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322 lines
13 KiB
C++
322 lines
13 KiB
C++
// modarith.h - written and placed in the public domain by Wei Dai
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//! \file modarith.h
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//! \brief Class file for performing modular arithmetic.
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#ifndef CRYPTOPP_MODARITH_H
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#define CRYPTOPP_MODARITH_H
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// implementations are in integer.cpp
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#include "cryptlib.h"
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#include "integer.h"
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#include "algebra.h"
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#include "secblock.h"
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#include "misc.h"
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NAMESPACE_BEGIN(CryptoPP)
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
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CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
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//! \class ModularArithmetic
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//! \brief Ring of congruence classes modulo n
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//! \details This implementation represents each congruence class as the smallest
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//! non-negative integer in that class.
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//! \details <tt>const Element&</tt> returned by member functions are references
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//! to internal data members. Since each object may have only
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//! one such data member for holding results, the following code
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//! will produce incorrect results:
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//! <pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
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//! But this should be fine:
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//! <pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
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class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
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{
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public:
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typedef int RandomizationParameter;
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typedef Integer Element;
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#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
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virtual ~ModularArithmetic() {}
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#endif
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//! \brief Construct a ModularArithmetic
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//! \param modulus congruence class modulus
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ModularArithmetic(const Integer &modulus = Integer::One())
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: AbstractRing<Integer>(), m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
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//! \brief Copy construct a ModularArithmetic
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//! \param ma other ModularArithmetic
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ModularArithmetic(const ModularArithmetic &ma)
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: AbstractRing<Integer>(), m_modulus(ma.m_modulus), m_result((word)0, ma.m_modulus.reg.size()) {}
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//! \brief Construct a ModularArithmetic
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//! \param bt BER encoded ModularArithmetic
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ModularArithmetic(BufferedTransformation &bt); // construct from BER encoded parameters
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//! \brief Clone a ModularArithmetic
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//! \returns pointer to a new ModularArithmetic
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//! \details Clone effectively copy constructs a new ModularArithmetic. The caller is
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//! responsible for deleting the pointer returned from this method.
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virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
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//! \brief Encodes in DER format
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//! \param bt BufferedTransformation object
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void DEREncode(BufferedTransformation &bt) const;
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//! \brief Encodes element in DER format
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//! \param out BufferedTransformation object
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//! \param a Element to encode
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void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
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//! \brief Decodes element in DER format
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//! \param in BufferedTransformation object
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//! \param a Element to decode
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void BERDecodeElement(BufferedTransformation &in, Element &a) const;
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//! \brief Retrieves the modulus
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//! \returns the modulus
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const Integer& GetModulus() const {return m_modulus;}
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//! \brief Sets the modulus
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//! \param newModulus the new modulus
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void SetModulus(const Integer &newModulus)
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{m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
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//! \brief Retrieves the representation
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//! \returns true if the representation is MontgomeryRepresentation, false otherwise
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virtual bool IsMontgomeryRepresentation() const {return false;}
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//! \brief Reduces an element in the congruence class
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//! \param a element to convert
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//! \returns the reduced element
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//! \details ConvertIn is useful for derived classes, like MontgomeryRepresentation, which
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//! must convert between representations.
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virtual Integer ConvertIn(const Integer &a) const
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{return a%m_modulus;}
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//! \brief Reduces an element in the congruence class
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//! \param a element to convert
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//! \returns the reduced element
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//! \details ConvertOut is useful for derived classes, like MontgomeryRepresentation, which
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//! must convert between representations.
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virtual Integer ConvertOut(const Integer &a) const
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{return a;}
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//! \brief TODO
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//! \param a element to convert
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const Integer& Half(const Integer &a) const;
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//! \brief Compare two elements for equality
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//! \param a first element
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//! \param b second element
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//! \returns true if the elements are equal, false otherwise
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//! \details Equal() tests the elements for equality using <tt>a==b</tt>
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bool Equal(const Integer &a, const Integer &b) const
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{return a==b;}
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//! \brief Provides the Identity element
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//! \returns the Identity element
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const Integer& Identity() const
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{return Integer::Zero();}
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//! \brief Adds elements in the ring
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//! \param a first element
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//! \param b second element
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//! \returns the sum of <tt>a</tt> and <tt>b</tt>
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const Integer& Add(const Integer &a, const Integer &b) const;
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//! \brief TODO
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//! \param a first element
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//! \param b second element
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//! \returns TODO
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Integer& Accumulate(Integer &a, const Integer &b) const;
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//! \brief Inverts the element in the ring
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//! \param a first element
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//! \returns the inverse of the element
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const Integer& Inverse(const Integer &a) const;
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//! \brief Subtracts elements in the ring
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//! \param a first element
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//! \param b second element
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//! \returns the difference of <tt>a</tt> and <tt>b</tt>. The element <tt>a</tt> must provide a Subtract member function.
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const Integer& Subtract(const Integer &a, const Integer &b) const;
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//! \brief TODO
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//! \param a first element
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//! \param b second element
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//! \returns TODO
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Integer& Reduce(Integer &a, const Integer &b) const;
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//! \brief Doubles an element in the ring
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//! \param a the element
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//! \returns the element doubled
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//! \details Double returns <tt>Add(a, a)</tt>. The element <tt>a</tt> must provide an Add member function.
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const Integer& Double(const Integer &a) const
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{return Add(a, a);}
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//! \brief Retrieves the multiplicative identity
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//! \returns the multiplicative identity
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//! \details the base class implementations returns 1.
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const Integer& MultiplicativeIdentity() const
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{return Integer::One();}
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//! \brief Multiplies elements in the ring
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//! \param a the multiplicand
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//! \param b the multiplier
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//! \returns the product of a and b
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//! \details Multiply returns <tt>a*b\%n</tt>.
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const Integer& Multiply(const Integer &a, const Integer &b) const
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{return m_result1 = a*b%m_modulus;}
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//! \brief Square an element in the ring
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//! \param a the element
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//! \returns the element squared
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//! \details Square returns <tt>a*a\%n</tt>. The element <tt>a</tt> must provide a Square member function.
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const Integer& Square(const Integer &a) const
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{return m_result1 = a.Squared()%m_modulus;}
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//! \brief Determines whether an element is a unit in the ring
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//! \param a the element
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//! \returns true if the element is a unit after reduction, false otherwise.
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bool IsUnit(const Integer &a) const
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{return Integer::Gcd(a, m_modulus).IsUnit();}
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//! \brief Calculate the multiplicative inverse of an element in the ring
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//! \param a the element
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//! \details MultiplicativeInverse returns <tt>a<sup>-1</sup>\%n</tt>. The element <tt>a</tt> must
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//! provide a InverseMod member function.
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const Integer& MultiplicativeInverse(const Integer &a) const
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{return m_result1 = a.InverseMod(m_modulus);}
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//! \brief Divides elements in the ring
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//! \param a the dividend
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//! \param b the divisor
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//! \returns the quotient
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//! \details Divide returns <tt>a*b<sup>-1</sup>\%n</tt>.
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const Integer& Divide(const Integer &a, const Integer &b) const
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{return Multiply(a, MultiplicativeInverse(b));}
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//! \brief TODO
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//! \param x first element
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//! \param e1 first exponent
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//! \param y second element
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//! \param e2 second exponent
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//! \returns TODO
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Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const;
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//! \brief Exponentiates a base to multiple exponents in the ring
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//! \param results an array of Elements
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//! \param base the base to raise to the exponents
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//! \param exponents an array of exponents
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//! \param exponentsCount the number of exponents in the array
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//! \details SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the
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//! result at the respective position in the results array.
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//! \details SimultaneousExponentiate() must be implemented in a derived class.
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//! \pre <tt>COUNTOF(results) == exponentsCount</tt>
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//! \pre <tt>COUNTOF(exponents) == exponentsCount</tt>
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void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
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//! \brief Provides the maximum bit size of an element in the ring
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//! \returns maximum bit size of an element
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unsigned int MaxElementBitLength() const
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{return (m_modulus-1).BitCount();}
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//! \brief Provides the maximum byte size of an element in the ring
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//! \returns maximum byte size of an element
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unsigned int MaxElementByteLength() const
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{return (m_modulus-1).ByteCount();}
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//! \brief Provides a random element in the ring
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//! \param rng RandomNumberGenerator used to generate material
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//! \param ignore_for_now unused
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//! \returns a random element that is uniformly distributed
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//! \details RandomElement constructs a new element in the range <tt>[0,n-1]</tt>, inclusive.
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//! The element's class must provide a constructor with the signature <tt>Element(RandomNumberGenerator rng,
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//! Element min, Element max)</tt>.
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Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0) const
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// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
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{
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CRYPTOPP_UNUSED(ignore_for_now);
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return Element(rng, Integer::Zero(), m_modulus - Integer::One()) ;
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}
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//! \brief Compares two ModularArithmetic for equality
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//! \param rhs other ModularArithmetic
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//! \returns true if this is equal to the other, false otherwise
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//! \details The operator tests for equality using <tt>this.m_modulus == rhs.m_modulus</tt>.
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bool operator==(const ModularArithmetic &rhs) const
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{return m_modulus == rhs.m_modulus;}
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static const RandomizationParameter DefaultRandomizationParameter ;
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protected:
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Integer m_modulus;
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mutable Integer m_result, m_result1;
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};
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// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;
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//! \class MontgomeryRepresentation
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//! \brief Performs modular arithmetic in Montgomery representation for increased speed
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//! \details The Montgomery representation represents each congruence class <tt>[a]</tt> as
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//! <tt>a*r\%n</tt>, where <tt>r</tt> is a convenient power of 2.
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//! \details <tt>const Element&</tt> returned by member functions are references
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//! to internal data members. Since each object may have only
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//! one such data member for holding results, the following code
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//! will produce incorrect results:
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//! <pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre>
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//! But this should be fine:
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//! <pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre>
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class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
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{
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public:
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#ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
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virtual ~MontgomeryRepresentation() {}
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#endif
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//! \brief Construct a IsMontgomeryRepresentation
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//! \param modulus congruence class modulus
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//! \note The modulus must be odd.
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MontgomeryRepresentation(const Integer &modulus);
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//! \brief Clone a MontgomeryRepresentation
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//! \returns pointer to a new MontgomeryRepresentation
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//! \details Clone effectively copy constructs a new MontgomeryRepresentation. The caller is
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//! responsible for deleting the pointer returned from this method.
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virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
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bool IsMontgomeryRepresentation() const {return true;}
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Integer ConvertIn(const Integer &a) const
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{return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
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Integer ConvertOut(const Integer &a) const;
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const Integer& MultiplicativeIdentity() const
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{return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_modulus;}
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const Integer& Multiply(const Integer &a, const Integer &b) const;
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const Integer& Square(const Integer &a) const;
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const Integer& MultiplicativeInverse(const Integer &a) const;
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Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const
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{return AbstractRing<Integer>::CascadeExponentiate(x, e1, y, e2);}
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void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
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{AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
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private:
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Integer m_u;
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mutable IntegerSecBlock m_workspace;
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};
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NAMESPACE_END
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#endif
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