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/*
* (C) 2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/monty.h>
#include <botan/reducer.h>
#include <botan/internal/mp_core.h>
namespace Botan {
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_negative() || p.is_even())
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 = 2*m_p_words + 2;
if(ws.size() < output_size)
ws.resize(output_size);
BigInt z = x;
z.grow_to(output_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 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::Positive, 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::Positive, 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 + 2;
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 + 2;
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 + 2;
if(ws.size() < output_size)
ws.resize(output_size);
BigInt z(BigInt::Positive, 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 + 2;
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(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(params),
m_v(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::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);
}
}