Botan::MontgomeryRep< Params > Class Template Reference

#include <pcurves_impl.h>

Public Types
using	Self = MontgomeryRep<Params>
typedef Params::W	W

Static Public Member Functions
static constexpr std::array< W, N >	from_rep (const std::array< W, N > &z)
static constexpr std::array< W, N >	one ()
static constexpr std::array< W, N >	redc (const std::array< W, 2 *N > &z)
static constexpr std::array< W, N >	to_rep (const std::array< W, N > &x)
static constexpr std::array< W, N >	wide_to_rep (const std::array< W, 2 *N > &x)

Static Public Attributes
static constexpr size_t	N = Params::N
static constexpr auto	P = Params::P
static constexpr auto	P_dash = monty_inverse(P[0])
static constexpr auto	R1 = montygomery_r(P)
static constexpr auto	R2 = mul_mod(R1, R1, P)
static constexpr auto	R3 = mul_mod(R1, R2, P)

Detailed Description

template<typename Params>
class Botan::MontgomeryRep< Params >

Montomgomery Representation of Integers

Integers modulo a prime (IntMod, see below) use some representation that allows for fast arithmetic.

The default representation used is Montgomery arithmetic. Curves with specialized fields (eg Mersenne primes, Solinas primes, or Crandall primes) provide a different type as the FieldRep parameter to the EllipticCurve template.

Since the curve parameters are public and known at compile time, we can similarly compute the Montgomery parameters at compile time.

Definition at line 80 of file pcurves_impl.h.

Member Typedef Documentation

Self

template<typename Params>

using Botan::MontgomeryRep< Params >::Self = MontgomeryRep<Params>

Definition at line 82 of file pcurves_impl.h.

W

template<typename Params>

typedef Params::W Botan::MontgomeryRep< Params >::W

Definition at line 86 of file pcurves_impl.h.

Member Function Documentation

from_rep()

template<typename Params>

constexpr std::array< W, N > Botan::MontgomeryRep< Params >::from_rep ( const std::array< W, N > & z )

inlinestaticconstexpr

Convert an integer out of Montgomery representation

Definition at line 137 of file pcurves_impl.h.

                                                                        {
         std::array<W, 2 * N> ze = {};
         copy_mem(std::span{ze}.template first<N>(), z);
         return Self::redc(ze);
      }

References Botan::copy_mem(), and redc().

one()

template<typename Params>

constexpr std::array< W, N > Botan::MontgomeryRep< Params >::one ( )

inlinestaticconstexpr

Return the constant one, pre-converted into Montgomery form

Definition at line 99 of file pcurves_impl.h.

{ return R1; }

References R1.

redc()

template<typename Params>

constexpr std::array< W, N > Botan::MontgomeryRep< Params >::redc ( const std::array< W, 2 *N > & z )

inlinestaticconstexpr

Modular reduction

Definition at line 104 of file pcurves_impl.h.

                                                                        {
         if constexpr(P_dash == 1) {
            return monty_redc_pdash1(z, P);
         } else {
            return monty_redc(z, P, P_dash);
         }
      }

References Botan::monty_redc(), Botan::monty_redc_pdash1(), P, and P_dash.

Referenced by from_rep(), to_rep(), and wide_to_rep().

to_rep()

template<typename Params>

constexpr std::array< W, N > Botan::MontgomeryRep< Params >::to_rep ( const std::array< W, N > & x )

inlinestaticconstexpr

Convert an integer into Montgomery representation

Definition at line 115 of file pcurves_impl.h.

                                                                      {
         std::array<W, 2 * N> z;  // NOLINT(*-member-init)
         comba_mul<N>(z.data(), x.data(), R2.data());
         return Self::redc(z);
      }

References Botan::comba_mul(), R2, and redc().

wide_to_rep()

template<typename Params>

constexpr std::array< W, N > Botan::MontgomeryRep< Params >::wide_to_rep ( const std::array< W, 2 *N > & x )

inlinestaticconstexpr

Wide reduction modulo the prime

Modular reduces an input of up to twice the length of the modulus, and converts it into Montgomery form.

Definition at line 127 of file pcurves_impl.h.

                                                                               {
         auto redc_x = Self::redc(x);
         std::array<W, 2 * N> z;  // NOLINT(*-member-init)
         comba_mul<N>(z.data(), redc_x.data(), R3.data());
         return Self::redc(z);
      }

References Botan::comba_mul(), R3, and redc().

Member Data Documentation

N

template<typename Params>

size_t Botan::MontgomeryRep< Params >::N = Params::N

staticconstexpr

Definition at line 85 of file pcurves_impl.h.

P

template<typename Params>

auto Botan::MontgomeryRep< Params >::P = Params::P

staticconstexpr

Definition at line 84 of file pcurves_impl.h.

Referenced by redc().

P_dash

template<typename Params>

auto Botan::MontgomeryRep< Params >::P_dash = monty_inverse(P[0])

staticconstexpr

Definition at line 90 of file pcurves_impl.h.

Referenced by redc().

R1

template<typename Params>

auto Botan::MontgomeryRep< Params >::R1 = montygomery_r(P)

staticconstexpr

Definition at line 92 of file pcurves_impl.h.

Referenced by one().

R2

template<typename Params>

auto Botan::MontgomeryRep< Params >::R2 = mul_mod(R1, R1, P)

staticconstexpr

Definition at line 93 of file pcurves_impl.h.

Referenced by to_rep().

R3

template<typename Params>

auto Botan::MontgomeryRep< Params >::R3 = mul_mod(R1, R2, P)

staticconstexpr

Definition at line 94 of file pcurves_impl.h.

Referenced by wide_to_rep().

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The documentation for this class was generated from the following file:

• src/lib/math/pcurves/pcurves_impl/pcurves_impl.h