1#ifndef CRYPTOPP_ALGEBRA_H
2#define CRYPTOPP_ALGEBRA_H
3
4#include "config.h"
5
6NAMESPACE_BEGIN(CryptoPP)
7
8class Integer;
9
10// "const Element&" returned by member functions are references
11// to internal data members. Since each object may have only
12// one such data member for holding results, the following code
13// will produce incorrect results:
14// abcd = group.Add(group.Add(a,b), group.Add(c,d));
15// But this should be fine:
16// abcd = group.Add(a, group.Add(b, group.Add(c,d));
17
18//! Abstract Group
19template <class T> class CRYPTOPP_NO_VTABLE AbstractGroup
20{
21public:
22	typedef T Element;
23
24	virtual ~AbstractGroup() {}
25
26	virtual bool Equal(const Element &a, const Element &b) const =0;
27	virtual const Element& Identity() const =0;
28	virtual const Element& Add(const Element &a, const Element &b) const =0;
29	virtual const Element& Inverse(const Element &a) const =0;
30	virtual bool InversionIsFast() const {return false;}
31
32	virtual const Element& Double(const Element &a) const;
33	virtual const Element& Subtract(const Element &a, const Element &b) const;
34	virtual Element& Accumulate(Element &a, const Element &b) const;
35	virtual Element& Reduce(Element &a, const Element &b) const;
36
37	virtual Element ScalarMultiply(const Element &a, const Integer &e) const;
38	virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
39
40	virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
41};
42
43//! Abstract Ring
44template <class T> class CRYPTOPP_NO_VTABLE AbstractRing : public AbstractGroup<T>
45{
46public:
47	typedef T Element;
48
49	AbstractRing() {m_mg.m_pRing = this;}
50	AbstractRing(const AbstractRing &source) {m_mg.m_pRing = this;}
51	AbstractRing& operator=(const AbstractRing &source) {return *this;}
52
53	virtual bool IsUnit(const Element &a) const =0;
54	virtual const Element& MultiplicativeIdentity() const =0;
55	virtual const Element& Multiply(const Element &a, const Element &b) const =0;
56	virtual const Element& MultiplicativeInverse(const Element &a) const =0;
57
58	virtual const Element& Square(const Element &a) const;
59	virtual const Element& Divide(const Element &a, const Element &b) const;
60
61	virtual Element Exponentiate(const Element &a, const Integer &e) const;
62	virtual Element CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const;
63
64	virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
65
66	virtual const AbstractGroup<T>& MultiplicativeGroup() const
67		{return m_mg;}
68
69private:
70	class MultiplicativeGroupT : public AbstractGroup<T>
71	{
72	public:
73		const AbstractRing<T>& GetRing() const
74			{return *m_pRing;}
75
76		bool Equal(const Element &a, const Element &b) const
77			{return GetRing().Equal(a, b);}
78
79		const Element& Identity() const
80			{return GetRing().MultiplicativeIdentity();}
81
82		const Element& Add(const Element &a, const Element &b) const
83			{return GetRing().Multiply(a, b);}
84
85		Element& Accumulate(Element &a, const Element &b) const
86			{return a = GetRing().Multiply(a, b);}
87
88		const Element& Inverse(const Element &a) const
89			{return GetRing().MultiplicativeInverse(a);}
90
91		const Element& Subtract(const Element &a, const Element &b) const
92			{return GetRing().Divide(a, b);}
93
94		Element& Reduce(Element &a, const Element &b) const
95			{return a = GetRing().Divide(a, b);}
96
97		const Element& Double(const Element &a) const
98			{return GetRing().Square(a);}
99
100		Element ScalarMultiply(const Element &a, const Integer &e) const
101			{return GetRing().Exponentiate(a, e);}
102
103		Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
104			{return GetRing().CascadeExponentiate(x, e1, y, e2);}
105
106		void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
107			{GetRing().SimultaneousExponentiate(results, base, exponents, exponentsCount);}
108
109		const AbstractRing<T> *m_pRing;
110	};
111
112	MultiplicativeGroupT m_mg;
113};
114
115// ********************************************************
116
117//! Base and Exponent
118template <class T, class E = Integer>
119struct BaseAndExponent
120{
121public:
122	BaseAndExponent() {}
123	BaseAndExponent(const T &base, const E &exponent) : base(base), exponent(exponent) {}
124	bool operator<(const BaseAndExponent<T, E> &rhs) const {return exponent < rhs.exponent;}
125	T base;
126	E exponent;
127};
128
129// VC60 workaround: incomplete member template support
130template <class Element, class Iterator>
131	Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group, Iterator begin, Iterator end);
132template <class Element, class Iterator>
133	Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring, Iterator begin, Iterator end);
134
135// ********************************************************
136
137//! Abstract Euclidean Domain
138template <class T> class CRYPTOPP_NO_VTABLE AbstractEuclideanDomain : public AbstractRing<T>
139{
140public:
141	typedef T Element;
142
143	virtual void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const =0;
144
145	virtual const Element& Mod(const Element &a, const Element &b) const =0;
146	virtual const Element& Gcd(const Element &a, const Element &b) const;
147
148protected:
149	mutable Element result;
150};
151
152// ********************************************************
153
154//! EuclideanDomainOf
155template <class T> class EuclideanDomainOf : public AbstractEuclideanDomain<T>
156{
157public:
158	typedef T Element;
159
160	EuclideanDomainOf() {}
161
162	bool Equal(const Element &a, const Element &b) const
163		{return a==b;}
164
165	const Element& Identity() const
166		{return Element::Zero();}
167
168	const Element& Add(const Element &a, const Element &b) const
169		{return result = a+b;}
170
171	Element& Accumulate(Element &a, const Element &b) const
172		{return a+=b;}
173
174	const Element& Inverse(const Element &a) const
175		{return result = -a;}
176
177	const Element& Subtract(const Element &a, const Element &b) const
178		{return result = a-b;}
179
180	Element& Reduce(Element &a, const Element &b) const
181		{return a-=b;}
182
183	const Element& Double(const Element &a) const
184		{return result = a.Doubled();}
185
186	const Element& MultiplicativeIdentity() const
187		{return Element::One();}
188
189	const Element& Multiply(const Element &a, const Element &b) const
190		{return result = a*b;}
191
192	const Element& Square(const Element &a) const
193		{return result = a.Squared();}
194
195	bool IsUnit(const Element &a) const
196		{return a.IsUnit();}
197
198	const Element& MultiplicativeInverse(const Element &a) const
199		{return result = a.MultiplicativeInverse();}
200
201	const Element& Divide(const Element &a, const Element &b) const
202		{return result = a/b;}
203
204	const Element& Mod(const Element &a, const Element &b) const
205		{return result = a%b;}
206
207	void DivisionAlgorithm(Element &r, Element &q, const Element &a, const Element &d) const
208		{Element::Divide(r, q, a, d);}
209
210	bool operator==(const EuclideanDomainOf<T> &rhs) const
211		{return true;}
212
213private:
214	mutable Element result;
215};
216
217//! Quotient Ring
218template <class T> class QuotientRing : public AbstractRing<typename T::Element>
219{
220public:
221	typedef T EuclideanDomain;
222	typedef typename T::Element Element;
223
224	QuotientRing(const EuclideanDomain &domain, const Element &modulus)
225		: m_domain(domain), m_modulus(modulus) {}
226
227	const EuclideanDomain & GetDomain() const
228		{return m_domain;}
229
230	const Element& GetModulus() const
231		{return m_modulus;}
232
233	bool Equal(const Element &a, const Element &b) const
234		{return m_domain.Equal(m_domain.Mod(m_domain.Subtract(a, b), m_modulus), m_domain.Identity());}
235
236	const Element& Identity() const
237		{return m_domain.Identity();}
238
239	const Element& Add(const Element &a, const Element &b) const
240		{return m_domain.Add(a, b);}
241
242	Element& Accumulate(Element &a, const Element &b) const
243		{return m_domain.Accumulate(a, b);}
244
245	const Element& Inverse(const Element &a) const
246		{return m_domain.Inverse(a);}
247
248	const Element& Subtract(const Element &a, const Element &b) const
249		{return m_domain.Subtract(a, b);}
250
251	Element& Reduce(Element &a, const Element &b) const
252		{return m_domain.Reduce(a, b);}
253
254	const Element& Double(const Element &a) const
255		{return m_domain.Double(a);}
256
257	bool IsUnit(const Element &a) const
258		{return m_domain.IsUnit(m_domain.Gcd(a, m_modulus));}
259
260	const Element& MultiplicativeIdentity() const
261		{return m_domain.MultiplicativeIdentity();}
262
263	const Element& Multiply(const Element &a, const Element &b) const
264		{return m_domain.Mod(m_domain.Multiply(a, b), m_modulus);}
265
266	const Element& Square(const Element &a) const
267		{return m_domain.Mod(m_domain.Square(a), m_modulus);}
268
269	const Element& MultiplicativeInverse(const Element &a) const;
270
271	bool operator==(const QuotientRing<T> &rhs) const
272		{return m_domain == rhs.m_domain && m_modulus == rhs.m_modulus;}
273
274protected:
275	EuclideanDomain m_domain;
276	Element m_modulus;
277};
278
279NAMESPACE_END
280
281#ifdef CRYPTOPP_MANUALLY_INSTANTIATE_TEMPLATES
282#include "algebra.cpp"
283#endif
284
285#endif
286