text: // modarith.h - originally written and placed in the public domain by Wei Dai
  
  /// \file modarith.h
  /// \brief Class file for performing modular arithmetic.
  
  #ifndef CRYPTOPP_MODARITH_H
  #define CRYPTOPP_MODARITH_H
  
  // implementations are in integer.cpp
  
  #include "cryptlib.h"
  #include "integer.h"
  #include "algebra.h"
  #include "secblock.h"
  #include "misc.h"
  
  #if CRYPTOPP_MSC_VERSION
  # pragma warning(push)
  # pragma warning(disable: 4231 4275)
  #endif
  
  NAMESPACE_BEGIN(CryptoPP)
  
  CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
  CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
  CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
  
  /// \brief Ring of congruence classes modulo n
  /// \details This implementation represents each congruence class as the smallest
  ///   non-negative integer in that class.
  /// \details <tt>const Element&</tt> 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:
  ///   <pre>    abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
  ///   But this should be fine:
  ///   <pre>    abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
  class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
  {
  public:
  
  	typedef int RandomizationParameter;
  	typedef Integer Element;
  
  	virtual ~ModularArithmetic() {}
  
  	/// \brief Construct a ModularArithmetic
  	/// \param modulus congruence class modulus
  	ModularArithmetic(const Integer &modulus = Integer::One())
  		: AbstractRing<Integer>(), m_modulus(modulus), m_result(static_cast<word>(0), modulus.reg.size()) {}
  
  	/// \brief Copy construct a ModularArithmetic
  	/// \param ma other ModularArithmetic
  	ModularArithmetic(const ModularArithmetic &ma)
  		: AbstractRing<Integer>(), m_modulus(ma.m_modulus), m_result(static_cast<word>(0), ma.m_modulus.reg.size()) {}
  
  	/// \brief Construct a ModularArithmetic
  	/// \param bt BER encoded ModularArithmetic
  	ModularArithmetic(BufferedTransformation &bt);	// construct from BER encoded parameters
  
  	/// \brief Clone a ModularArithmetic
  	/// \returns pointer to a new ModularArithmetic
  	/// \details Clone effectively copy constructs a new ModularArithmetic. The caller is
  	///   responsible for deleting the pointer returned from this method.
  	virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
  
  	/// \brief Encodes in DER format
  	/// \param bt BufferedTransformation object
  	void DEREncode(BufferedTransformation &bt) const;
  
  	/// \brief Encodes element in DER format
  	/// \param out BufferedTransformation object
  	/// \param a Element to encode
  	void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
  
  	/// \brief Decodes element in DER format
  	/// \param in BufferedTransformation object
  	/// \param a Element to decode
  	void BERDecodeElement(BufferedTransformation &in, Element &a) const;
  
  	/// \brief Retrieves the modulus
  	/// \returns the modulus
  	const Integer& GetModulus() const {return m_modulus;}
  
  	/// \brief Sets the modulus
  	/// \param newModulus the new modulus
  	void SetModulus(const Integer &newModulus)
  		{m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
  
  	/// \brief Retrieves the representation
  	/// \returns true if the if the modulus is in Montgomery form for multiplication, false otherwise
  	virtual bool IsMontgomeryRepresentation() const {return false;}
  
  	/// \brief Reduces an element in the congruence class
  	/// \param a element to convert
  	/// \returns the reduced element
  	/// \details ConvertIn is useful for derived classes, like MontgomeryRepresentation, which
  	///   must convert between representations.
  	virtual Integer ConvertIn(const Integer &a) const
  		{return a%m_modulus;}
  
  	/// \brief Reduces an element in the congruence class
  	/// \param a element to convert
  	/// \returns the reduced element
  	/// \details ConvertOut is useful for derived classes, like MontgomeryRepresentation, which
  	///   must convert between representations.
  	virtual Integer ConvertOut(const Integer &a) const
  		{return a;}
  
  	/// \brief Divides an element by 2
  	/// \param a element to convert
  	const Integer& Half(const Integer &a) const;
  
  	/// \brief Compare two elements for equality
  	/// \param a first element
  	/// \param b second element
  	/// \returns true if the elements are equal, false otherwise
  	/// \details Equal() tests the elements for equality using <tt>a==b</tt>
  	bool Equal(const Integer &a, const Integer &b) const
  		{return a==b;}
  
  	/// \brief Provides the Identity element
  	/// \returns the Identity element
  	const Integer& Identity() const
  		{return Integer::Zero();}
  
  	/// \brief Adds elements in the ring
  	/// \param a first element
  	/// \param b second element
  	/// \returns the sum of <tt>a</tt> and <tt>b</tt>
  	const Integer& Add(const Integer &a, const Integer &b) const;
  
  	/// \brief TODO
  	/// \param a first element
  	/// \param b second element
  	/// \returns TODO
  	Integer& Accumulate(Integer &a, const Integer &b) const;
  
  	/// \brief Inverts the element in the ring
  	/// \param a first element
  	/// \returns the inverse of the element
  	const Integer& Inverse(const Integer &a) const;
  
  	/// \brief Subtracts elements in the ring
  	/// \param a first element
  	/// \param b second element
  	/// \returns the difference of <tt>a</tt> and <tt>b</tt>. The element <tt>a</tt> must provide a Subtract member function.
  	const Integer& Subtract(const Integer &a, const Integer &b) const;
  
  	/// \brief TODO
  	/// \param a first element
  	/// \param b second element
  	/// \returns TODO
  	Integer& Reduce(Integer &a, const Integer &b) const;
  
  	/// \brief Doubles an element in the ring
  	/// \param a the element
  	/// \returns the element doubled
  	/// \details Double returns <tt>Add(a, a)</tt>. The element <tt>a</tt> must provide an Add member function.
  	const Integer& Double(const Integer &a) const
  		{return Add(a, a);}
  
  	/// \brief Retrieves the multiplicative identity
  	/// \returns the multiplicative identity
  	/// \details the base class implementations returns 1.
  	const Integer& MultiplicativeIdentity() const
  		{return Integer::One();}
  
  	/// \brief Multiplies elements in the ring
  	/// \param a the multiplicand
  	/// \param b the multiplier
  	/// \returns the product of a and b
  	/// \details Multiply returns <tt>a*b\%n</tt>.
  	const Integer& Multiply(const Integer &a, const Integer &b) const
  		{return m_result1 = a*b%m_modulus;}
  
  	/// \brief Square an element in the ring
  	/// \param a the element
  	/// \returns the element squared
  	/// \details Square returns <tt>a*a\%n</tt>. The element <tt>a</tt> must provide a Square member function.
  	const Integer& Square(const Integer &a) const
  		{return m_result1 = a.Squared()%m_modulus;}
  
  	/// \brief Determines whether an element is a unit in the ring
  	/// \param a the element
  	/// \returns true if the element is a unit after reduction, false otherwise.
  	bool IsUnit(const Integer &a) const
  		{return Integer::Gcd(a, m_modulus).IsUnit();}
  
  	/// \brief Calculate the multiplicative inverse of an element in the ring
  	/// \param a the element
  	/// \details MultiplicativeInverse returns <tt>a<sup>-1</sup>\%n</tt>. The element <tt>a</tt> must
  	///   provide a InverseMod member function.
  	const Integer& MultiplicativeInverse(const Integer &a) const
  		{return m_result1 = a.InverseMod(m_modulus);}
  
  	/// \brief Divides elements in the ring
  	/// \param a the dividend
  	/// \param b the divisor
  	/// \returns the quotient
  	/// \details Divide returns <tt>a*b<sup>-1</sup>\%n</tt>.
  	const Integer& Divide(const Integer &a, const Integer &b) const
  		{return Multiply(a, MultiplicativeInverse(b));}
  
  	/// \brief TODO
  	/// \param x first element
  	/// \param e1 first exponent
  	/// \param y second element
  	/// \param e2 second exponent
  	/// \returns TODO
  	Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
  
  	/// \brief Exponentiates a base to multiple exponents in the ring
  	/// \param results an array of Elements
  	/// \param base the base to raise to the exponents
  	/// \param exponents an array of exponents
  	/// \param exponentsCount the number of exponents in the array
  	/// \details SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the
  	///   result at the respective position in the results array.
  	/// \details SimultaneousExponentiate() must be implemented in a derived class.
  	/// \pre <tt>COUNTOF(results) == exponentsCount</tt>
  	/// \pre <tt>COUNTOF(exponents) == exponentsCount</tt>
  	void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
  
  	/// \brief Provides the maximum bit size of an element in the ring
  	/// \returns maximum bit size of an element
  	unsigned int MaxElementBitLength() const
  		{return (m_modulus-1).BitCount();}
  
  	/// \brief Provides the maximum byte size of an element in the ring
  	/// \returns maximum byte size of an element
  	unsigned int MaxElementByteLength() const
  		{return (m_modulus-1).ByteCount();}
  
  	/// \brief Provides a random element in the ring
  	/// \param rng RandomNumberGenerator used to generate material
  	/// \param ignore_for_now unused
  	/// \returns a random element that is uniformly distributed
  	/// \details RandomElement constructs a new element in the range <tt>[0,n-1]</tt>, inclusive.
  	///   The element's class must provide a constructor with the signature <tt>Element(RandomNumberGenerator rng,
  	///   Element min, Element max)</tt>.
  	Element RandomElement(RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0) const
  		// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
  	{
  		CRYPTOPP_UNUSED(ignore_for_now);
  		return Element(rng, Integer::Zero(), m_modulus - Integer::One()) ;
  	}
  
  	/// \brief Compares two ModularArithmetic for equality
  	/// \param rhs other ModularArithmetic
  	/// \returns true if this is equal to the other, false otherwise
  	/// \details The operator tests for equality using <tt>this.m_modulus == rhs.m_modulus</tt>.
  	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 ;
  
  /// \brief Performs modular arithmetic in Montgomery representation for increased speed
  /// \details The Montgomery representation represents each congruence class <tt>[a]</tt> as
  ///   <tt>a*r\%n</tt>, where <tt>r</tt> is a convenient power of 2.
  /// \details <tt>const Element&</tt> 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:
  ///   <pre>    abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
  ///   But this should be fine:
  ///   <pre>    abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
  class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
  {
  public:
  	virtual ~MontgomeryRepresentation() {}
  
  	/// \brief Construct a MontgomeryRepresentation
  	/// \param modulus congruence class modulus
  	/// \note The modulus must be odd.
  	MontgomeryRepresentation(const Integer &modulus);
  
  	/// \brief Clone a MontgomeryRepresentation
  	/// \returns pointer to a new MontgomeryRepresentation
  	/// \details Clone effectively copy constructs a new MontgomeryRepresentation. The caller is
  	///   responsible for deleting the pointer returned from this method.
  	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
  
  #if CRYPTOPP_MSC_VERSION
  # pragma warning(pop)
  #endif
  
  #endif
  