));
//! Abstract Group
template <class T> class CRYPTOPP_NO_VTABLE AbstractGroup
{
public:
typedef T Element;
virtual ~AbstractGroup() {}
virtual bool Equal(const Element &a, const Element &b) const =0;
virtual const Element& Identity() const =0;
virtual const Element& Add(const Element &a, const Element &b) const =0;
virtual const Element& Inverse(const Element &a) const =0;
virtual bool InversionIsFast() const {return false;}
virtual const Element& Double(const Element &a) const;
virtual const Element& Subtract(const Element &a, const Element &b) const;
virtual Element& Accumulate(Element &a, const Element &b) const;
virtual Element& Reduce(Element &a, const Element &b) const;
virtual Element ScalarMultiply(const Element &a, const Integer &e) const;
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
};
//! Abstract Ring
template <class T> class CRYPTOPP_NO_VTABLE AbstractRing : public AbstractGroup<T>
{
public:
typedef T Element;
AbstractRing() {m_mg.m_pRing = this;}
AbstractRing(const AbstractRing &source) {m_mg.m_pRing = this;}
AbstractRing& operator=(const AbstractRing &source) {return *this;}
virtual bool IsUnit(const Element &a) const =0;
virtual const Element& MultiplicativeIdentity() const =0;
virtual const Element& Multiply(const Element &a, const Element &b) const =0;
virtual const Element& MultiplicativeInverse(const Element &a) const =0;
virtual const Element& Square(const Element &a) const;
virtual const Element& Divide(const Element &a, const Element &b) const;
virtual Element Exponentiate(const Element &a, const Integer &e) const;
virtual Element CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
virtual const AbstractGroup<T>& MultiplicativeGroup() const
{return m_mg;}
private:
class MultiplicativeGroupT : public AbstractGroup<T>
{
public:
const AbstractRing<T>& GetRing() const
{return *m_pRing;}
bool Equal(const Element &a, const Element &b) const
{return GetRing().Equal(a, b);}
const Element& Identity() const
{return GetRing().MultiplicativeIdentity();}
const Element& Add(const Element &a, const Element &b) const
{return GetRing().Multiply(a, b);}
Element& Accumulate(Element &a, const Element &b) const
{return a = GetRing().Multiply(a, b);}
const Element& Inverse(const Element &a) const
{return GetRing().MultiplicativeInverse(a);}
const Element& Subtract(const Element &a, const Element &b) const
{return GetRing().Divide(a, b);}
Element& Reduce(Element &a, const Element &b) const
{return a = GetRing().Divide(a, b);}
const Element& Double(const Element &a) const
{return GetRing().Square(a);}
Element ScalarMultiply(const Element &a, const Integer &e) const
{return GetRing().Exponentiate(a, e);}
Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
{return GetRing().CascadeExponentiate(x, e1, y, e2);}
void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
{GetRing().SimultaneousExponentiate(results, base, exponents, exponentsCount);}
const AbstractRing<T> *m_pRing;
};
MultiplicativeGroupT m_mg;
};
// ********************************************************
//! Base and Exponent
template <class T, class E = Integer>
struct BaseAndExponent
{
public:
BaseAndExponent() {}
BaseAndExponent(const T &base, const E &exponent) : base(base), exponent(exponent) {}
bool operator<(const BaseAndExponent<T, E> &rhs) const {return exponent < rhs.exponent;}
T base;
E exponent;
};
// VC60 workaround: incomplete member template support
template <class Element, class Iterator>
Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group, Iterator begin, Iterator end);
template <class Element, class Iterator>
Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring, Iterator begin, Iterator end);
// ********************************************************
//! Abstract Euclidean Domain
template <class T> class CRYPTOPP_NO_VTABLE AbstractEuclideanDomain : public AbstractRing<T>
{
public:
typedef T Element;
virtual void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const =0;
virtual const Element& Mod(const Element &a, const Element &b) const =0;
virtual const Element& Gcd(const Element &a, const Element &b) const;
protected:
mutable Element result;
};
// ********************************************************
//! EuclideanDomainOf
template <class T> class EuclideanDomainOf : public AbstractEuclideanDomain<T>
{
public:
typedef T Element;
EuclideanDomainOf() {}
bool Equal(const Element &a, const Element &b) const
{return a==b;}
const Element& Identity() const
{return Element::Zero();}
const Element& Add(const Element &a, const Element &b) const
{return result = a+b;}
Element& Accumulate(Element &a, const Element &b) const
{return a+=b;}
const Element& Inverse(const Element &a) const
{return result = -a;}
const Element& Subtract(const Element &a, const Element &b) const
{return result = a-b;}
Element& Reduce(Element &a, const Element &b) const
{return a-=b;}
const Element& Double(const Element &a) const
{return result = a.Doubled();}
const Element& MultiplicativeIdentity() const
{return Element::One();}
const Element& Multiply(const Element &a, const Element &b) const
{return result = a*b;}
const Element& Square(const Element &a) const
{return result = a.Squared();}
bool IsUnit(const Element &a) const
{return a.IsUnit();}
const Element& MultiplicativeInverse(const Element &a) const
{return result = a.MultiplicativeInverse();}
const Element& Divide(const Element &a, const Element &b) const
{return result = a/b;}
const Element& Mod(const Element &a, const Element &b) const
{return result = a%b;}
void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const
{Element::Divide(r, q, a, d);}
bool operator==(const EuclideanDomainOf<T> &rhs) const
{return true;}
private:
mutable Element result;
};
//! Quotient Ring
template <class T> class QuotientRing : public AbstractRing<typename T::Element>
{
public:
typedef T EuclideanDomain;
typedef typename T::Element Element;
QuotientRing(const EuclideanDomain &domain, const Element &modulus)
: m_domain(domain), m_modulus(modulus) {}
const EuclideanDomain & GetDomain() const
{return m_domain;}
const Element& GetModulus() const
{return m_modulus;}
bool Equal(const Element &a, const Element &b) const
{return m_domain.Equal(m_domain.Mod(m_domain.Subtract(a, b), m_modulus), m_domain.Identity());}
const Element& Identity() const
{return m_domain.Identity();}
const Element& Add(const Element &a, const Element &b) const
{return m_domain.Add(a, b);}
Element& Accumulate(Element &a, const Element &b) const
{return m_domain.Accumulate(a, b);}
const Element& Inverse(const Element &a) const
{return m_domain.Inverse(a);}
const Element& Subtract(const Element &a, const Element &b) const
{return m_domain.Subtract(a, b);}
Element& Reduce(Element &a, const Element &b) const
{return m_domain.Reduce(a, b);}
const Element& Double(const Element &a) const
{return m_domain.Double(a);}
bool IsUnit(const Element &a) const
{return m_domain.IsUnit(m_domain.Gcd(a, m_modulus));}
const Element& MultiplicativeIdentity() const
{return m_domain.MultiplicativeIdentity();}
const Element& Multiply(const Element &a, const Element &b) const
{return m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
const Element& Square(const Element &a) const
{return m_domain.Mod(m_domain.Square(a), m_modulus);}
const Element& MultiplicativeInverse(const Element &a) const;
bool operator==(const QuotientRing<T> &rhs) const
{return m_domain == rhs.m_domain && m_modulus == rhs.m_modulus;}
protected:
EuclideanDomain m_domain;
Element m_modulus;
};
NAMESPACE_END
#ifdef CRYPTOPP_MANUALLY_INSTANTIATE_TEMPLATES
#include "algebra.cpp"
#endif
#endif
|