1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
|
/*************************************************
* Karatsuba Squaring Source File *
* (C) 1999-2006 The Botan Project *
*************************************************/
#include <botan/mp_core.h>
#include <botan/mem_ops.h>
namespace Botan {
namespace {
/*************************************************
* Karatsuba Squaring Operation *
*************************************************/
void karatsuba_sqr(word z[], const word x[], u32bit N, word workspace[])
{
const u32bit KARATSUBA_SQR_LOWER_SIZE = BOTAN_KARAT_SQR_THRESHOLD;
if(N == 6)
bigint_comba_sqr6(z, x);
else if(N == 8)
bigint_comba_sqr8(z, x);
else if(N < KARATSUBA_SQR_LOWER_SIZE || N % 2)
bigint_simple_mul(z, x, N, x, N);
else
{
const u32bit 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);
word carry = bigint_add3_nc(workspace+N, z0, N, z1, N);
carry += bigint_add2_nc(z + N2, N, workspace + N, N);
bigint_add2_nc(z + N + N2, N2, &carry, 1);
if(cmp == 0)
bigint_add2(z + N2, 2*N-N2, workspace, N);
else
bigint_sub2(z + N2, 2*N-N2, workspace, N);
}
}
/*************************************************
* Pick a good size for the Karatsuba squaring *
*************************************************/
u32bit karatsuba_size(u32bit z_size, u32bit x_size, u32bit x_sw)
{
if(x_sw == x_size)
{
if(x_sw % 2)
return 0;
return x_sw;
}
for(u32bit 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;
}
/*************************************************
* Handle small operand squarings *
*************************************************/
void handle_small_sqr(word z[], u32bit z_size,
const word x[], u32bit x_size, u32bit 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
bigint_simple_mul(z, x, x_sw, x, x_sw);
}
}
/*************************************************
* Squaring Algorithm Dispatcher *
*************************************************/
void bigint_sqr(word z[], u32bit z_size, word workspace[],
const word x[], u32bit x_size, u32bit x_sw)
{
if(x_size <= 8 || x_sw <= 8)
{
handle_small_sqr(z, z_size, x, x_size, x_sw);
return;
}
const u32bit N = karatsuba_size(z_size, x_size, x_sw);
if(N)
{
clear_mem(workspace, 2*N);
karatsuba_sqr(z, x, N, workspace);
}
else
bigint_simple_mul(z, x, x_sw, x, x_sw);
}
}
|
