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/*
* Division Algorithm
* (C) 1999-2007,2012,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/divide.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_madd.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/bit_ops.h>
namespace Botan {
namespace {
/*
* Handle signed operands, if necessary
*/
void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r)
{
if(x.sign() != y.sign())
q.flip_sign();
if(x.is_negative() && r.is_nonzero())
{
q -= 1;
r = y.abs() - r;
}
}
inline bool division_check(word q, word y2, word y1,
word x3, word x2, word x1)
{
/*
Compute (y3,y2,y1) = (y2,y1) * q
and return true if (y3,y2,y1) > (x3,x2,x1)
*/
word y3 = 0;
y1 = word_madd2(q, y1, &y3);
y2 = word_madd2(q, y2, &y3);
const word x[3] = { x1, x2, x3 };
const word y[3] = { y1, y2, y3 };
return bigint_ct_is_lt(x, 3, y, 3).is_set();
}
}
void ct_divide(const BigInt& x, const BigInt& y, BigInt& q_out, BigInt& r_out)
{
const size_t x_words = x.sig_words();
const size_t y_words = y.sig_words();
const size_t x_bits = x.bits();
BigInt q(BigInt::Positive, x_words);
BigInt r(BigInt::Positive, y_words);
BigInt t(BigInt::Positive, y_words); // a temporary
for(size_t i = 0; i != x_bits; ++i)
{
const size_t b = x_bits - 1 - i;
const bool x_b = x.get_bit(b);
r *= 2;
r.conditionally_set_bit(0, x_b);
const bool r_gte_y = bigint_sub3(t.mutable_data(), r.data(), r.size(), y.data(), y_words) == 0;
q.conditionally_set_bit(b, r_gte_y);
r.ct_cond_swap(r_gte_y, t);
}
sign_fixup(x, y, q, r);
r_out = r;
q_out = q;
}
void ct_divide_u8(const BigInt& x, uint8_t y, BigInt& q_out, uint8_t& r_out)
{
const size_t x_words = x.sig_words();
const size_t x_bits = x.bits();
BigInt q(BigInt::Positive, x_words);
uint32_t r = 0;
for(size_t i = 0; i != x_bits; ++i)
{
const size_t b = x_bits - 1 - i;
const bool x_b = x.get_bit(b);
r *= 2;
r += x_b;
const auto r_gte_y = CT::Mask<uint32_t>::is_gte(r, y);
q.conditionally_set_bit(b, r_gte_y.is_set());
r = r_gte_y.select(r - y, r);
}
if(x.is_negative())
{
q.flip_sign();
if(r != 0)
{
--q;
r = y - r;
}
}
r_out = static_cast<uint8_t>(r);
q_out = q;
}
BigInt ct_modulo(const BigInt& x, const BigInt& y)
{
if(y.is_negative() || y.is_zero())
throw Invalid_Argument("ct_modulo requires y > 0");
const size_t y_words = y.sig_words();
const size_t x_bits = x.bits();
BigInt r(BigInt::Positive, y_words);
BigInt t(BigInt::Positive, y_words);
for(size_t i = 0; i != x_bits; ++i)
{
const size_t b = x_bits - 1 - i;
const bool x_b = x.get_bit(b);
r *= 2;
r.conditionally_set_bit(0, x_b);
const bool r_gte_y = bigint_sub3(t.mutable_data(), r.data(), r.size(), y.data(), y_words) == 0;
r.ct_cond_swap(r_gte_y, t);
}
if(x.is_negative())
{
if(r.is_nonzero())
{
r = y - r;
}
}
return r;
}
/*
* Solve x = q * y + r
*
* See Handbook of Applied Cryptography section 14.2.5
*/
void divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out)
{
if(y_arg.is_zero())
throw BigInt::DivideByZero();
const size_t y_words = y_arg.sig_words();
BOTAN_ASSERT_NOMSG(y_words > 0);
BigInt y = y_arg;
BigInt r = x;
BigInt q = 0;
secure_vector<word> ws;
r.set_sign(BigInt::Positive);
y.set_sign(BigInt::Positive);
// Calculate shifts needed to normalize y with high bit set
const size_t shifts = BOTAN_MP_WORD_BITS - high_bit(y.word_at(y_words-1));
y <<= shifts;
r <<= shifts;
// we know y has not changed size, since we only shifted up to set high bit
const size_t t = y_words - 1;
const size_t n = std::max(y_words, r.sig_words()) - 1; // r may have changed size however
BOTAN_ASSERT_NOMSG(n >= t);
q.grow_to(n - t + 1);
word* q_words = q.mutable_data();
BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n-t));
// Set q_{n-t} to number of times r > shifted_y
q_words[n-t] = r.reduce_below(shifted_y, ws);
const word y_t0 = y.word_at(t);
const word y_t1 = y.word_at(t-1);
for(size_t j = n; j != t; --j)
{
const word x_j0 = r.word_at(j);
const word x_j1 = r.word_at(j-1);
const word x_j2 = r.word_at(j-2);
word qjt = bigint_divop(x_j0, x_j1, y_t0);
qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(MP_WORD_MAX, qjt);
// Per HAC 14.23, this operation is required at most twice
qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);
qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);
BOTAN_DEBUG_ASSERT(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2) == false);
shifted_y >>= BOTAN_MP_WORD_BITS;
// Now shifted_y == y << (BOTAN_MP_WORD_BITS * (j-t-1))
// TODO this sequence could be better
r -= qjt * shifted_y;
qjt -= r.is_negative();
r += static_cast<word>(r.is_negative()) * shifted_y;
q_words[j-t-1] = qjt;
}
r >>= shifts;
sign_fixup(x, y_arg, q, r);
r_out = r;
q_out = q;
}
}
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