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/*
* Karatsuba Multiplication/Squaring
* (C) 1999-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_asmi.h>
#include <botan/mem_ops.h>
namespace Botan {
namespace {
static const size_t KARATSUBA_MULTIPLY_THRESHOLD = 32;
static const size_t KARATSUBA_SQUARE_THRESHOLD = 32;
/*
* 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)
{
if(N == 6)
return bigint_comba_mul6(z, x, y);
else if(N == 8)
return bigint_comba_mul8(z, x, y);
else if(N == 16)
return bigint_comba_mul16(z, x, y);
else
return bigint_simple_mul(z, 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;
const s32bit cmp0 = bigint_cmp(x0, N2, x1, N2);
const s32bit cmp1 = bigint_cmp(y1, N2, y0, N2);
clear_mem(workspace, 2*N);
//if(cmp0 && cmp1)
{
if(cmp0 > 0)
bigint_sub3(z0, x0, N2, x1, N2);
else
bigint_sub3(z0, x1, N2, x0, N2);
if(cmp1 > 0)
bigint_sub3(z1, y1, N2, y0, N2);
else
bigint_sub3(z1, y0, N2, y1, N2);
karatsuba_mul(workspace, z0, z1, N2, workspace+N);
}
karatsuba_mul(z0, x0, y0, N2, workspace+N);
karatsuba_mul(z1, x1, y1, N2, workspace+N);
const word ws_carry = bigint_add3_nc(workspace + N, z0, N, z1, N);
word z_carry = bigint_add2_nc(z + N2, N, workspace + N, N);
z_carry += bigint_add2_nc(z + N + N2, N2, &ws_carry, 1);
bigint_add2_nc(z + N + N2, N2, &z_carry, 1);
if((cmp0 == cmp1) || (cmp0 == 0) || (cmp1 == 0))
bigint_add2(z + N2, 2*N-N2, workspace, N);
else
bigint_sub2(z + N2, 2*N-N2, workspace, N);
}
/*
* Karatsuba Squaring Operation
*/
void karatsuba_sqr(word z[], const word x[], size_t N, word workspace[])
{
if(N < KARATSUBA_SQUARE_THRESHOLD || N % 2)
{
if(N == 6)
return bigint_comba_sqr6(z, x);
else if(N == 8)
return bigint_comba_sqr8(z, x);
else if(N == 16)
return bigint_comba_sqr16(z, x);
else
return bigint_simple_sqr(z, x, N);
}
const size_t N2 = N / 2;
const word* x0 = x;
const word* x1 = x + N2;
word* z0 = z;
word* z1 = z + N;
const s32bit cmp = bigint_cmp(x0, N2, x1, N2);
clear_mem(workspace, 2*N);
//if(cmp)
{
if(cmp > 0)
bigint_sub3(z0, x0, N2, x1, N2);
else
bigint_sub3(z0, x1, N2, x0, N2);
karatsuba_sqr(workspace, z0, N2, workspace+N);
}
karatsuba_sqr(z0, x0, N2, workspace+N);
karatsuba_sqr(z1, x1, N2, workspace+N);
const word ws_carry = bigint_add3_nc(workspace + N, z0, N, z1, N);
word z_carry = bigint_add2_nc(z + N2, N, workspace + N, 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 is != 0, however
* if cmp==0 then workspace[0:N] == 0 and avoiding the jump
* hides a timing channel.
*/
bigint_sub2(z + N2, 2*N-N2, workspace, 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;
}
}
/*
* Multiplication Algorithm Dispatcher
*/
void bigint_mul(word z[], size_t z_size, word workspace[],
const word x[], size_t x_size, size_t x_sw,
const word y[], size_t y_size, size_t y_sw)
{
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(x_sw <= 4 && x_size >= 4 &&
y_sw <= 4 && y_size >= 4 && z_size >= 8)
{
bigint_comba_mul4(z, x, y);
}
else if(x_sw <= 6 && x_size >= 6 &&
y_sw <= 6 && y_size >= 6 && z_size >= 12)
{
bigint_comba_mul6(z, x, y);
}
else if(x_sw <= 8 && x_size >= 8 &&
y_sw <= 8 && y_size >= 8 && z_size >= 16)
{
bigint_comba_mul8(z, x, y);
}
else if(x_sw <= 16 && x_size >= 16 &&
y_sw <= 16 && y_size >= 16 && z_size >= 32)
{
bigint_comba_mul16(z, x, y);
}
else if(x_sw < KARATSUBA_MULTIPLY_THRESHOLD ||
y_sw < KARATSUBA_MULTIPLY_THRESHOLD ||
!workspace)
{
bigint_simple_mul(z, 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)
karatsuba_mul(z, x, y, N, workspace);
else
bigint_simple_mul(z, x, x_sw, y, y_sw);
}
}
/*
* Squaring Algorithm Dispatcher
*/
void bigint_sqr(word z[], size_t z_size, word workspace[],
const word x[], size_t x_size, size_t x_sw)
{
if(x_sw == 1)
{
bigint_linmul3(z, x, x_sw, x[0]);
}
else if(x_sw <= 4 && x_size >= 4 && z_size >= 8)
{
bigint_comba_sqr4(z, x);
}
else if(x_sw <= 6 && x_size >= 6 && z_size >= 12)
{
bigint_comba_sqr6(z, x);
}
else if(x_sw <= 8 && x_size >= 8 && z_size >= 16)
{
bigint_comba_sqr8(z, x);
}
else if(x_sw <= 16 && x_size >= 16 && z_size >= 32)
{
bigint_comba_sqr16(z, x);
}
else if(x_size < KARATSUBA_SQUARE_THRESHOLD || !workspace)
{
bigint_simple_sqr(z, x, x_sw);
}
else
{
const size_t N = karatsuba_size(z_size, x_size, x_sw);
if(N)
karatsuba_sqr(z, x, N, workspace);
else
bigint_simple_sqr(z, x, x_sw);
}
}
}
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