Botan::Modular_Reducer Class Reference

#include <reducer.h>

Public Member Functions
BigInt	cube (const BigInt &x) const
const BigInt &	get_modulus () const
bool	initialized () const
	Modular_Reducer ()
	Modular_Reducer (const BigInt &mod)
BigInt	multiply (const BigInt &x, const BigInt &y) const
BigInt	reduce (const BigInt &x) const
BigInt	square (const BigInt &x) const

Detailed Description

Modular Reducer (using Barrett's technique)

Definition at line 18 of file reducer.h.

Constructor & Destructor Documentation

Modular_Reducer() [1/2]

Botan::Modular_Reducer::Modular_Reducer ( )

inline

Definition at line 52 of file reducer.h.

{ mod_words = 0; }

Referenced by Botan::Blinder::Blinder(), Botan::DSA_Verification_Operation::DSA_Verification_Operation(), Botan::ElGamal_Decryption_Operation::ElGamal_Decryption_Operation(), Botan::ElGamal_Encryption_Operation::ElGamal_Encryption_Operation(), Botan::Fixed_Window_Exponentiator::Fixed_Window_Exponentiator(), and Botan::NR_Verification_Operation::NR_Verification_Operation().

Modular_Reducer() [2/2]

Botan::Modular_Reducer::Modular_Reducer

(

const BigInt &

mod

)

Definition at line 16 of file reducer.cpp.

   {
   if(mod <= 0)
      throw Invalid_Argument("Modular_Reducer: modulus must be positive");
 
   modulus = mod;
   mod_words = modulus.sig_words();
 
   modulus_2 = Botan::square(modulus);
 
   mu = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words) / modulus;
   }

References Botan::BigInt::BigInt(), Botan::MP_WORD_BITS, Botan::BigInt::Power2, Botan::BigInt::sig_words(), and Botan::square().

Member Function Documentation

cube()

BigInt Botan::Modular_Reducer::cube ( const BigInt & x ) const

inline

Cube mod p

Parameters

x

Returns

(x * x * x) % p

Definition at line 47 of file reducer.h.

         { return multiply(x, this->square(x)); }

References multiply(), and square().

get_modulus()

const BigInt & Botan::Modular_Reducer::get_modulus ( ) const

inline

Definition at line 21 of file reducer.h.

{ return modulus; }

initialized()

bool Botan::Modular_Reducer::initialized ( ) const

inline

Definition at line 50 of file reducer.h.

{ return (mod_words != 0); }

multiply()

BigInt Botan::Modular_Reducer::multiply ( const BigInt & x, const BigInt & y ) const

inline

Multiply mod p

Parameters

x
y

Returns

(x * y) % p

Definition at line 31 of file reducer.h.

         { return reduce(x * y); }

References reduce().

Referenced by cube(), and Botan::ressol().

reduce()

BigInt Botan::Modular_Reducer::reduce

(

const BigInt &

x

)

const

Definition at line 32 of file reducer.cpp.

   {
   if(mod_words == 0)
      throw Invalid_State("Modular_Reducer: Never initalized");
 
   if(x.cmp(modulus, false) < 0)
      {
      if(x.is_negative())
         return x + modulus; // make positive
      return x;
      }
   else if(x.cmp(modulus_2, false) < 0)
      {
      BigInt t1 = x;
      t1.set_sign(BigInt::Positive);
      t1 >>= (MP_WORD_BITS * (mod_words - 1));
      t1 *= mu;
 
      t1 >>= (MP_WORD_BITS * (mod_words + 1));
      t1 *= modulus;
 
      t1.mask_bits(MP_WORD_BITS * (mod_words + 1));
 
      BigInt t2 = x;
      t2.set_sign(BigInt::Positive);
      t2.mask_bits(MP_WORD_BITS * (mod_words + 1));
 
      t2 -= t1;
 
      if(t2.is_negative())
         {
         BigInt b_to_k1(BigInt::Power2, MP_WORD_BITS * (mod_words + 1));
         t2 += b_to_k1;
         }
 
      while(t2 >= modulus)
         t2 -= modulus;
 
      if(x.is_positive())
         return t2;
      else
         return (modulus - t2);
      }
   else
      {
      // too big, fall back to normal division
      return (x % modulus);
      }
   }

References Botan::BigInt::cmp(), Botan::Invalid_State::Invalid_State(), Botan::BigInt::is_negative(), Botan::BigInt::is_positive(), Botan::BigInt::mask_bits(), Botan::MP_WORD_BITS, Botan::BigInt::Positive, Botan::BigInt::Power2, and Botan::BigInt::set_sign().

Referenced by multiply(), and square().

square()

BigInt Botan::Modular_Reducer::square ( const BigInt & x ) const

inline

Square mod p

Parameters

x

Returns

(x * x) % p

Definition at line 39 of file reducer.h.

         { return reduce(Botan::square(x)); }

References reduce(), and Botan::square().

Referenced by cube(), and Botan::ressol().

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

• src/math/numbertheory/reducer.h
• src/math/numbertheory/reducer.cpp