1 files changed, 285 insertions, 0 deletions

diff --git a/lib/cryptopp/algebra.h b/lib/cryptopp/algebra.h
new file mode 100644
index 000000000..13038bd80
--- /dev/null
+++ b/lib/cryptopp/algebra.h
@@ -0,0 +1,285 @@
+#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