/*
* math.c
*
* crypto math operations and data types
*
* David A. McGrew
* Cisco Systems, Inc.
*/
/*
*
* Copyright (c) 2001-2006 Cisco Systems, Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
*
* Neither the name of the Cisco Systems, Inc. nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
*
*/
#include "crypto_math.h"
int
octet_weight[256] = {
0, 1, 1, 2, 1, 2, 2, 3,
1, 2, 2, 3, 2, 3, 3, 4,
1, 2, 2, 3, 2, 3, 3, 4,
2, 3, 3, 4, 3, 4, 4, 5,
1, 2, 2, 3, 2, 3, 3, 4,
2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
1, 2, 2, 3, 2, 3, 3, 4,
2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6,
4, 5, 5, 6, 5, 6, 6, 7,
1, 2, 2, 3, 2, 3, 3, 4,
2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6,
4, 5, 5, 6, 5, 6, 6, 7,
2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6,
4, 5, 5, 6, 5, 6, 6, 7,
3, 4, 4, 5, 4, 5, 5, 6,
4, 5, 5, 6, 5, 6, 6, 7,
4, 5, 5, 6, 5, 6, 6, 7,
5, 6, 6, 7, 6, 7, 7, 8
};
int
low_bit[256] = {
-1, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
6, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
7, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
6, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0
};
int
high_bit[256] = {
-1, 0, 1, 1, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7
};
int
octet_get_weight(uint8_t octet) {
extern int octet_weight[256];
return octet_weight[octet];
}
unsigned char
v32_weight(v32_t a) {
unsigned int wt = 0;
wt += octet_weight[a.v8[0]]; /* note: endian-ness makes no difference */
wt += octet_weight[a.v8[1]];
wt += octet_weight[a.v8[2]];
wt += octet_weight[a.v8[3]];
return wt;
}
inline unsigned char
v32_distance(v32_t x, v32_t y) {
x.value ^= y.value;
return v32_weight(x);
}
unsigned int
v32_dot_product(v32_t a, v32_t b) {
a.value &= b.value;
return v32_weight(a) & 1;
}
/*
* _bit_string returns a NULL-terminated character string suitable for
* printing
*/
#define MAX_STRING_LENGTH 1024
char bit_string[MAX_STRING_LENGTH];
char *
octet_bit_string(uint8_t x) {
int mask, index;
for (mask = 1, index = 0; mask < 256; mask <<= 1)
if ((x & mask) == 0)
bit_string[index++] = '0';
else
bit_string[index++] = '1';
bit_string[index++] = 0; /* NULL terminate string */
return bit_string;
}
char *
v16_bit_string(v16_t x) {
int i, mask, index;
for (i = index = 0; i < 2; i++) {
for (mask = 1; mask < 256; mask <<= 1)
if ((x.v8[i] & mask) == 0)
bit_string[index++] = '0';
else
bit_string[index++] = '1';
}
bit_string[index++] = 0; /* NULL terminate string */
return bit_string;
}
char *
v32_bit_string(v32_t x) {
int i, mask, index;
for (i = index = 0; i < 4; i++) {
for (mask = 128; mask > 0; mask >>= 1)
if ((x.v8[i] & mask) == 0)
bit_string[index++] = '0';
else
bit_string[index++] = '1';
}
bit_string[index++] = 0; /* NULL terminate string */
return bit_string;
}
char *
v64_bit_string(const v64_t *x) {
int i, mask, index;
for (i = index = 0; i < 8; i++) {
for (mask = 1; mask < 256; mask <<= 1)
if ((x->v8[i] & mask) == 0)
bit_string[index++] = '0';
else
bit_string[index++] = '1';
}
bit_string[index++] = 0; /* NULL terminate string */
return bit_string;
}
char *
v128_bit_string(v128_t *x) {
int j, index;
uint32_t mask;
for (j=index=0; j < 4; j++) {
for (mask=0x80000000; mask > 0; mask >>= 1) {
if (x->v32[j] & mask)
bit_string[index] = '1';
else
bit_string[index] = '0';
++index;
}
}
bit_string[128] = 0; /* null terminate string */
return bit_string;
}
uint8_t
nibble_to_hex_char(uint8_t nibble) {
char buf[16] = {'0', '1', '2', '3', '4', '5', '6', '7',
'8', '9', 'a', 'b', 'c', 'd', 'e', 'f' };
return buf[nibble & 0xF];
}
char *
octet_hex_string(uint8_t x) {
bit_string[0] = nibble_to_hex_char(x >> 4);
bit_string[1] = nibble_to_hex_char(x & 0xF);
bit_string[2] = 0; /* null terminate string */
return bit_string;
}
char *
octet_string_hex_string(const void *str, int length) {
const uint8_t *s = str;
int i;
/* double length, since one octet takes two hex characters */
length *= 2;
/* truncate string if it would be too long */
if (length > MAX_STRING_LENGTH)
length = MAX_STRING_LENGTH-1;
for (i=0; i < length; i+=2) {
bit_string[i] = nibble_to_hex_char(*s >> 4);
bit_string[i+1] = nibble_to_hex_char(*s++ & 0xF);
}
bit_string[i] = 0; /* null terminate string */
return bit_string;
}
char *
v16_hex_string(v16_t x) {
int i, j;
for (i=j=0; i < 2; i++) {
bit_string[j++] = nibble_to_hex_char(x.v8[i] >> 4);
bit_string[j++] = nibble_to_hex_char(x.v8[i] & 0xF);
}
bit_string[j] = 0; /* null terminate string */
return bit_string;
}
char *
v32_hex_string(v32_t x) {
int i, j;
for (i=j=0; i < 4; i++) {
bit_string[j++] = nibble_to_hex_char(x.v8[i] >> 4);
bit_string[j++] = nibble_to_hex_char(x.v8[i] & 0xF);
}
bit_string[j] = 0; /* null terminate string */
return bit_string;
}
char *
v64_hex_string(const v64_t *x) {
int i, j;
for (i=j=0; i < 8; i++) {
bit_string[j++] = nibble_to_hex_char(x->v8[i] >> 4);
bit_string[j++] = nibble_to_hex_char(x->v8[i] & 0xF);
}
bit_string[j] = 0; /* null terminate string */
return bit_string;
}
char *
v128_hex_string(v128_t *x) {
int i, j;
for (i=j=0; i < 16; i++) {
bit_string[j++] = nibble_to_hex_char(x->v8[i] >> 4);
bit_string[j++] = nibble_to_hex_char(x->v8[i] & 0xF);
}
bit_string[j] = 0; /* null terminate string */
return bit_string;
}
char *
char_to_hex_string(char *x, int num_char) {
int i, j;
if (num_char >= 16)
num_char = 16;
for (i=j=0; i < num_char; i++) {
bit_string[j++] = nibble_to_hex_char(x[i] >> 4);
bit_string[j++] = nibble_to_hex_char(x[i] & 0xF);
}
bit_string[j] = 0; /* null terminate string */
return bit_string;
}
int
hex_char_to_nibble(uint8_t c) {
switch(c) {
case ('0'): return 0x0;
case ('1'): return 0x1;
case ('2'): return 0x2;
case ('3'): return 0x3;
case ('4'): return 0x4;
case ('5'): return 0x5;
case ('6'): return 0x6;
case ('7'): return 0x7;
case ('8'): return 0x8;
case ('9'): return 0x9;
case ('a'): return 0xa;
case ('A'): return 0xa;
case ('b'): return 0xb;
case ('B'): return 0xb;
case ('c'): return 0xc;
case ('C'): return 0xc;
case ('d'): return 0xd;
case ('D'): return 0xd;
case ('e'): return 0xe;
case ('E'): return 0xe;
case ('f'): return 0xf;
case ('F'): return 0xf;
default: return -1; /* this flags an error */
}
/* NOTREACHED */
return -1; /* this keeps compilers from complaining */
}
int
is_hex_string(char *s) {
while(*s != 0)
if (hex_char_to_nibble(*s++) == -1)
return 0;
return 1;
}
uint8_t
hex_string_to_octet(char *s) {
uint8_t x;
x = (hex_char_to_nibble(s[0]) << 4)
| hex_char_to_nibble(s[1] & 0xFF);
return x;
}
/*
* hex_string_to_octet_string converts a hexadecimal string
* of length 2 * len to a raw octet string of length len
*/
int
hex_string_to_octet_string(char *raw, char *hex, int len) {
uint8_t x;
int tmp;
int hex_len;
hex_len = 0;
while (hex_len < len) {
tmp = hex_char_to_nibble(hex[0]);
if (tmp == -1)
return hex_len;
x = (tmp << 4);
hex_len++;
tmp = hex_char_to_nibble(hex[1]);
if (tmp == -1)
return hex_len;
x |= (tmp & 0xff);
hex_len++;
*raw++ = x;
hex += 2;
}
return hex_len;
}
v16_t
hex_string_to_v16(char *s) {
v16_t x;
int i, j;
for (i=j=0; i < 4; i += 2, j++) {
x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
| hex_char_to_nibble(s[i+1] & 0xFF);
}
return x;
}
v32_t
hex_string_to_v32(char *s) {
v32_t x;
int i, j;
for (i=j=0; i < 8; i += 2, j++) {
x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
| hex_char_to_nibble(s[i+1] & 0xFF);
}
return x;
}
v64_t
hex_string_to_v64(char *s) {
v64_t x;
int i, j;
for (i=j=0; i < 16; i += 2, j++) {
x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
| hex_char_to_nibble(s[i+1] & 0xFF);
}
return x;
}
v128_t
hex_string_to_v128(char *s) {
v128_t x;
int i, j;
for (i=j=0; i < 32; i += 2, j++) {
x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
| hex_char_to_nibble(s[i+1] & 0xFF);
}
return x;
}
/*
* the matrix A[] is stored in column format, i.e., A[i] is the ith
* column of the matrix
*/
uint8_t
A_times_x_plus_b(uint8_t A[8], uint8_t x, uint8_t b) {
int index = 0;
unsigned mask;
for (mask=1; mask < 256; mask *= 2) {
if (x & mask)
b^= A[index];
++index;
}
return b;
}
inline void
v16_copy_octet_string(v16_t *x, const uint8_t s[2]) {
x->v8[0] = s[0];
x->v8[1] = s[1];
}
inline void
v32_copy_octet_string(v32_t *x, const uint8_t s[4]) {
x->v8[0] = s[0];
x->v8[1] = s[1];
x->v8[2] = s[2];
x->v8[3] = s[3];
}
inline void
v64_copy_octet_string(v64_t *x, const uint8_t s[8]) {
x->v8[0] = s[0];
x->v8[1] = s[1];
x->v8[2] = s[2];
x->v8[3] = s[3];
x->v8[4] = s[4];
x->v8[5] = s[5];
x->v8[6] = s[6];
x->v8[7] = s[7];
}
void
v128_copy_octet_string(v128_t *x, const uint8_t s[16]) {
x->v8[0] = s[0];
x->v8[1] = s[1];
x->v8[2] = s[2];
x->v8[3] = s[3];
x->v8[4] = s[4];
x->v8[5] = s[5];
x->v8[6] = s[6];
x->v8[7] = s[7];
x->v8[8] = s[8];
x->v8[9] = s[9];
x->v8[10] = s[10];
x->v8[11] = s[11];
x->v8[12] = s[12];
x->v8[13] = s[13];
x->v8[14] = s[14];
x->v8[15] = s[15];
}
#ifndef DATATYPES_USE_MACROS /* little functions are not macros */
void
v128_set_to_zero(v128_t *x) {
_v128_set_to_zero(x);
}
void
v128_copy(v128_t *x, const v128_t *y) {
_v128_copy(x, y);
}
void
v128_xor(v128_t *z, v128_t *x, v128_t *y) {
_v128_xor(z, x, y);
}
void
v128_and(v128_t *z, v128_t *x, v128_t *y) {
_v128_and(z, x, y);
}
void
v128_or(v128_t *z, v128_t *x, v128_t *y) {
_v128_or(z, x, y);
}
void
v128_complement(v128_t *x) {
_v128_complement(x);
}
int
v128_is_eq(const v128_t *x, const v128_t *y) {
return _v128_is_eq(x, y);
}
int
v128_get_bit(const v128_t *x, int i) {
return _v128_get_bit(x, i);
}
void
v128_set_bit(v128_t *x, int i) {
_v128_set_bit(x, i);
}
void
v128_clear_bit(v128_t *x, int i){
_v128_clear_bit(x, i);
}
void
v128_set_bit_to(v128_t *x, int i, int y){
_v128_set_bit_to(x, i, y);
}
#endif /* DATATYPES_USE_MACROS */
inline void
v128_left_shift2(v128_t *x, int num_bits) {
int i;
int word_shift = num_bits >> 5;
int bit_shift = num_bits & 31;
for (i=0; i < (4-word_shift); i++) {
x->v32[i] = x->v32[i+word_shift] << bit_shift;
}
for ( ; i < word_shift; i++) {
x->v32[i] = 0;
}
}
void
v128_right_shift(v128_t *x, int index) {
const int base_index = index >> 5;
const int bit_index = index & 31;
int i, from;
uint32_t b;
if (index > 127) {
v128_set_to_zero(x);
return;
}
if (bit_index == 0) {
/* copy each word from left size to right side */
x->v32[4-1] = x->v32[4-1-base_index];
for (i=4-1; i > base_index; i--)
x->v32[i-1] = x->v32[i-1-base_index];
} else {
/* set each word to the "or" of the two bit-shifted words */
for (i = 4; i > base_index; i--) {
from = i-1 - base_index;
b = x->v32[from] << bit_index;
if (from > 0)
b |= x->v32[from-1] >> (32-bit_index);
x->v32[i-1] = b;
}
}
/* now wrap up the final portion */
for (i=0; i < base_index; i++)
x->v32[i] = 0;
}
void
v128_left_shift(v128_t *x, int index) {
int i;
const int base_index = index >> 5;
const int bit_index = index & 31;
if (index > 127) {
v128_set_to_zero(x);
return;
}
if (bit_index == 0) {
for (i=0; i < 4 - base_index; i++)
x->v32[i] = x->v32[i+base_index];
} else {
for (i=0; i < 4 - base_index - 1; i++)
x->v32[i] = (x->v32[i+base_index] << bit_index) ^
(x->v32[i+base_index+1] >> (32 - bit_index));
x->v32[4 - base_index-1] = x->v32[4-1] << bit_index;
}
/* now wrap up the final portion */
for (i = 4 - base_index; i < 4; i++)
x->v32[i] = 0;
}
#if 0
void
v128_add(v128_t *z, v128_t *x, v128_t *y) {
/* integer addition modulo 2^128 */
#ifdef WORDS_BIGENDIAN
uint64_t tmp;
tmp = x->v32[3] + y->v32[3];
z->v32[3] = (uint32_t) tmp;
tmp = x->v32[2] + y->v32[2] + (tmp >> 32);
z->v32[2] = (uint32_t) tmp;
tmp = x->v32[1] + y->v32[1] + (tmp >> 32);
z->v32[1] = (uint32_t) tmp;
tmp = x->v32[0] + y->v32[0] + (tmp >> 32);
z->v32[0] = (uint32_t) tmp;
#else /* assume little endian architecture */
uint64_t tmp;
tmp = htonl(x->v32[3]) + htonl(y->v32[3]);
z->v32[3] = ntohl((uint32_t) tmp);
tmp = htonl(x->v32[2]) + htonl(y->v32[2]) + htonl(tmp >> 32);
z->v32[2] = ntohl((uint32_t) tmp);
tmp = htonl(x->v32[1]) + htonl(y->v32[1]) + htonl(tmp >> 32);
z->v32[1] = ntohl((uint32_t) tmp);
tmp = htonl(x->v32[0]) + htonl(y->v32[0]) + htonl(tmp >> 32);
z->v32[0] = ntohl((uint32_t) tmp);
#endif /* WORDS_BIGENDIAN */
}
#endif
int
octet_string_is_eq(uint8_t *a, uint8_t *b, int len) {
uint8_t *end = b + len;
while (b < end)
if (*a++ != *b++)
return 1;
return 0;
}
void
octet_string_set_to_zero(uint8_t *s, int len) {
uint8_t *end = s + len;
do {
*s = 0;
} while (++s < end);
}
/* functions below not yet tested! */
int
v32_low_bit(v32_t *w) {
int value;
value = low_bit[w->v8[0]];
if (value != -1)
return value;
value = low_bit[w->v8[1]];
if (value != -1)
return value + 8;
value = low_bit[w->v8[2]];
if (value != -1)
return value + 16;
value = low_bit[w->v8[3]];
if (value == -1)
return -1;
return value + 24;
}
/* high_bit not done yet */