667 lines
15 KiB
C
667 lines
15 KiB
C
/*
|
|
* file: mp.c
|
|
*
|
|
* DESCRIPTION
|
|
*
|
|
* These functions comprise a multi-precision integer arithmetic
|
|
* and discrete function package.
|
|
*/
|
|
|
|
#include "include/genutils.h"
|
|
|
|
#define MAXPLEN 384
|
|
|
|
|
|
/*****************************************
|
|
** greater - Test if x > y *
|
|
** *
|
|
** Returns TRUE (1) if x greater than y, *
|
|
** otherwise FALSE (0). *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** x Address of array x *
|
|
** y Address of array y *
|
|
** l Length both x and y in bytes *
|
|
** *
|
|
******************************************/
|
|
int greater(BYTE *x, BYTE *y, int l)
|
|
{
|
|
int i;
|
|
|
|
for ( i=0; i<l; i++ )
|
|
if ( x[i] != y[i] )
|
|
break;
|
|
|
|
if ( i == l )
|
|
return 0;
|
|
|
|
if ( x[i] > y[i] )
|
|
return 1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** less - Test if x < y *
|
|
** *
|
|
** Returns TRUE (1) if x less than y, *
|
|
** otherwise FALSE (0). *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** x Address of array x *
|
|
** y Address of array y *
|
|
** l Length both x and y in bytes *
|
|
** *
|
|
******************************************/
|
|
int less(BYTE *x, BYTE *y, int l)
|
|
{
|
|
int i;
|
|
|
|
for ( i=0; i<l; i++ )
|
|
if ( x[i] != y[i] )
|
|
break;
|
|
|
|
if ( i == l ) {
|
|
return 0;
|
|
}
|
|
|
|
if ( x[i] < y[i] ) {
|
|
return 1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** bshl - shifts array left *
|
|
** by one bit. *
|
|
** *
|
|
** x = x * 2 *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** x Address of array x *
|
|
** l Length array x in bytes *
|
|
** *
|
|
******************************************/
|
|
BYTE bshl(BYTE *x, int l)
|
|
{
|
|
BYTE *p;
|
|
int c1, c2;
|
|
|
|
p = x + l - 1;
|
|
c1 = 0;
|
|
c2 = 0;
|
|
while ( p != x ) {
|
|
if ( *p & 0x80 )
|
|
c2 = 1;
|
|
*p <<= 1; /* shift the word left once (ls bit = 0) */
|
|
if ( c1 )
|
|
*p |= 1;
|
|
c1 = c2;
|
|
c2 = 0;
|
|
p--;
|
|
}
|
|
|
|
if ( *p & 0x80 )
|
|
c2 = 1;
|
|
*p <<= 1; /* shift the word left once (ls bit = 0) */
|
|
if ( c1 )
|
|
*p |= (DIGIT)1;
|
|
|
|
return (BYTE)c2;
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** bshr - shifts array right *
|
|
** by one bit. *
|
|
** *
|
|
** x = x / 2 *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** x Address of array x *
|
|
** l Length array x in bytes *
|
|
** *
|
|
******************************************/
|
|
void bshr(BYTE *x, int l)
|
|
{
|
|
BYTE *p;
|
|
int c1,c2;
|
|
|
|
p = x;
|
|
c1 = 0;
|
|
c2 = 0;
|
|
while ( p != x+l-1 ) {
|
|
if ( *p & 0x01 )
|
|
c2 = 1;
|
|
*p >>= 1; /* shift the word right once (ms bit = 0) */
|
|
if ( c1 )
|
|
*p |= 0x80;
|
|
c1 = c2;
|
|
c2 = 0;
|
|
p++;
|
|
}
|
|
|
|
*p >>= 1; /* shift the word right once (ms bit = 0) */
|
|
if ( c1 )
|
|
*p |= 0x80;
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** Mult - Multiply two integers *
|
|
** *
|
|
** A = B * C *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of the result *
|
|
** B Address of the multiplier *
|
|
** C Address of the multiplicand *
|
|
** LB Length of B in bytes *
|
|
** LC Length of C in bytes *
|
|
** *
|
|
** NOTE: A MUST be LB+LC in length *
|
|
** *
|
|
******************************************/
|
|
int Mult(BYTE *A, BYTE *B, int LB, BYTE *C, int LC)
|
|
{
|
|
int i, j, k, LA;
|
|
DIGIT result;
|
|
|
|
LA = LB + LC;
|
|
|
|
for ( i=LB-1; i>=0; i-- ) {
|
|
result = 0;
|
|
for ( j=LC-1; j>=0; j-- ) {
|
|
k = i+j+1;
|
|
result = (DIGIT)A[k] + ((DIGIT)(B[i] * C[j])) + (result >> 8);
|
|
A[k] = (BYTE)result;
|
|
}
|
|
A[--k] = (BYTE)(result >> 8);
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
void ModSqr(BYTE *A, BYTE *B, int LB, BYTE *M, int LM)
|
|
{
|
|
|
|
Square(A, B, LB);
|
|
Mod(A, 2*LB, M, LM);
|
|
}
|
|
|
|
void ModMult(BYTE *A, BYTE *B, int LB, BYTE *C, int LC, BYTE *M, int LM)
|
|
{
|
|
Mult(A, B, LB, C, LC);
|
|
Mod(A, (LB+LC), M, LM);
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** smult - Multiply array by a scalar. *
|
|
** *
|
|
** A = b * C *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of the result *
|
|
** b Scalar (1 BYTE) *
|
|
** C Address of the multiplicand *
|
|
** L Length of C in bytes *
|
|
** *
|
|
** NOTE: A MUST be L+1 in length *
|
|
** *
|
|
******************************************/
|
|
void smult(BYTE *A, BYTE b, BYTE *C, int L)
|
|
{
|
|
int i;
|
|
DIGIT result;
|
|
|
|
result = 0;
|
|
for ( i=L-1; i>0; i-- ) {
|
|
result = A[i] + ((DIGIT)b * C[i]) + (result >> 8);
|
|
A[i] = (BYTE)(result & 0xff);
|
|
A[i-1] = (BYTE)(result >> 8);
|
|
}
|
|
}
|
|
|
|
/*****************************************
|
|
** Square() - Square an integer *
|
|
** *
|
|
** A = B^2 *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of the result *
|
|
** B Address of the operand *
|
|
** L Length of B in bytes *
|
|
** *
|
|
** NOTE: A MUST be 2*L in length *
|
|
** *
|
|
******************************************/
|
|
void Square(BYTE *A, BYTE *B, int L)
|
|
{
|
|
Mult(A, B, L, B, L);
|
|
}
|
|
|
|
/*****************************************
|
|
** ModExp - Modular Exponentiation *
|
|
** *
|
|
** A = B ** C (MOD M) *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of result *
|
|
** B Address of mantissa *
|
|
** C Address of exponent *
|
|
** M Address of modulus *
|
|
** LB Length of B in bytes *
|
|
** LC Length of C in bytes *
|
|
** LM Length of M in bytes *
|
|
** *
|
|
** NOTE: The integer B must be less *
|
|
** than the modulus M. *
|
|
** NOTE: A must be at least 3*LM *
|
|
** bytes long. However, the *
|
|
** result stored in A will be *
|
|
** only LM bytes long. *
|
|
******************************************/
|
|
void ModExp(BYTE *A, BYTE *B, int LB, BYTE *C, int LC, BYTE *M, int LM)
|
|
{
|
|
BYTE wmask;
|
|
int bits;
|
|
|
|
bits = LC*8;
|
|
wmask = 0x80;
|
|
|
|
A[LM-1] = 1;
|
|
|
|
while ( !sniff_bit(C,wmask) ) {
|
|
wmask >>= 1;
|
|
bits--;
|
|
if ( !wmask ) {
|
|
wmask = 0x80;
|
|
C++;
|
|
}
|
|
}
|
|
|
|
while ( bits-- ) {
|
|
memset(A+LM, 0x00, LM*2);
|
|
|
|
/* temp = A*A (MOD M) */
|
|
ModSqr(A+LM, A,LM, M,LM);
|
|
|
|
/* A = lower L bytes of temp */
|
|
memcpy(A, A+LM*2, LM);
|
|
memset(A+LM, 0x00, 2*LM);
|
|
|
|
if ( sniff_bit(C,wmask) ) {
|
|
memset(A+LM, 0x00, (LM+LB));
|
|
ModMult(A+LM, B,LB, A,LM, M,LM); /* temp = B * A (MOD M) */
|
|
memcpy(A, A+LM+(LM+LB)-LM, LM); /* A = lower LM bytes of temp */
|
|
memset(A+LM, 0x00, 2*LM);
|
|
}
|
|
|
|
wmask >>= 1;
|
|
if ( !wmask ) {
|
|
wmask = 0x80;
|
|
C++;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/* DivMod:
|
|
*
|
|
* computes:
|
|
* quot = x / n
|
|
* rem = x % n
|
|
* returns:
|
|
* length of "quot"
|
|
*
|
|
* len of rem is lenx+1
|
|
*/
|
|
int DivMod(BYTE *x, int lenx, BYTE *n, int lenn, BYTE *quot, BYTE *rem)
|
|
{
|
|
BYTE *tx, *tn, *ttx, *ts, bmult[1];
|
|
int i, shift, lgth_x, lgth_n, t_len, lenq;
|
|
DIGIT tMSn, mult;
|
|
unsigned long tMSx;
|
|
int underflow;
|
|
|
|
tx = x;
|
|
tn = n;
|
|
|
|
/* point to the MSD of n */
|
|
for ( i=0, lgth_n=lenn; i<lenn; i++, lgth_n-- ) {
|
|
if ( *tn )
|
|
break;
|
|
tn++;
|
|
}
|
|
if ( !lgth_n )
|
|
return 0;
|
|
|
|
/* point to the MSD of x */
|
|
for ( i=0, lgth_x=lenx; i<lenx; i++, lgth_x-- ) {
|
|
if ( *tx )
|
|
break;
|
|
tx++;
|
|
}
|
|
if ( !lgth_x )
|
|
return 0;
|
|
|
|
if ( lgth_x < lgth_n )
|
|
lenq = 1;
|
|
else
|
|
lenq = lgth_x - lgth_n + 1;
|
|
memset(quot, 0x00, lenq);
|
|
|
|
/* Loop while x > n, WATCH OUT if lgth_x == lgth_n */
|
|
while ( (lgth_x > lgth_n) || ((lgth_x == lgth_n) && !less(tx, tn, lgth_n)) ) {
|
|
shift = 1;
|
|
if ( lgth_n == 1 ) {
|
|
if ( *tx < *tn ) {
|
|
tMSx = (DIGIT) (((*tx) << 8) | *(tx+1));
|
|
tMSn = *tn;
|
|
shift = 0;
|
|
}
|
|
else {
|
|
tMSx = *tx;
|
|
tMSn = *tn;
|
|
}
|
|
}
|
|
else if ( lgth_n > 1 ) {
|
|
tMSx = (DIGIT) (((*tx) << 8) | *(tx+1));
|
|
tMSn = (DIGIT) (((*tn) << 8) | *(tn+1));
|
|
if ( (tMSx < tMSn) || ((tMSx == tMSn) && less(tx, tn, lgth_n)) ) {
|
|
tMSx = (tMSx << 8) | *(tx+2);
|
|
shift = 0;
|
|
}
|
|
}
|
|
else {
|
|
tMSx = (DIGIT) (((*tx) << 8) | *(tx+1));
|
|
tMSn = *tn;
|
|
shift = 0;
|
|
}
|
|
|
|
mult = (DIGIT) (tMSx / tMSn);
|
|
if ( mult > 0xff )
|
|
mult = 0xff;
|
|
bmult[0] = mult & 0xff;
|
|
|
|
ts = rem;
|
|
do {
|
|
memset(ts, 0x00, lgth_x+1);
|
|
Mult(ts, tn, lgth_n, bmult, 1);
|
|
|
|
underflow = 0;
|
|
if ( shift ) {
|
|
if ( ts[0] != 0 )
|
|
underflow = 1;
|
|
else {
|
|
for ( i=0; i<lgth_x; i++ )
|
|
ts[i] = ts[i+1];
|
|
ts[lgth_x] = 0x00;
|
|
}
|
|
}
|
|
if ( greater(ts, tx, lgth_x) || underflow ) {
|
|
bmult[0]--;
|
|
underflow = 1;
|
|
}
|
|
else
|
|
underflow = 0;
|
|
} while ( underflow );
|
|
sub(tx, lgth_x, ts, lgth_x);
|
|
if ( shift )
|
|
quot[lenq - (lgth_x - lgth_n) - 1] = bmult[0];
|
|
else
|
|
quot[lenq - (lgth_x - lgth_n)] = bmult[0];
|
|
|
|
ttx = tx;
|
|
t_len = lgth_x;
|
|
for ( i=0, lgth_x=t_len; i<t_len; i++, lgth_x-- ) {
|
|
if ( *ttx )
|
|
break;
|
|
ttx++;
|
|
}
|
|
tx = ttx;
|
|
}
|
|
memset(rem, 0x00, lenn);
|
|
if ( lgth_x )
|
|
memcpy(rem+lenn-lgth_x, tx, lgth_x);
|
|
|
|
return lenq;
|
|
}
|
|
|
|
|
|
/*
|
|
* Mod - Computes an integer modulo another integer
|
|
*
|
|
* x = x (mod n)
|
|
*
|
|
*/
|
|
void Mod(BYTE *x, int lenx, BYTE *n, int lenn)
|
|
{
|
|
BYTE quot[MAXPLEN+1], rem[2*MAXPLEN+1];
|
|
|
|
memset(quot, 0x00, sizeof(quot));
|
|
memset(rem, 0x00, sizeof(rem));
|
|
if ( DivMod(x, lenx, n, lenn, quot, rem) ) {
|
|
memset(x, 0x00, lenx);
|
|
memcpy(x+lenx-lenn, rem, lenn);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Div - Computes the integer division of two numbers
|
|
*
|
|
* x = x / n
|
|
*
|
|
*/
|
|
void Div(BYTE *x, int lenx, BYTE *n, int lenn)
|
|
{
|
|
BYTE quot[MAXPLEN+1], rem[2*MAXPLEN+1];
|
|
int lenq;
|
|
|
|
memset(quot, 0x00, sizeof(quot));
|
|
memset(rem, 0x00, sizeof(rem));
|
|
if ( (lenq = DivMod(x, lenx, n, lenn, quot, rem)) != 0 ) {
|
|
memset(x, 0x00, lenx);
|
|
memcpy(x+lenx-lenq, quot, lenq);
|
|
}
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** sub - Subtract two integers *
|
|
** *
|
|
** A = A - B *
|
|
** *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of subtrahend integer *
|
|
** B Address of subtractor integer *
|
|
** L Length of A and B in bytes *
|
|
** *
|
|
** NOTE: In order to save RAM, B is *
|
|
** two's complemented twice, *
|
|
** rather than using a copy of B *
|
|
** *
|
|
******************************************/
|
|
void sub(BYTE *A, int LA, BYTE *B, int LB)
|
|
{
|
|
BYTE *tb;
|
|
|
|
tb = (BYTE *)calloc(LA, 1);
|
|
memcpy(tb, B, LB);
|
|
negate(tb, LB);
|
|
add(A, LA, tb, LA);
|
|
|
|
FREE(tb);
|
|
}
|
|
|
|
|
|
/*****************************************
|
|
** negate - Negate an integer *
|
|
** *
|
|
** A = -A *
|
|
** *
|
|
** *
|
|
** Parameters: *
|
|
** *
|
|
** A Address of integer to negate *
|
|
** L Length of A in bytes *
|
|
** *
|
|
******************************************/
|
|
int negate(BYTE *A, int L)
|
|
{
|
|
int i, tL;
|
|
DIGIT accum;
|
|
|
|
/* Take one's complement of A */
|
|
for ( i=0; i<L; i++ )
|
|
A[i] = ~(A[i]);
|
|
|
|
/* Add one to get two's complement of A */
|
|
accum = 1;
|
|
tL = L-1;
|
|
while ( accum && (tL >= 0) ) {
|
|
accum += A[tL];
|
|
A[tL--] = (BYTE)(accum & 0xff);
|
|
accum = accum >> 8;
|
|
}
|
|
|
|
return accum;
|
|
}
|
|
|
|
|
|
/*
|
|
* add()
|
|
*
|
|
* A = A + B
|
|
*
|
|
* LB must be <= LA
|
|
*
|
|
*/
|
|
BYTE add(BYTE *A, int LA, BYTE *B, int LB)
|
|
{
|
|
int i, indexA, indexB;
|
|
DIGIT accum;
|
|
|
|
indexA = LA - 1; /* LSD of result */
|
|
indexB = LB - 1; /* LSD of B */
|
|
|
|
accum = 0;
|
|
for ( i = 0; i < LB; i++ ) {
|
|
accum += A[indexA];
|
|
accum += B[indexB--];
|
|
A[indexA--] = (BYTE)(accum & 0xff);
|
|
accum = accum >> 8;
|
|
}
|
|
|
|
if ( LA > LB )
|
|
while ( accum && (indexA >= 0) ) {
|
|
accum += A[indexA];
|
|
A[indexA--] = (BYTE)(accum & 0xff);
|
|
accum = accum >> 8;
|
|
}
|
|
|
|
return (BYTE)accum;
|
|
}
|
|
|
|
|
|
void prettyprintBstr(char *S, BYTE *A, int L)
|
|
{
|
|
int i, extra, ctrb, ctrl;
|
|
|
|
if ( L == 0 )
|
|
printf("%s <empty>", S);
|
|
else
|
|
printf("%s\n\t", S);
|
|
extra = L % 24;
|
|
if ( extra ) {
|
|
ctrb = 0;
|
|
for ( i=0; i<24-extra; i++ ) {
|
|
printf(" ");
|
|
if ( ++ctrb == 4) {
|
|
printf(" ");
|
|
ctrb = 0;
|
|
}
|
|
}
|
|
|
|
for ( i=0; i<extra; i++ ) {
|
|
printf("%02X", A[i]);
|
|
if ( ++ctrb == 4) {
|
|
printf(" ");
|
|
ctrb = 0;
|
|
}
|
|
}
|
|
printf("\n\t");
|
|
}
|
|
|
|
ctrb = ctrl = 0;
|
|
for ( i=extra; i<L; i++ ) {
|
|
printf("%02X", A[i]);
|
|
if ( ++ctrb == 4) {
|
|
ctrl++;
|
|
if ( ctrl == 6 ) {
|
|
printf("\n\t");
|
|
ctrl = 0;
|
|
}
|
|
else
|
|
printf(" ");
|
|
ctrb = 0;
|
|
}
|
|
}
|
|
printf("\n\n");
|
|
}
|
|
|
|
|
|
/**********************************************************************/
|
|
/* Performs byte reverse for PC based implementation (little endian) */
|
|
/**********************************************************************/
|
|
void byteReverse(unsigned long *buffer, int byteCount)
|
|
{
|
|
unsigned long value;
|
|
int count;
|
|
|
|
byteCount /= sizeof( unsigned long );
|
|
for( count = 0; count < byteCount; count++ ) {
|
|
value = ( buffer[ count ] << 16 ) | ( buffer[ count ] >> 16 );
|
|
buffer[ count ] = ( ( value & 0xFF00FF00L ) >> 8 ) | ( ( value & 0x00FF00FFL ) << 8 );
|
|
}
|
|
}
|
|
|
|
void
|
|
ahtopb (char *ascii_hex, BYTE *p_binary, int bin_len)
|
|
{
|
|
BYTE nibble;
|
|
int i;
|
|
|
|
for ( i=0; i<bin_len; i++ ) {
|
|
nibble = ascii_hex[i * 2];
|
|
if ( nibble > 'F' )
|
|
nibble -= 0x20;
|
|
if ( nibble > '9' )
|
|
nibble -= 7;
|
|
nibble -= '0';
|
|
p_binary[i] = nibble << 4;
|
|
|
|
nibble = ascii_hex[i * 2 + 1];
|
|
if ( nibble > 'F' )
|
|
nibble -= 0x20;
|
|
if ( nibble > '9' )
|
|
nibble -= 7;
|
|
nibble -= '0';
|
|
p_binary[i] += nibble;
|
|
}
|
|
} |