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/*
* Multiplication and Squaring
* (C) 1999-2010,2018 Jack Lloyd
* 2016 Matthias Gierlings
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_asmi.h>
#include <botan/internal/ct_utils.h>
#include <botan/mem_ops.h>
#include <botan/exceptn.h>
namespace Botan {
namespace {
const size_t KARATSUBA_MULTIPLY_THRESHOLD = 32;
const size_t KARATSUBA_SQUARE_THRESHOLD = 32;
/*
* Simple O(N^2) Multiplication
*/
void basecase_mul(word z[], size_t z_size,
const word x[], size_t x_size,
const word y[], size_t y_size)
{
if(z_size < x_size + y_size)
throw Invalid_Argument("basecase_mul z_size too small");
const size_t x_size_8 = x_size - (x_size % 8);
clear_mem(z, z_size);
for(size_t i = 0; i != y_size; ++i)
{
const word y_i = y[i];
word carry = 0;
for(size_t j = 0; j != x_size_8; j += 8)
carry = word8_madd3(z + i + j, x + j, y_i, carry);
for(size_t j = x_size_8; j != x_size; ++j)
z[i+j] = word_madd3(x[j], y_i, z[i+j], &carry);
z[x_size+i] = carry;
}
}
void basecase_sqr(word z[], size_t z_size,
const word x[], size_t x_size)
{
if(z_size < 2*x_size)
throw Invalid_Argument("basecase_sqr z_size too small");
const size_t x_size_8 = x_size - (x_size % 8);
clear_mem(z, z_size);
for(size_t i = 0; i != x_size; ++i)
{
const word x_i = x[i];
word carry = 0;
for(size_t j = 0; j != x_size_8; j += 8)
carry = word8_madd3(z + i + j, x + j, x_i, carry);
for(size_t j = x_size_8; j != x_size; ++j)
z[i+j] = word_madd3(x[j], x_i, z[i+j], &carry);
z[x_size+i] = carry;
}
}
/*
* Karatsuba Multiplication Operation
*/
void karatsuba_mul(word z[], const word x[], const word y[], size_t N,
word workspace[])
{
if(N < KARATSUBA_MULTIPLY_THRESHOLD || N % 2)
{
switch(N)
{
case 6:
return bigint_comba_mul6(z, x, y);
case 8:
return bigint_comba_mul8(z, x, y);
case 9:
return bigint_comba_mul9(z, x, y);
case 16:
return bigint_comba_mul16(z, x, y);
case 24:
return bigint_comba_mul24(z, x, y);
default:
return basecase_mul(z, 2*N, x, N, y, N);
}
}
const size_t N2 = N / 2;
const word* x0 = x;
const word* x1 = x + N2;
const word* y0 = y;
const word* y1 = y + N2;
word* z0 = z;
word* z1 = z + N;
word* ws0 = workspace;
word* ws1 = workspace + N;
clear_mem(workspace, 2*N);
/*
* If either of cmp0 or cmp1 is zero then z0 or z1 resp is zero here,
* resulting in a no-op - z0*z1 will be equal to zero so we don't need to do
* anything, clear_mem above already set the correct result.
*
* However we ignore the result of the comparisons and always perform the
* subtractions and recursively multiply to avoid the timing channel.
*/
// First compute (X_lo - X_hi)*(Y_hi - Y_lo)
const auto cmp0 = bigint_sub_abs(z0, x0, x1, N2, workspace);
const auto cmp1 = bigint_sub_abs(z1, y1, y0, N2, workspace);
const auto neg_mask = ~(cmp0 ^ cmp1);
karatsuba_mul(ws0, z0, z1, N2, ws1);
// Compute X_lo * Y_lo
karatsuba_mul(z0, x0, y0, N2, ws1);
// Compute X_hi * Y_hi
karatsuba_mul(z1, x1, y1, N2, ws1);
const word ws_carry = bigint_add3_nc(ws1, z0, N, z1, N);
word z_carry = bigint_add2_nc(z + N2, N, ws1, N);
z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1);
bigint_add2_nc(z + N + N2, N2, &z_carry, 1);
clear_mem(workspace + N, N2);
bigint_cnd_add_or_sub(neg_mask, z + N2, workspace, 2*N-N2);
}
/*
* Karatsuba Squaring Operation
*/
void karatsuba_sqr(word z[], const word x[], size_t N, word workspace[])
{
if(N < KARATSUBA_SQUARE_THRESHOLD || N % 2)
{
switch(N)
{
case 6:
return bigint_comba_sqr6(z, x);
case 8:
return bigint_comba_sqr8(z, x);
case 9:
return bigint_comba_sqr9(z, x);
case 16:
return bigint_comba_sqr16(z, x);
case 24:
return bigint_comba_sqr24(z, x);
default:
return basecase_sqr(z, 2*N, x, N);
}
}
const size_t N2 = N / 2;
const word* x0 = x;
const word* x1 = x + N2;
word* z0 = z;
word* z1 = z + N;
word* ws0 = workspace;
word* ws1 = workspace + N;
clear_mem(workspace, 2*N);
// See comment in karatsuba_mul
bigint_sub_abs(z0, x0, x1, N2, workspace);
karatsuba_sqr(ws0, z0, N2, ws1);
karatsuba_sqr(z0, x0, N2, ws1);
karatsuba_sqr(z1, x1, N2, ws1);
const word ws_carry = bigint_add3_nc(ws1, z0, N, z1, N);
word z_carry = bigint_add2_nc(z + N2, N, ws1, N);
z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1);
bigint_add2_nc(z + N + N2, N2, &z_carry, 1);
/*
* This is only actually required if cmp (result of bigint_sub_abs) is != 0,
* however if cmp==0 then ws0[0:N] == 0 and avoiding the jump hides a
* timing channel.
*/
bigint_sub2(z + N2, 2*N-N2, ws0, N);
}
/*
* Pick a good size for the Karatsuba multiply
*/
size_t karatsuba_size(size_t z_size,
size_t x_size, size_t x_sw,
size_t y_size, size_t y_sw)
{
if(x_sw > x_size || x_sw > y_size || y_sw > x_size || y_sw > y_size)
return 0;
if(((x_size == x_sw) && (x_size % 2)) ||
((y_size == y_sw) && (y_size % 2)))
return 0;
const size_t start = (x_sw > y_sw) ? x_sw : y_sw;
const size_t end = (x_size < y_size) ? x_size : y_size;
if(start == end)
{
if(start % 2)
return 0;
return start;
}
for(size_t j = start; j <= end; ++j)
{
if(j % 2)
continue;
if(2*j > z_size)
return 0;
if(x_sw <= j && j <= x_size && y_sw <= j && j <= y_size)
{
if(j % 4 == 2 &&
(j+2) <= x_size && (j+2) <= y_size && 2*(j+2) <= z_size)
return j+2;
return j;
}
}
return 0;
}
/*
* Pick a good size for the Karatsuba squaring
*/
size_t karatsuba_size(size_t z_size, size_t x_size, size_t x_sw)
{
if(x_sw == x_size)
{
if(x_sw % 2)
return 0;
return x_sw;
}
for(size_t j = x_sw; j <= x_size; ++j)
{
if(j % 2)
continue;
if(2*j > z_size)
return 0;
if(j % 4 == 2 && (j+2) <= x_size && 2*(j+2) <= z_size)
return j+2;
return j;
}
return 0;
}
template<size_t SZ>
inline bool sized_for_comba_mul(size_t x_sw, size_t x_size,
size_t y_sw, size_t y_size,
size_t z_size)
{
return (x_sw <= SZ && x_size >= SZ &&
y_sw <= SZ && y_size >= SZ &&
z_size >= 2*SZ);
}
template<size_t SZ>
inline bool sized_for_comba_sqr(size_t x_sw, size_t x_size,
size_t z_size)
{
return (x_sw <= SZ && x_size >= SZ && z_size >= 2*SZ);
}
}
void bigint_mul(word z[], size_t z_size,
const word x[], size_t x_size, size_t x_sw,
const word y[], size_t y_size, size_t y_sw,
word workspace[], size_t ws_size)
{
clear_mem(z, z_size);
if(x_sw == 1)
{
bigint_linmul3(z, y, y_sw, x[0]);
}
else if(y_sw == 1)
{
bigint_linmul3(z, x, x_sw, y[0]);
}
else if(sized_for_comba_mul<4>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul4(z, x, y);
}
else if(sized_for_comba_mul<6>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul6(z, x, y);
}
else if(sized_for_comba_mul<8>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul8(z, x, y);
}
else if(sized_for_comba_mul<9>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul9(z, x, y);
}
else if(sized_for_comba_mul<16>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul16(z, x, y);
}
else if(sized_for_comba_mul<24>(x_sw, x_size, y_sw, y_size, z_size))
{
bigint_comba_mul24(z, x, y);
}
else if(x_sw < KARATSUBA_MULTIPLY_THRESHOLD ||
y_sw < KARATSUBA_MULTIPLY_THRESHOLD ||
!workspace)
{
basecase_mul(z, z_size, x, x_sw, y, y_sw);
}
else
{
const size_t N = karatsuba_size(z_size, x_size, x_sw, y_size, y_sw);
if(N && z_size >= 2*N && ws_size >= 2*N)
karatsuba_mul(z, x, y, N, workspace);
else
basecase_mul(z, z_size, x, x_sw, y, y_sw);
}
}
/*
* Squaring Algorithm Dispatcher
*/
void bigint_sqr(word z[], size_t z_size,
const word x[], size_t x_size, size_t x_sw,
word workspace[], size_t ws_size)
{
clear_mem(z, z_size);
BOTAN_ASSERT(z_size/2 >= x_sw, "Output size is sufficient");
if(x_sw == 1)
{
bigint_linmul3(z, x, x_sw, x[0]);
}
else if(sized_for_comba_sqr<4>(x_sw, x_size, z_size))
{
bigint_comba_sqr4(z, x);
}
else if(sized_for_comba_sqr<6>(x_sw, x_size, z_size))
{
bigint_comba_sqr6(z, x);
}
else if(sized_for_comba_sqr<8>(x_sw, x_size, z_size))
{
bigint_comba_sqr8(z, x);
}
else if(sized_for_comba_sqr<9>(x_sw, x_size, z_size))
{
bigint_comba_sqr9(z, x);
}
else if(sized_for_comba_sqr<16>(x_sw, x_size, z_size))
{
bigint_comba_sqr16(z, x);
}
else if(sized_for_comba_sqr<24>(x_sw, x_size, z_size))
{
bigint_comba_sqr24(z, x);
}
else if(x_size < KARATSUBA_SQUARE_THRESHOLD || !workspace)
{
basecase_sqr(z, z_size, x, x_sw);
}
else
{
const size_t N = karatsuba_size(z_size, x_size, x_sw);
if(N && z_size >= 2*N && ws_size >= 2*N)
karatsuba_sqr(z, x, N, workspace);
else
basecase_sqr(z, z_size, x, x_sw);
}
}
}