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/*
* Arithmetic for prime fields GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2009-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_GFP_ELEMENT_H__
#define BOTAN_GFP_ELEMENT_H__
#include <botan/bigint.h>
#include <botan/gfp_modulus.h>
#include <iosfwd>
namespace Botan {
struct BOTAN_DLL Illegal_Transformation : public Exception
{
Illegal_Transformation(const std::string& err =
"Requested transformation is not possible") :
Exception(err) {}
};
/**
* This class represents one element in GF(p). Enables the convenient,
* transparent use of the montgomery multiplication.
*/
class BOTAN_DLL GFpElement
{
public:
/** construct an element of GF(p) with the given value.
* use_montg defaults to false and determines wether Montgomery
* multiplications will be use when applying operators *, *=
* @param p the prime number of the field
* @param value the element value
* @param use_montgm whether this object will use Montgomery multiplication
*/
GFpElement(const BigInt& p, const BigInt& value, bool use_montgm = true);
// GFpElement(const GFpElement& other) = default;
// const GFpElement& operator=(const GFpElement& other) = default;
/**
* Switch Montgomery multiplcation optimizations ON
*/
void turn_on_sp_red_mul();
/**
* Switch Montgomery multiplcation optimizations OFF
*/
void turn_off_sp_red_mul();
/**
* += Operator
* @param rhs the GFpElement to add to the local value
* @result *this
*/
GFpElement& operator+=(const GFpElement& rhs);
/**
* -= Operator
* @param rhs the GFpElement to subtract from the local value
* @result *this
*/
GFpElement& operator-=(const GFpElement& rhs);
/**
* *= Operator
* @param rhs the GFpElement to multiply with the local value
* @result *this
*/
GFpElement& operator*=(const GFpElement& rhs);
/**
* /= Operator
* @param rhs the GFpElement to divide the local value by
* @result *this
*/
GFpElement& operator/=(const GFpElement& rhs);
/**
* *= Operator
* @param rhs the value to multiply with the local value
* @result *this
*/
GFpElement& operator*=(u32bit rhs);
/**
* Negate internal value(*this *= -1 )
* @return *this
*/
GFpElement& negate();
/**
* Assigns the inverse of *this to *this, i.e.
* *this = (*this)^(-1)
* @result *this
*/
GFpElement& inverse_in_place();
/**
* checks whether the value is zero (without provoking
* a backtransformation to the ordinary-residue)
* @result true, if the value is zero, false otherwise.
*/
bool is_zero();
/**
* return prime number of GF(p)
* @result a prime number
*/
const BigInt& get_p() const;
/**
* Return the represented value in GF(p)
* @result The value in GF(p)
*/
const BigInt& get_value() const;
/**
* Tells whether this GFpElement is currently transformed to an m-residue,
* i.e. in the form x_bar = x * r mod m.
* @result true if it is currently transformed to its m-residue.
*/
bool is_trf_to_mres() const;
/**
* Transforms this to x_bar = x * r mod m
* @result return the value x_bar.
*/
const BigInt& get_mres() const;
/**
* Check, if montgomery multiplication is used.
* @result true, if montgomery multiplication is used, false otherwise
*/
bool is_use_montgm() const
{
return m_use_montgm;
}
/**
* Transforms the arguments in such way that either both
* are in m-residue representation (returns true) or both are
* in ordinary residue representation (returns false).
* m-residue is prefered in case of ambiguity.
* does not toggle m_use_montgm of the arguments.
* Don't be confused about the constness of the arguments:
* the transformation between normal residue and m-residue is
* considered as leaving the object const.
* @param lhs the first operand to be aligned
* @param rhs the second operand to be aligned
* @result true if both are transformed to their m-residue,
* false it both are transformed to their normal residue.
*/
static bool align_operands_res(const GFpElement& lhs, const GFpElement& rhs);
/**
* swaps the states of *this and other, does not throw!
* @param other The value to swap with
*/
void swap(GFpElement& other);
private:
void ensure_montgm_precomp();
void trf_to_mres() const;
void trf_to_ordres() const;
GFpModulus modulus;
mutable BigInt m_value; // ordinary residue or m-residue respectively
// data members for montgomery multiplication
bool m_use_montgm;
mutable bool m_is_trf; // if m_value is montgomery
};
// relational operators
bool BOTAN_DLL operator==(const GFpElement& lhs, const GFpElement& rhs);
inline bool operator!=(const GFpElement& lhs, const GFpElement& rhs )
{
return !operator==(lhs, rhs);
}
// arithmetic operators
GFpElement BOTAN_DLL operator+(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator-(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator-(const GFpElement& lhs);
GFpElement BOTAN_DLL operator*(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator/(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator*(const GFpElement& lhs, u32bit rhs);
GFpElement BOTAN_DLL operator*(u32bit rhs, const GFpElement& lhs);
/**
* write a GFpElement to an output stream.
* @param output the output stream to write to
* @param elem the object to write
* @result the output stream
*/
BOTAN_DLL std::ostream& operator<<(std::ostream& output, const GFpElement& elem);
// return (*this)^(-1)
GFpElement BOTAN_DLL inverse(const GFpElement& elem);
// encoding and decoding
SecureVector<byte> BOTAN_DLL FE2OSP(const GFpElement& elem);
GFpElement BOTAN_DLL OS2FEP(MemoryRegion<byte> const& os, BigInt p);
inline void swap(GFpElement& x, GFpElement& y)
{
x.swap(y);
}
}
namespace std {
template<> inline
void swap<Botan::GFpElement>(Botan::GFpElement& x,
Botan::GFpElement& y)
{
x.swap(y);
}
}
#endif
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