monty.cpp

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/*
* (C) 2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/internal/monty.h>
#include <botan/reducer.h>
#include <botan/internal/mp_core.h>
 
#include <utility>
 
namespace Botan {
 
word monty_inverse(word a)
   {
   if(a % 2 == 0)
      throw Invalid_Argument("monty_inverse only valid for odd integers");
 
   /*
   * From "A New Algorithm for Inversion mod p^k" by Çetin Kaya Koç
   * https://eprint.iacr.org/2017/411.pdf sections 5 and 7.
   */
 
   word b = 1;
   word r = 0;
 
   for(size_t i = 0; i != BOTAN_MP_WORD_BITS; ++i)
      {
      const word bi = b % 2;
      r >>= 1;
      r += bi << (BOTAN_MP_WORD_BITS - 1);
 
      b -= a * bi;
      b >>= 1;
      }
 
   // Now invert in addition space
   r = (MP_WORD_MAX - r) + 1;
 
   return r;
   }
 
Montgomery_Params::Montgomery_Params(const BigInt& p,
                                     const Modular_Reducer& mod_p)
   {
   if(p.is_even() || p < 3)
      throw Invalid_Argument("Montgomery_Params invalid modulus");
 
   m_p = p;
   m_p_words = m_p.sig_words();
   m_p_dash = monty_inverse(m_p.word_at(0));
 
   const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
 
   m_r1 = mod_p.reduce(r);
   m_r2 = mod_p.square(m_r1);
   m_r3 = mod_p.multiply(m_r1, m_r2);
   }
 
Montgomery_Params::Montgomery_Params(const BigInt& p)
   {
   if(p.is_even() || p < 3)
      throw Invalid_Argument("Montgomery_Params invalid modulus");
 
   m_p = p;
   m_p_words = m_p.sig_words();
   m_p_dash = monty_inverse(m_p.word_at(0));
 
   const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
 
   // It might be faster to use ct_modulo here vs setting up Barrett reduction?
   Modular_Reducer mod_p(p);
 
   m_r1 = mod_p.reduce(r);
   m_r2 = mod_p.square(m_r1);
   m_r3 = mod_p.multiply(m_r1, m_r2);
   }
 
BigInt Montgomery_Params::inv_mod_p(const BigInt& x) const
   {
   // TODO use Montgomery inverse here?
   return inverse_mod(x, p());
   }
 
BigInt Montgomery_Params::redc(const BigInt& x, secure_vector<word>& ws) const
   {
   const size_t output_size = m_p_words + 1;
 
   if(ws.size() < output_size)
      ws.resize(output_size);
 
   BigInt z = x;
   z.grow_to(2*m_p_words);
 
   bigint_monty_redc(z.mutable_data(),
                     m_p.data(), m_p_words, m_p_dash,
                     ws.data(), ws.size());
 
   return z;
   }
 
BigInt Montgomery_Params::mul(const BigInt& x, const BigInt& y,
                              secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words + 2;
 
   if(ws.size() < output_size)
      ws.resize(output_size);
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
   BOTAN_DEBUG_ASSERT(y.sig_words() <= m_p_words);
 
   BigInt z = BigInt::with_capacity(output_size);
   bigint_mul(z.mutable_data(), z.size(),
              x.data(), x.size(), std::min(m_p_words, x.size()),
              y.data(), y.size(), std::min(m_p_words, y.size()),
              ws.data(), ws.size());
 
   bigint_monty_redc(z.mutable_data(),
                     m_p.data(), m_p_words, m_p_dash,
                     ws.data(), ws.size());
 
   return z;
   }
 
BigInt Montgomery_Params::mul(const BigInt& x,
                              const secure_vector<word>& y,
                              secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words + 2;
   if(ws.size() < output_size)
      ws.resize(output_size);
   BigInt z = BigInt::with_capacity(output_size);
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
 
   bigint_mul(z.mutable_data(), z.size(),
              x.data(), x.size(), std::min(m_p_words, x.size()),
              y.data(), y.size(), std::min(m_p_words, y.size()),
              ws.data(), ws.size());
 
   bigint_monty_redc(z.mutable_data(),
                     m_p.data(), m_p_words, m_p_dash,
                     ws.data(), ws.size());
 
   return z;
   }
 
void Montgomery_Params::mul_by(BigInt& x,
                               const secure_vector<word>& y,
                               secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words;
 
   if(ws.size() < 2*output_size)
      ws.resize(2*output_size);
 
   word* z_data = &ws[0];
   word* ws_data = &ws[output_size];
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
 
   bigint_mul(z_data, output_size,
              x.data(), x.size(), std::min(m_p_words, x.size()),
              y.data(), y.size(), std::min(m_p_words, y.size()),
              ws_data, output_size);
 
   bigint_monty_redc(z_data,
                     m_p.data(), m_p_words, m_p_dash,
                     ws_data, output_size);
 
   if(x.size() < output_size)
      x.grow_to(output_size);
   copy_mem(x.mutable_data(), z_data, output_size);
   }
 
void Montgomery_Params::mul_by(BigInt& x,
                               const BigInt& y,
                               secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words;
 
   if(ws.size() < 2*output_size)
      ws.resize(2*output_size);
 
   word* z_data = &ws[0];
   word* ws_data = &ws[output_size];
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
 
   bigint_mul(z_data, output_size,
              x.data(), x.size(), std::min(m_p_words, x.size()),
              y.data(), y.size(), std::min(m_p_words, y.size()),
              ws_data, output_size);
 
   bigint_monty_redc(z_data,
                     m_p.data(), m_p_words, m_p_dash,
                     ws_data, output_size);
 
   if(x.size() < output_size)
      x.grow_to(output_size);
   copy_mem(x.mutable_data(), z_data, output_size);
   }
 
BigInt Montgomery_Params::sqr(const BigInt& x, secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words;
 
   if(ws.size() < output_size)
      ws.resize(output_size);
 
   BigInt z = BigInt::with_capacity(output_size);
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
 
   bigint_sqr(z.mutable_data(), z.size(),
              x.data(), x.size(), std::min(m_p_words, x.size()),
              ws.data(), ws.size());
 
   bigint_monty_redc(z.mutable_data(),
                     m_p.data(), m_p_words, m_p_dash,
                     ws.data(), ws.size());
 
   return z;
   }
 
void Montgomery_Params::square_this(BigInt& x,
                                    secure_vector<word>& ws) const
   {
   const size_t output_size = 2*m_p_words;
 
   if(ws.size() < 2*output_size)
      ws.resize(2*output_size);
 
   word* z_data = &ws[0];
   word* ws_data = &ws[output_size];
 
   BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
 
   bigint_sqr(z_data, output_size,
              x.data(), x.size(), std::min(m_p_words, x.size()),
              ws_data, output_size);
 
   bigint_monty_redc(z_data,
                     m_p.data(), m_p_words, m_p_dash,
                     ws_data, output_size);
 
   if(x.size() < output_size)
      x.grow_to(output_size);
   copy_mem(x.mutable_data(), z_data, output_size);
   }
 
Montgomery_Int::Montgomery_Int(const std::shared_ptr<const Montgomery_Params>& params,
                               const BigInt& v,
                               bool redc_needed) :
   m_params(params)
   {
   if(redc_needed == false)
      {
      m_v = v;
      }
   else
      {
      BOTAN_ASSERT_NOMSG(m_v < m_params->p());
      secure_vector<word> ws;
      m_v = m_params->mul(v, m_params->R2(), ws);
      }
   }
 
Montgomery_Int::Montgomery_Int(const std::shared_ptr<const Montgomery_Params>& params,
                               const uint8_t bits[], size_t len,
                               bool redc_needed) :
   m_params(params),
   m_v(bits, len)
   {
   if(redc_needed)
      {
      BOTAN_ASSERT_NOMSG(m_v < m_params->p());
      secure_vector<word> ws;
      m_v = m_params->mul(m_v, m_params->R2(), ws);
      }
   }
 
Montgomery_Int::Montgomery_Int(std::shared_ptr<const Montgomery_Params> params,
                               const word words[], size_t len,
                               bool redc_needed) :
   m_params(std::move(params))
   {
   m_v.set_words(words, len);
 
   if(redc_needed)
      {
      BOTAN_ASSERT_NOMSG(m_v < m_params->p());
      secure_vector<word> ws;
      m_v = m_params->mul(m_v, m_params->R2(), ws);
      }
   }
 
void Montgomery_Int::fix_size()
   {
   const size_t p_words = m_params->p_words();
 
   if(m_v.sig_words() > p_words)
      throw Internal_Error("Montgomery_Int::fix_size v too large");
 
   m_v.grow_to(p_words);
   }
 
bool Montgomery_Int::operator==(const Montgomery_Int& other) const
   {
   return m_v == other.m_v && m_params->p() == other.m_params->p();
   }
 
std::vector<uint8_t> Montgomery_Int::serialize() const
   {
   std::vector<uint8_t> v(size());
   BigInt::encode_1363(v.data(), v.size(), value());
   return v;
   }
 
size_t Montgomery_Int::size() const
   {
   return m_params->p().bytes();
   }
 
bool Montgomery_Int::is_one() const
   {
   return m_v == m_params->R1();
   }
 
bool Montgomery_Int::is_zero() const
   {
   return m_v.is_zero();
   }
 
BigInt Montgomery_Int::value() const
   {
   secure_vector<word> ws;
   return m_params->redc(m_v, ws);
   }
 
Montgomery_Int Montgomery_Int::operator+(const Montgomery_Int& other) const
   {
   secure_vector<word> ws;
   BigInt z = m_v;
   z.mod_add(other.m_v, m_params->p(), ws);
   return Montgomery_Int(m_params, z, false);
   }
 
Montgomery_Int Montgomery_Int::operator-(const Montgomery_Int& other) const
   {
   secure_vector<word> ws;
   BigInt z = m_v;
   z.mod_sub(other.m_v, m_params->p(), ws);
   return Montgomery_Int(m_params, z, false);
   }
 
Montgomery_Int& Montgomery_Int::operator+=(const Montgomery_Int& other)
   {
   secure_vector<word> ws;
   return this->add(other, ws);
   }
 
Montgomery_Int& Montgomery_Int::add(const Montgomery_Int& other, secure_vector<word>& ws)
   {
   m_v.mod_add(other.m_v, m_params->p(), ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::operator-=(const Montgomery_Int& other)
   {
   secure_vector<word> ws;
   return this->sub(other, ws);
   }
 
Montgomery_Int& Montgomery_Int::sub(const Montgomery_Int& other, secure_vector<word>& ws)
   {
   m_v.mod_sub(other.m_v, m_params->p(), ws);
   return (*this);
   }
 
Montgomery_Int Montgomery_Int::operator*(const Montgomery_Int& other) const
   {
   secure_vector<word> ws;
   return Montgomery_Int(m_params, m_params->mul(m_v, other.m_v, ws), false);
   }
 
Montgomery_Int Montgomery_Int::mul(const Montgomery_Int& other,
                                   secure_vector<word>& ws) const
   {
   return Montgomery_Int(m_params, m_params->mul(m_v, other.m_v, ws), false);
   }
 
Montgomery_Int& Montgomery_Int::mul_by(const Montgomery_Int& other,
                                       secure_vector<word>& ws)
   {
   m_params->mul_by(m_v, other.m_v, ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::mul_by(const secure_vector<word>& other,
                                       secure_vector<word>& ws)
   {
   m_params->mul_by(m_v, other, ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::operator*=(const Montgomery_Int& other)
   {
   secure_vector<word> ws;
   return mul_by(other, ws);
   }
 
Montgomery_Int& Montgomery_Int::operator*=(const secure_vector<word>& other)
   {
   secure_vector<word> ws;
   return mul_by(other, ws);
   }
 
Montgomery_Int& Montgomery_Int::square_this_n_times(secure_vector<word>& ws, size_t n)
   {
   for(size_t i = 0; i != n; ++i)
      m_params->square_this(m_v, ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::square_this(secure_vector<word>& ws)
   {
   m_params->square_this(m_v, ws);
   return (*this);
   }
 
Montgomery_Int Montgomery_Int::square(secure_vector<word>& ws) const
   {
   return Montgomery_Int(m_params, m_params->sqr(m_v, ws), false);
   }
 
Montgomery_Int Montgomery_Int::cube(secure_vector<word>& ws) const
   {
   return Montgomery_Int(m_params, m_params->sqr(m_v, ws), false);
   }
 
Montgomery_Int Montgomery_Int::multiplicative_inverse() const
   {
   secure_vector<word> ws;
   const BigInt iv = m_params->mul(m_params->inv_mod_p(m_v), m_params->R3(), ws);
   return Montgomery_Int(m_params, iv, false);
   }
 
Montgomery_Int Montgomery_Int::additive_inverse() const
   {
   return Montgomery_Int(m_params, m_params->p()) - (*this);
   }
 
Montgomery_Int& Montgomery_Int::mul_by_2(secure_vector<word>& ws)
   {
   m_v.mod_mul(2, m_params->p(), ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::mul_by_3(secure_vector<word>& ws)
   {
   m_v.mod_mul(3, m_params->p(), ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::mul_by_4(secure_vector<word>& ws)
   {
   m_v.mod_mul(4, m_params->p(), ws);
   return (*this);
   }
 
Montgomery_Int& Montgomery_Int::mul_by_8(secure_vector<word>& ws)
   {
   m_v.mod_mul(8, m_params->p(), ws);
   return (*this);
   }
 
}