/* reduces a modulo n where n is of the form 2**p - d
This differs from reduce_2k since "d" can be larger
than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
{
mp_int q;
int p, res;
if ((res = mp_init(&q)) != MP_OKAY) {
return res;
}
p = mp_count_bits(n);
top:
/* q = a/2**p, a = a mod 2**p */
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
/* q = q * d */
if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
goto LBL_ERR;
}
/* a = a + q */
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
s_mp_sub(a, n, a);
goto top;
}
LBL_ERR:
mp_clear(&q);
return res;
}
/* high level subtraction (handles signs) */
int
mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
int sa, sb, res;
sa = a->sign;
sb = b->sign;
if (sa != sb) {
/* subtract a negative from a positive, OR */
/* subtract a positive from a negative. */
/* In either case, ADD their magnitudes, */
/* and use the sign of the first number. */
c->sign = sa;
res = s_mp_add (a, b, c);
} else {
/* subtract a positive from a positive, OR */
/* subtract a negative from a negative. */
/* First, take the difference between their */
/* magnitudes, then... */
if (mp_cmp_mag (a, b) != MP_LT) {
/* Copy the sign from the first */
c->sign = sa;
/* The first has a larger or equal magnitude */
res = s_mp_sub (a, b, c);
} else {
/* The result has the *opposite* sign from */
/* the first number. */
c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
/* The second has a larger magnitude */
res = s_mp_sub (b, a, c);
}
}
return res;
}
/* high level addition (handles signs) */
int mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
int sa, sb, res;
/* get sign of both inputs */
sa = a->sign;
sb = b->sign;
/* handle two cases, not four */
if (sa == sb) {
/* both positive or both negative */
/* add their magnitudes, copy the sign */
c->sign = sa;
res = s_mp_add(a, b, c);
} else {
/* one positive, the other negative */
/* subtract the one with the greater magnitude from */
/* the one of the lesser magnitude. The result gets */
/* the sign of the one with the greater magnitude. */
if (mp_cmp_mag(a, b) == MP_LT) {
c->sign = sb;
res = s_mp_sub(b, a, c);
} else {
c->sign = sa;
res = s_mp_sub(a, b, c);
}
}
return res;
}
/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
if (b->used > 1) {
if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
return res;
}
} else {
mp_set(a, 1);
bits = 1;
}
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
return res;
}
if (mp_cmp_mag (a, b) != MP_LT) {
if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
return res;
}
}
}
return MP_OKAY;
}
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
* Based on algorithm from the paper
*
* "Generating Efficient Primes for Discrete Log Cryptosystems"
* Chae Hoon Lim, Pil Joong Lee,
* POSTECH Information Research Laboratories
*
* The modulus must be of a special format [see manual]
*
* Has been modified to use algorithm 7.10 from the LTM book instead
*
* Input x must be in the range 0 <= x <= (n-1)**2
*/
int
mp_dr_reduce(mp_int *x, mp_int *n, mp_digit k) {
int err, i, m;
mp_word r;
mp_digit mu, *tmpx1, *tmpx2;
/* m = digits in modulus */
m = n->used;
/* ensure that "x" has at least 2m digits */
if (x->alloc < (m + m)) {
if ((err = mp_grow(x, m + m)) != MP_OKAY) {
return err;
}
}
/* top of loop, this is where the code resumes if
* another reduction pass is required.
*/
top:
/* aliases for digits */
/* alias for lower half of x */
tmpx1 = x->dp;
/* alias for upper half of x, or x/B**m */
tmpx2 = x->dp + m;
/* set carry to zero */
mu = 0;
/* compute (x mod B**m) + k * [x/B**m] inline and inplace */
for (i = 0; i < m; i++) {
r = (((mp_word) * tmpx2++) * (mp_word)k) + *tmpx1 + mu;
*tmpx1++ = (mp_digit)(r & MP_MASK);
mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
}
/* set final carry */
*tmpx1++ = mu;
/* zero words above m */
for (i = m + 1; i < x->used; i++) {
*tmpx1++ = 0;
}
/* clamp, sub and return */
mp_clamp(x);
/* if x >= n then subtract and reduce again
* Each successive "recursion" makes the input smaller and smaller.
*/
if (mp_cmp_mag(x, n) != MP_LT) {
if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
return err;
}
goto top;
}
return MP_OKAY;
}
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
{
int res;
mp_int t1,t2;
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* easy out */
if (mp_iszero(arg) == MP_YES) {
mp_zero(ret);
return MP_OKAY;
}
if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
/* First approx. (not very bad for large arg) */
mp_rshd (&t1,t1.used/2);
/* t1 > 0 */
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* And now t1 > sqrt(arg) */
do {
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1,&t2) == MP_GT);
mp_exch(&t1,ret);
E1: mp_clear(&t2);
E2: mp_clear(&t1);
return res;
}
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
/* compare based on sign */
if (a->sign != b->sign) {
if (a->sign == MP_NEG) {
return MP_LT;
} else {
return MP_GT;
}
}
/* compare digits */
if (a->sign == MP_NEG) {
/* if negative compare opposite direction */
return mp_cmp_mag(b, a);
} else {
return mp_cmp_mag(a, b);
}
}
/* reduces a modulo n where n is of the form 2**p - k */
int
mp_reduce_2k(mp_int *a, mp_int *n, mp_digit k)
{
mp_int q;
int p, res;
if ((res = mp_init(&q)) != MP_OKAY) {
return res;
}
p = mp_count_bits(n);
top:
/* q = a/2**p, a = a mod 2**p */
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto ERR;
}
if (k != 1) {
/* q = q * k */
if ((res = mp_mul_d(&q, k, &q)) != MP_OKAY) {
goto ERR;
}
}
/* a = a + q */
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
goto ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
s_mp_sub(a, n, a);
goto top;
}
ERR:
mp_clear(&q);
return res;
}
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
{
int res;
mp_int t1, t2;
if ((res = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) {
return res;
}
/* t1 = get the GCD of the two inputs */
if ((res = mp_gcd(a, b, &t1)) != MP_OKAY) {
goto LBL_T;
}
/* divide the smallest by the GCD */
if (mp_cmp_mag(a, b) == MP_LT) {
/* store quotient in t2 such that t2 * b is the LCM */
if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
goto LBL_T;
}
res = mp_mul(b, &t2, c);
} else {
/* store quotient in t2 such that t2 * a is the LCM */
if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
goto LBL_T;
}
res = mp_mul(a, &t2, c);
}
/* fix the sign to positive */
c->sign = MP_ZPOS;
LBL_T:
mp_clear_multi(&t1, &t2, NULL);
return res;
}
/* Store non-zero to ret if arg is square, and zero if not */
int mp_is_square(mp_int *arg,int *ret)
{
int res;
mp_digit c;
mp_int t;
unsigned long r;
/* Default to Non-square :) */
*ret = MP_NO;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* digits used? (TSD) */
if (arg->used == 0) {
return MP_OKAY;
}
/* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
if (rem_128[127 & DIGIT(arg,0)] == 1) {
return MP_OKAY;
}
/* Next check mod 105 (3*5*7) */
if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
return res;
}
if (rem_105[c] == 1) {
return MP_OKAY;
}
/* product of primes less than 2^31 */
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
goto ERR;
}
r = mp_get_int(&t);
/* Check for other prime modules, note it's not an ERROR but we must
* free "t" so the easiest way is to goto ERR. We know that res
* is already equal to MP_OKAY from the mp_mod call
*/
if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
/* Final check - is sqr(sqrt(arg)) == arg ? */
if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
goto ERR;
}
*ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
return res;
}
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
* HAC pp.598 Algorithm 14.20
*
* Note that the description in HAC is horribly
* incomplete. For example, it doesn't consider
* the case where digits are removed from 'x' in
* the inner loop. It also doesn't consider the
* case that y has fewer than three digits, etc..
*
* The overall algorithm is as described as
* 14.20 from HAC but fixed to treat these cases.
*/
int mp_div MPA(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
/* is divisor zero ? */
if (mp_iszero (b) == 1) {
return MP_VAL;
}
/* if a < b then q=0, r = a */
if (mp_cmp_mag (a, b) == MP_LT) {
if (d != NULL) {
res = mp_copy (MPST, a, d);
} else {
res = MP_OKAY;
}
if (c != NULL) {
mp_zero (c);
}
return res;
}
if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
return res;
}
q.used = a->used + 2;
if ((res = mp_init (&t1)) != MP_OKAY) {
goto LBL_Q;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init_copy (MPST, &x, a)) != MP_OKAY) {
goto LBL_T2;
}
if ((res = mp_init_copy (MPST, &y, b)) != MP_OKAY) {
goto LBL_X;
}
/* fix the sign */
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
x.sign = y.sign = MP_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = mp_count_bits(&y) % DIGIT_BIT;
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
if ((res = mp_mul_2d (MPST, &x, norm, &x)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_mul_2d (MPST, &y, norm, &y)) != MP_OKAY) {
goto LBL_Y;
}
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
if ((res = mp_lshd (MPST, &y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
goto LBL_Y;
}
while (mp_cmp (&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((res = mp_sub (MPST, &x, &y, &x)) != MP_OKAY) {
goto LBL_Y;
}
}
/* reset y by shifting it back down */
mp_rshd (&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
} else {
mp_word tmp;
tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
tmp |= ((mp_word) x.dp[i - 1]);
tmp /= ((mp_word) y.dp[t]);
if (tmp > (mp_word) MP_MASK)
tmp = MP_MASK;
q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
/* find left hand */
mp_zero (&t1);
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((res = mp_mul_d (MPST, &t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
goto LBL_Y;
}
/* find right hand */
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
if ((res = mp_mul_d (MPST, &y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_lshd (MPST, &t1, i - t - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_sub (MPST, &x, &t1, &x)) != MP_OKAY) {
goto LBL_Y;
}
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == MP_NEG) {
if ((res = mp_copy (MPST, &y, &t1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_lshd (MPST, &t1, i - t - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_add (MPST, &x, &t1, &x)) != MP_OKAY) {
goto LBL_Y;
}
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
}
}
/* now q is the quotient and x is the remainder
* [which we have to normalize]
*/
/* get sign before writing to c */
x.sign = x.used == 0 ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp (&q);
mp_managed_copy (MPST, &q, c);
c->sign = neg;
}
if (d != NULL) {
mp_div_2d (MPST, &x, norm, &x, NULL);
mp_managed_copy (MPST, &x, d);
}
res = MP_OKAY;
LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
LBL_Q:mp_clear (&q);
return res;
}
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(const mp_int *arg, mp_int *ret)
{
int res;
mp_int t1, t2;
int i, j, k;
#ifndef NO_FLOATING_POINT
volatile double d;
mp_digit dig;
#endif
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* easy out */
if (mp_iszero(arg) == MP_YES) {
mp_zero(ret);
return MP_OKAY;
}
i = (arg->used / 2) - 1;
j = 2 * i;
if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
for (k = 0; k < i; ++k) {
t1.dp[k] = (mp_digit) 0;
}
#ifndef NO_FLOATING_POINT
/* Estimate the square root using the hardware floating point unit. */
d = 0.0;
for (k = arg->used-1; k >= j; --k) {
d = ldexp(d, DIGIT_BIT) + (double)(arg->dp[k]);
}
/*
* At this point, d is the nearest floating point number to the most
* significant 1 or 2 mp_digits of arg. Extract its square root.
*/
d = sqrt(d);
/* dig is the most significant mp_digit of the square root */
dig = (mp_digit) ldexp(d, -DIGIT_BIT);
/*
* If the most significant digit is nonzero, find the next digit down
* by subtracting DIGIT_BIT times thie most significant digit.
* Subtract one from the result so that our initial estimate is always
* low.
*/
if (dig) {
t1.used = i+2;
d -= ldexp((double) dig, DIGIT_BIT);
if (d >= 1.0) {
t1.dp[i+1] = dig;
t1.dp[i] = ((mp_digit) d) - 1;
} else {
t1.dp[i+1] = dig-1;
t1.dp[i] = MP_DIGIT_MAX;
}
} else {
t1.used = i+1;
t1.dp[i] = ((mp_digit) d) - 1;
}
#else
/* Estimate the square root as having 1 in the most significant place. */
t1.used = i + 2;
t1.dp[i+1] = (mp_digit) 1;
t1.dp[i] = (mp_digit) 0;
#endif
/* t1 > 0 */
if ((res = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
/* And now t1 > sqrt(arg) */
do {
if ((res = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
mp_exch(&t1, ret);
E1:
mp_clear(&t2);
E2:
mp_clear(&t1);
return res;
}
/*
Sets ret to nonzero value if arg is square, 0 if not
Sets t to the square root of arg if one is available, 0 if not
*/
static int mp_issquare(mp_int *arg, int *ret, mp_int *t)
{
int res;
mp_digit c;
mp_int tmp;
unsigned long r;
/* Default to Non-square :) */
*ret = MP_NO;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* digits used? (TSD) */
if (arg->used == 0) {
return MP_OKAY;
}
/* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
if (rem_128[127 & DIGIT(arg, 0)] == 1) {
mp_set_int(t, (mp_digit)(0));
return MP_OKAY;
}
/* Next check mod 105 (3*5*7) */
if ((res = mp_mod_d(arg, 105, &c)) != MP_OKAY) {
mp_set_int(t, (mp_digit)(0));
return res;
}
if (rem_105[c] == 1) {
mp_set_int(t, (mp_digit)(0));
return MP_OKAY;
}
if ((res =
mp_init_set_int(t,
11L * 13L * 17L * 19L * 23L * 29L * 31L)) != MP_OKAY) {
mp_set_int(t, (mp_digit)(0));
return res;
}
if ((res = mp_mod(arg, t, t)) != MP_OKAY) {
goto ERR;
}
r = mp_get_int(t);
/* Check for other prime modules. We know that res
* is already equal to MP_OKAY from the mp_mod call
*/
if ((1L << (r % 11)) & 0x5C4L)
goto ERR;
if ((1L << (r % 13)) & 0x9E4L)
goto ERR;
if ((1L << (r % 17)) & 0x5CE8L)
goto ERR;
if ((1L << (r % 19)) & 0x4F50CL)
goto ERR;
if ((1L << (r % 23)) & 0x7ACCA0L)
goto ERR;
if ((1L << (r % 29)) & 0xC2EDD0CL)
goto ERR;
if ((1L << (r % 31)) & 0x6DE2B848L)
goto ERR;
/* Final check - is sqr(sqrt(arg)) == arg ? */
if ((res = mp_sqrt(arg, t)) != MP_OKAY) {
goto ERR;
}
mp_init(&tmp);
if ((res = mp_sqr(t, &tmp)) != MP_OKAY) {
goto ERR;
}
*ret = (mp_cmp_mag(&tmp, arg) == MP_EQ) ? MP_YES : MP_NO;
mp_clear(&tmp);
return res;
ERR:
mp_set_int(t, (mp_digit)(0));
mp_clear(&tmp);
return res;
}
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
{
int res;
mp_int t1,t2;
int i, j, k;
#ifndef NO_FLOATING_POINT
double d;
mp_digit dig;
#endif
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* easy out */
if (mp_iszero(arg) == MP_YES) {
mp_zero(ret);
return MP_OKAY;
}
i = (arg->used / 2) - 1;
j = 2 * i;
if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
for (k = 0; k < i; ++k) {
t1.dp[k] = (mp_digit) 0;
}
#ifndef NO_FLOATING_POINT
/* Estimate the square root using the hardware floating point unit. */
d = 0.0;
for (k = arg->used-1; k >= j; --k) {
d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]);
}
d = sqrt(d);
dig = (mp_digit) ldexp(d, -DIGIT_BIT);
if (dig) {
t1.used = i+2;
d -= ldexp((double) dig, DIGIT_BIT);
if (d != 0.0) {
t1.dp[i+1] = dig;
t1.dp[i] = ((mp_digit) d) - 1;
} else {
t1.dp[i+1] = dig-1;
t1.dp[i] = MP_DIGIT_MAX;
}
} else {
t1.used = i+1;
t1.dp[i] = ((mp_digit) d) - 1;
}
#else
/* Estimate the square root as having 1 in the most significant place. */
t1.used = i + 2;
t1.dp[i+1] = (mp_digit) 1;
t1.dp[i] = (mp_digit) 0;
#endif
/* t1 > 0 */
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* And now t1 > sqrt(arg) */
do {
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1,&t2) == MP_GT);
mp_exch(&t1,ret);
E1: mp_clear(&t2);
E2: mp_clear(&t1);
return res;
}
lnc_key_t *lnc_gen_key(const size_t size, int *status) {
mp_int small_prime, random, mul, s, tmp;
mp_int modulus, root, public_key, secret_key;
int test_small, test_full;
uint32_t smallsize = lnc_suggest_subgroup(size);
int ret;
lnc_key_t *out;
if(size > UINT_MAX) {
*status = LNC_ERR_OVER;
return NULL;
}
test_small = mp_prime_rabin_miller_trials((int)smallsize);
test_full = mp_prime_rabin_miller_trials((int)size);
if((ret = mp_init_multi(&small_prime, &random, &mul, &s, &tmp, &modulus, &root, &secret_key, &public_key, NULL)) != MP_OKAY) {
*status = LNC_ERR_LTM;
return NULL;
}
/*
* The modulus is created in the form p = q * r + 1. This aids
* in finding g and guarantees a large prime factor (q) in the
* order of the group. I the order of the group contains only
* small prime factors, the key can be attacked easily.
*/
printf("libnetcrypt: Generating small prime (%d bits)...\n", smallsize);
mp_prime_random_ex(&small_prime, test_small, smallsize, 0, lnc_fill_random, NULL);
printf("libnetcrypt: Generating modulus... (%d bits)\n", size);
do {
do {
mp_random(&random, size - smallsize);
} while(mp_cmp_d(&random, 0) == MP_EQ);
mp_mul(&small_prime, &random, &mul);
mp_add1(&mul, &modulus);
mp_prime_is_prime(&modulus, test_full, &ret);
} while(!ret);
/* Specified in FIPS 186-4 A.2.1 */
printf("libnetcrypt: Generating generator...\n");
do {
mp_random(&s, size - smallsize);
mp_exptmod(&s, &random, &modulus, &root);
} while(mp_cmp_d(&root, 1) == MP_EQ);
/*
* We make sure a and g^a != 1 as these would make
* determining the shared secret trivial.
*/
printf("libnetcrypt: Generating secret and public key...\n");
do {
do {
mp_random(&secret_key, size);
} while((mp_cmp_d(&secret_key, 1) == MP_EQ) || (mp_cmp_mag(&secret_key, &modulus) != MP_LT));
mp_exptmod(&root, &secret_key, &modulus, &public_key);
} while(mp_cmp_d(&public_key, 1) == MP_EQ);
out = malloc(sizeof(lnc_key_t));
out->generator = root;
out->modulus = modulus;
out->secret_key = secret_key;
out->public_key = public_key;
printf("libnetcrypt: Done.\n");
mp_clear_multi(&small_prime, &random, &mul, &s, &tmp, NULL);
*status = LNC_OK;
return out;
}
int main(void)
{
mp_int a, b, c, d, e, f;
unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n, t;
unsigned rr;
int i, n, err, cnt, ix, old_kara_m, old_kara_s;
mp_digit mp;
mp_init(&a);
mp_init(&b);
mp_init(&c);
mp_init(&d);
mp_init(&e);
mp_init(&f);
srand(time(NULL));
#if 0
// test montgomery
printf("Testing montgomery...\n");
for (i = 1; i < 10; i++) {
printf("Testing digit size: %d\n", i);
for (n = 0; n < 1000; n++) {
mp_rand(&a, i);
a.dp[0] |= 1;
// let's see if R is right
mp_montgomery_calc_normalization(&b, &a);
mp_montgomery_setup(&a, &mp);
// now test a random reduction
for (ix = 0; ix < 100; ix++) {
mp_rand(&c, 1 + abs(rand()) % (2*i));
mp_copy(&c, &d);
mp_copy(&c, &e);
mp_mod(&d, &a, &d);
mp_montgomery_reduce(&c, &a, mp);
mp_mulmod(&c, &b, &a, &c);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); exit(EXIT_FAILURE); }
}
}
}
printf("done\n");
// test mp_get_int
printf("Testing: mp_get_int\n");
for (i = 0; i < 1000; ++i) {
t = ((unsigned long) rand() * rand() + 1) & 0xFFFFFFFF;
mp_set_int(&a, t);
if (t != mp_get_int(&a)) {
printf("mp_get_int() bad result!\n");
return 1;
}
}
mp_set_int(&a, 0);
if (mp_get_int(&a) != 0) {
printf("mp_get_int() bad result!\n");
return 1;
}
mp_set_int(&a, 0xffffffff);
if (mp_get_int(&a) != 0xffffffff) {
printf("mp_get_int() bad result!\n");
return 1;
}
// test mp_sqrt
printf("Testing: mp_sqrt\n");
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
n = (rand() & 15) + 1;
mp_rand(&a, n);
if (mp_sqrt(&a, &b) != MP_OKAY) {
printf("mp_sqrt() error!\n");
return 1;
}
mp_n_root(&a, 2, &a);
if (mp_cmp_mag(&b, &a) != MP_EQ) {
printf("mp_sqrt() bad result!\n");
return 1;
}
}
printf("\nTesting: mp_is_square\n");
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
/* test mp_is_square false negatives */
n = (rand() & 7) + 1;
mp_rand(&a, n);
mp_sqr(&a, &a);
if (mp_is_square(&a, &n) != MP_OKAY) {
printf("fn:mp_is_square() error!\n");
return 1;
}
if (n == 0) {
printf("fn:mp_is_square() bad result!\n");
return 1;
}
/* test for false positives */
mp_add_d(&a, 1, &a);
if (mp_is_square(&a, &n) != MP_OKAY) {
printf("fp:mp_is_square() error!\n");
return 1;
}
if (n == 1) {
printf("fp:mp_is_square() bad result!\n");
return 1;
}
}
printf("\n\n");
/* test for size */
for (ix = 10; ix < 128; ix++) {
printf("Testing (not safe-prime): %9d bits \r", ix);
fflush(stdout);
err =
mp_prime_random_ex(&a, 8, ix,
(rand() & 1) ? LTM_PRIME_2MSB_OFF :
LTM_PRIME_2MSB_ON, myrng, NULL);
if (err != MP_OKAY) {
printf("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits(&a) != ix) {
printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
return EXIT_FAILURE;
}
}
for (ix = 16; ix < 128; ix++) {
printf("Testing ( safe-prime): %9d bits \r", ix);
fflush(stdout);
err =
mp_prime_random_ex(&a, 8, ix,
((rand() & 1) ? LTM_PRIME_2MSB_OFF :
LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng,
NULL);
if (err != MP_OKAY) {
printf("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits(&a) != ix) {
printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
return EXIT_FAILURE;
}
/* let's see if it's really a safe prime */
mp_sub_d(&a, 1, &a);
mp_div_2(&a, &a);
mp_prime_is_prime(&a, 8, &cnt);
if (cnt != MP_YES) {
printf("sub is not prime!\n");
return EXIT_FAILURE;
}
}
printf("\n\n");
mp_read_radix(&a, "123456", 10);
mp_toradix_n(&a, buf, 10, 3);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 4);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 30);
printf("a == %s\n", buf);
#if 0
for (;;) {
fgets(buf, sizeof(buf), stdin);
mp_read_radix(&a, buf, 10);
mp_prime_next_prime(&a, 5, 1);
mp_toradix(&a, buf, 10);
printf("%s, %lu\n", buf, a.dp[0] & 3);
}
#endif
/* test mp_cnt_lsb */
printf("testing mp_cnt_lsb...\n");
mp_set(&a, 1);
for (ix = 0; ix < 1024; ix++) {
if (mp_cnt_lsb(&a) != ix) {
printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
return 0;
}
mp_mul_2(&a, &a);
}
/* test mp_reduce_2k */
printf("Testing mp_reduce_2k...\n");
for (cnt = 3; cnt <= 128; ++cnt) {
mp_digit tmp;
mp_2expt(&a, cnt);
mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */
printf("\nTesting %4d bits", cnt);
printf("(%d)", mp_reduce_is_2k(&a));
mp_reduce_2k_setup(&a, &tmp);
printf("(%d)", tmp);
for (ix = 0; ix < 1000; ix++) {
if (!(ix & 127)) {
printf(".");
fflush(stdout);
}
mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2);
mp_copy(&c, &b);
mp_mod(&c, &a, &c);
mp_reduce_2k(&b, &a, 2);
if (mp_cmp(&c, &b)) {
printf("FAILED\n");
exit(0);
}
}
}
/* test mp_div_3 */
printf("Testing mp_div_3...\n");
mp_set(&d, 3);
for (cnt = 0; cnt < 10000;) {
mp_digit r1, r2;
if (!(++cnt & 127))
printf("%9d\r", cnt);
mp_rand(&a, abs(rand()) % 128 + 1);
mp_div(&a, &d, &b, &e);
mp_div_3(&a, &c, &r2);
if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
printf("\n\nmp_div_3 => Failure\n");
}
}
printf("\n\nPassed div_3 testing\n");
/* test the DR reduction */
printf("testing mp_dr_reduce...\n");
for (cnt = 2; cnt < 32; cnt++) {
printf("%d digit modulus\n", cnt);
mp_grow(&a, cnt);
mp_zero(&a);
for (ix = 1; ix < cnt; ix++) {
a.dp[ix] = MP_MASK;
}
a.used = cnt;
a.dp[0] = 3;
mp_rand(&b, cnt - 1);
mp_copy(&b, &c);
rr = 0;
do {
if (!(rr & 127)) {
printf("%9lu\r", rr);
fflush(stdout);
}
mp_sqr(&b, &b);
mp_add_d(&b, 1, &b);
mp_copy(&b, &c);
mp_mod(&b, &a, &b);
mp_dr_reduce(&c, &a, (((mp_digit) 1) << DIGIT_BIT) - a.dp[0]);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("Failed on trial %lu\n", rr);
exit(-1);
}
} while (++rr < 500);
printf("Passed DR test for %d digits\n", cnt);
}
#endif
/* test the mp_reduce_2k_l code */
#if 0
#if 0
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
mp_2expt(&a, 1024);
mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
mp_sub(&a, &b, &a);
#elif 1
/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */
mp_2expt(&a, 2048);
mp_read_radix(&b,
"1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
16);
mp_sub(&a, &b, &a);
#endif
mp_todecimal(&a, buf);
printf("p==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
if (mp_reduce_is_2k_l(&a) != 1) {
printf("mp_reduce_is_2k_l() return 0, should be 1\n");
return EXIT_FAILURE;
}
mp_reduce_2k_setup_l(&a, &d);
/* now do a million square+1 to see if it varies */
mp_rand(&b, 64);
mp_mod(&b, &a, &b);
mp_copy(&b, &c);
printf("testing mp_reduce_2k_l...");
fflush(stdout);
for (cnt = 0; cnt < (1UL << 20); cnt++) {
mp_sqr(&b, &b);
mp_add_d(&b, 1, &b);
mp_reduce_2k_l(&b, &a, &d);
mp_sqr(&c, &c);
mp_add_d(&c, 1, &c);
mp_mod(&c, &a, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("mp_reduce_2k_l() failed at step %lu\n", cnt);
mp_tohex(&b, buf);
printf("b == %s\n", buf);
mp_tohex(&c, buf);
printf("c == %s\n", buf);
return EXIT_FAILURE;
}
}
printf("...Passed\n");
#endif
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
sub_d_n = 0;
/* force KARA and TOOM to enable despite cutoffs */
KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;
for (;;) {
/* randomly clear and re-init one variable, this has the affect of triming the alloc space */
switch (abs(rand()) % 7) {
case 0:
mp_clear(&a);
mp_init(&a);
break;
case 1:
mp_clear(&b);
mp_init(&b);
break;
case 2:
mp_clear(&c);
mp_init(&c);
break;
case 3:
mp_clear(&d);
mp_init(&d);
break;
case 4:
mp_clear(&e);
mp_init(&e);
break;
case 5:
mp_clear(&f);
mp_init(&f);
break;
case 6:
break; /* don't clear any */
}
printf
("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
fgets(cmd, 4095, stdin);
cmd[strlen(cmd) - 1] = 0;
printf("%s ]\r", cmd);
fflush(stdout);
if (!strcmp(cmd, "mul2d")) {
++mul2d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_mul_2d(&a, rr, &a);
a.sign = b.sign;
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mul2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "div2d")) {
++div2d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_div_2d(&a, rr, &a, &e);
a.sign = b.sign;
if (a.used == b.used && a.used == 0) {
a.sign = b.sign = MP_ZPOS;
}
if (mp_cmp(&a, &b) != MP_EQ) {
printf("div2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "add")) {
++add_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_add(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("add %lu failure!\n", add_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
/* test the sign/unsigned storage functions */
rr = mp_signed_bin_size(&c);
mp_to_signed_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mp_signed_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
rr = mp_unsigned_bin_size(&c);
mp_to_unsigned_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp_mag(&c, &d) != MP_EQ) {
printf("mp_unsigned_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "sub")) {
++sub_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_sub(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("sub %lu failure!\n", sub_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "mul")) {
++mul_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_mul(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mul %lu failure!\n", mul_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "div")) {
++div_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&d, buf, 64);
mp_div(&a, &b, &e, &f);
if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
mp_cmp(&d, &f));
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
draw(&f);
return 0;
}
} else if (!strcmp(cmd, "sqr")) {
++sqr_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_copy(&a, &c);
mp_sqr(&c, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sqr %lu failure!\n", sqr_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "gcd")) {
++gcd_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_gcd(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("gcd %lu failure!\n", gcd_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "lcm")) {
++lcm_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_lcm(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("lcm %lu failure!\n", lcm_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "expt")) {
++expt_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&d, buf, 64);
mp_copy(&a, &e);
mp_exptmod(&e, &b, &c, &e);
if (mp_cmp(&d, &e) != MP_EQ) {
printf("expt %lu failure!\n", expt_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
return 0;
}
} else if (!strcmp(cmd, "invmod")) {
++inv_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_invmod(&a, &b, &d);
mp_mulmod(&d, &a, &b, &e);
if (mp_cmp_d(&e, 1) != MP_EQ) {
printf("inv [wrong value from MPI?!] failure\n");
draw(&a);
draw(&b);
draw(&c);
draw(&d);
mp_gcd(&a, &b, &e);
draw(&e);
return 0;
}
} else if (!strcmp(cmd, "div2")) {
++div2_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_div_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("div_2 %lu failure\n", div2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "mul2")) {
++mul2_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_mul_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("mul_2 %lu failure\n", mul2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "add_d")) {
++add_d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &ix);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_add_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("add_d %lu failure\n", add_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return 0;
}
} else if (!strcmp(cmd, "sub_d")) {
++sub_d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &ix);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_sub_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sub_d %lu failure\n", sub_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return 0;
}
}
}
return 0;
}
/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, A, B, C, D;
int res;
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
return res;
}
/* x = a, y = b */
if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
goto LBL_ERR;
}
/* 2. [modified] if x,y are both even then return an error! */
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto LBL_ERR;
}
mp_set (&A, 1);
mp_set (&D, 1);
top:
/* 4. while u is even do */
while (mp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
goto LBL_ERR;
}
/* 4.2 if A or B is odd then */
if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 5. while v is even do */
while (mp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
goto LBL_ERR;
}
/* 5.2 if C or D is odd then */
if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, A = A - C, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero (&u) == 0)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
goto LBL_ERR;
}
/* if its too low */
while (mp_cmp_d(&C, 0) == MP_LT) {
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* too big */
while (mp_cmp_mag(&C, b) != MP_LT) {
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
}
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
mp_int u, v;
int k, u_lsb, v_lsb, res;
/* either zero than gcd is the largest */
if (mp_iszero (a) == MP_YES) {
return mp_abs (b, c);
}
if (mp_iszero (b) == MP_YES) {
return mp_abs (a, c);
}
/* get copies of a and b we can modify */
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
goto LBL_U;
}
/* must be positive for the remainder of the algorithm */
u.sign = v.sign = MP_ZPOS;
/* B1. Find the common power of two for u and v */
u_lsb = mp_cnt_lsb(&u);
v_lsb = mp_cnt_lsb(&v);
k = MIN(u_lsb, v_lsb);
if (k > 0) {
/* divide the power of two out */
if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
goto LBL_V;
}
if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
/* divide any remaining factors of two out */
if (u_lsb != k) {
if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
if (v_lsb != k) {
if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
while (mp_iszero(&v) == MP_NO) {
/* make sure v is the largest */
if (mp_cmp_mag(&u, &v) == MP_GT) {
/* swap u and v to make sure v is >= u */
mp_exch(&u, &v);
}
/* subtract smallest from largest */
if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
goto LBL_V;
}
/* Divide out all factors of two */
if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
/* multiply by 2**k which we divided out at the beginning */
if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
goto LBL_V;
}
c->sign = MP_ZPOS;
res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
return res;
}
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
* This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
* Based on Algorithm 14.32 on pp.601 of HAC.
*/
int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
int ix, res, olduse;
mp_word W[MP_WARRAY] = { 0 };
/* get old used count */
olduse = x->used;
/* grow a as required */
if (x->alloc < n->used + 1) {
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
return res;
}
}
/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
{
register mp_word *_W;
register mp_digit *tmpx;
/* alias for the W[] array */
_W = W;
/* alias for the digits of x*/
tmpx = x->dp;
/* copy the digits of a into W[0..a->used-1] */
for (ix = 0; ix < x->used; ix++) {
*_W++ = *tmpx++;
}
/* zero the high words of W[a->used..m->used*2] */
for (; ix < n->used * 2 + 1; ix++) {
*_W++ = 0;
}
}
/* now we proceed to zero successive digits
* from the least significant upwards
*/
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b
*
* We avoid a double precision multiplication (which isn't required)
* by casting the value down to a mp_digit. Note this requires
* that W[ix-1] have the carry cleared (see after the inner loop)
*/
register mp_digit mu;
mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
/* a = a + mu * m * b**i
*
* This is computed in place and on the fly. The multiplication
* by b**i is handled by offseting which columns the results
* are added to.
*
* Note the comba method normally doesn't handle carries in the
* inner loop In this case we fix the carry from the previous
* column since the Montgomery reduction requires digits of the
* result (so far) [see above] to work. This is
* handled by fixing up one carry after the inner loop. The
* carry fixups are done in order so after these loops the
* first m->used words of W[] have the carries fixed
*/
{
register int iy;
register mp_digit *tmpn;
register mp_word *_W;
/* alias for the digits of the modulus */
tmpn = n->dp;
/* Alias for the columns set by an offset of ix */
_W = W + ix;
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
register mp_digit *tmpx;
register mp_word *_W, *_W1;
/* nox fix rest of carries */
/* alias for current word */
_W1 = W + ix;
/* alias for next word, where the carry goes */
_W = W + ++ix;
for (; ix <= n->used * 2 + 1; ix++) {
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
}
/* copy out, A = A/b**n
*
* The result is A/b**n but instead of converting from an
* array of mp_word to mp_digit than calling mp_rshd
* we just copy them in the right order
*/
/* alias for destination word */
tmpx = x->dp;
/* alias for shifted double precision result */
_W = W + n->used;
for (ix = 0; ix < n->used + 1; ix++) {
*tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
}
/* zero oldused digits, if the input a was larger than
* m->used+1 we'll have to clear the digits
*/
for (; ix < olduse; ix++) {
*tmpx++ = 0;
}
}
/* set the max used and clamp */
x->used = n->used + 1;
mp_clamp (x);
/* if A >= m then A = A - m */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}
return MP_OKAY;
}
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
int ix, res, digs;
mp_digit mu;
/* can the fast reduction [comba] method be used?
*
* Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
digs = n->used * 2 + 1;
if ((digs < MP_WARRAY) &&
n->used <
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_mp_montgomery_reduce (x, n, rho);
}
/* grow the input as required */
if (x->alloc < digs) {
if ((res = mp_grow (x, digs)) != MP_OKAY) {
return res;
}
}
x->used = digs;
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
* montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
/* a = a + mu * m * b**i */
{
register int iy;
register mp_digit *tmpn, *tmpx, u;
register mp_word r;
/* alias for digits of the modulus */
tmpn = n->dp;
/* alias for the digits of x [the input] */
tmpx = x->dp + ix;
/* set the carry to zero */
u = 0;
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
/* compute product and sum */
r = ((mp_word)mu) * ((mp_word)*tmpn++) +
((mp_word) u) + ((mp_word) * tmpx);
/* get carry */
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
/* fix digit */
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
}
/* At this point the ix'th digit of x should be zero */
/* propagate carries upwards as required*/
while (u) {
*tmpx += u;
u = *tmpx >> DIGIT_BIT;
*tmpx++ &= MP_MASK;
}
}
}
/* at this point the n.used'th least
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/
/* x = x/b**n.used */
mp_clamp(x);
mp_rshd (x, n->used);
/* if x >= n then x = x - n */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}
return MP_OKAY;
}
/* slower bit-bang division... also smaller */
int mp_div MPA(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
mp_int ta, tb, tq, q;
int res, n, n2;
/* is divisor zero ? */
if (mp_iszero (b) == 1) {
return MP_VAL;
}
/* if a < b then q=0, r = a */
if (mp_cmp_mag (a, b) == MP_LT) {
if (d != NULL) {
res = mp_copy (a, d);
} else {
res = MP_OKAY;
}
if (c != NULL) {
mp_zero (c);
}
return res;
}
/* init our temps */
if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
return res;
}
mp_set(&tq, 1);
n = mp_count_bits(a) - mp_count_bits(b);
if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
((res = mp_abs(b, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
goto LBL_ERR;
}
while (n-- >= 0) {
if (mp_cmp(&tb, &ta) != MP_GT) {
if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
goto LBL_ERR;
}
}
if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
goto LBL_ERR;
}
}
/* now q == quotient and ta == remainder */
n = a->sign;
n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
if (c != NULL) {
mp_exch(c, &q);
c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
}
if (d != NULL) {
mp_exch(d, &ta);
d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
}
LBL_ERR:
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
return res;
}
int main(void)
{
unsigned rr;
int cnt, ix;
#if LTM_DEMO_TEST_VS_MTEST
unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n;
char* ret;
#else
unsigned long s, t;
unsigned long long q, r;
mp_digit mp;
int i, n, err, should;
#endif
if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY)
return EXIT_FAILURE;
atexit(_cleanup);
#if defined(LTM_DEMO_REAL_RAND)
if (!fd_urandom) {
fd_urandom = fopen("/dev/urandom", "r");
if (!fd_urandom) {
#if !defined(_WIN32)
fprintf(stderr, "\ncould not open /dev/urandom\n");
#endif
}
}
#endif
srand(LTM_DEMO_RAND_SEED);
#ifdef MP_8BIT
printf("Digit size 8 Bit \n");
#endif
#ifdef MP_16BIT
printf("Digit size 16 Bit \n");
#endif
#ifdef MP_32BIT
printf("Digit size 32 Bit \n");
#endif
#ifdef MP_64BIT
printf("Digit size 64 Bit \n");
#endif
printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit));
printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word));
printf("DIGIT_BIT: %d\n", DIGIT_BIT);
printf("MP_PREC: %d\n", MP_PREC);
#if LTM_DEMO_TEST_VS_MTEST == 0
// trivial stuff
// a: 0->5
mp_set_int(&a, 5);
// a: 5-> b: -5
mp_neg(&a, &b);
if (mp_cmp(&a, &b) != MP_GT) {
return EXIT_FAILURE;
}
if (mp_cmp(&b, &a) != MP_LT) {
return EXIT_FAILURE;
}
// a: 5-> a: -5
mp_neg(&a, &a);
if (mp_cmp(&b, &a) != MP_EQ) {
return EXIT_FAILURE;
}
// a: -5-> b: 5
mp_abs(&a, &b);
if (mp_isneg(&b) != MP_NO) {
return EXIT_FAILURE;
}
// a: -5-> b: -4
mp_add_d(&a, 1, &b);
if (mp_isneg(&b) != MP_YES) {
return EXIT_FAILURE;
}
if (mp_get_int(&b) != 4) {
return EXIT_FAILURE;
}
// a: -5-> b: 1
mp_add_d(&a, 6, &b);
if (mp_get_int(&b) != 1) {
return EXIT_FAILURE;
}
// a: -5-> a: 1
mp_add_d(&a, 6, &a);
if (mp_get_int(&a) != 1) {
return EXIT_FAILURE;
}
mp_zero(&a);
// a: 0-> a: 6
mp_add_d(&a, 6, &a);
if (mp_get_int(&a) != 6) {
return EXIT_FAILURE;
}
mp_set_int(&a, 0);
mp_set_int(&b, 1);
if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) {
printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err));
return EXIT_FAILURE;
}
if (i != 1) {
printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i);
return EXIT_FAILURE;
}
for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) {
mp_set_int(&b, jacobi[cnt].n);
/* only test positive values of a */
for (n = -5; n <= 10; ++n) {
mp_set_int(&a, abs(n));
should = MP_OKAY;
if (n < 0) {
mp_neg(&a, &a);
/* Until #44 is fixed the negative a's must fail */
should = MP_VAL;
}
if ((err = mp_jacobi(&a, &b, &i)) != should) {
printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err));
return EXIT_FAILURE;
}
if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) {
printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]);
return EXIT_FAILURE;
}
}
}
// test mp_get_int
printf("\n\nTesting: mp_get_int");
for (i = 0; i < 1000; ++i) {
t = ((unsigned long) rand () * rand () + 1) & 0xFFFFFFFF;
mp_set_int (&a, t);
if (t != mp_get_int (&a)) {
printf ("\nmp_get_int() bad result!");
return EXIT_FAILURE;
}
}
mp_set_int(&a, 0);
if (mp_get_int(&a) != 0) {
printf("\nmp_get_int() bad result!");
return EXIT_FAILURE;
}
mp_set_int(&a, 0xffffffff);
if (mp_get_int(&a) != 0xffffffff) {
printf("\nmp_get_int() bad result!");
return EXIT_FAILURE;
}
printf("\n\nTesting: mp_get_long\n");
for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) {
t = (1ULL << (i+1)) - 1;
if (!t)
t = -1;
printf(" t = 0x%lx i = %d\r", t, i);
do {
if (mp_set_long(&a, t) != MP_OKAY) {
printf("\nmp_set_long() error!");
return EXIT_FAILURE;
}
s = mp_get_long(&a);
if (s != t) {
printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t);
return EXIT_FAILURE;
}
t <<= 1;
} while(t);
}
printf("\n\nTesting: mp_get_long_long\n");
for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) {
r = (1ULL << (i+1)) - 1;
if (!r)
r = -1;
printf(" r = 0x%llx i = %d\r", r, i);
do {
if (mp_set_long_long(&a, r) != MP_OKAY) {
printf("\nmp_set_long_long() error!");
return EXIT_FAILURE;
}
q = mp_get_long_long(&a);
if (q != r) {
printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r);
return EXIT_FAILURE;
}
r <<= 1;
} while(r);
}
// test mp_sqrt
printf("\n\nTesting: mp_sqrt\n");
for (i = 0; i < 1000; ++i) {
printf ("%6d\r", i);
fflush (stdout);
n = (rand () & 15) + 1;
mp_rand (&a, n);
if (mp_sqrt (&a, &b) != MP_OKAY) {
printf ("\nmp_sqrt() error!");
return EXIT_FAILURE;
}
mp_n_root_ex (&a, 2, &c, 0);
mp_n_root_ex (&a, 2, &d, 1);
if (mp_cmp_mag (&c, &d) != MP_EQ) {
printf ("\nmp_n_root_ex() bad result!");
return EXIT_FAILURE;
}
if (mp_cmp_mag (&b, &c) != MP_EQ) {
printf ("mp_sqrt() bad result!\n");
return EXIT_FAILURE;
}
}
printf("\n\nTesting: mp_is_square\n");
for (i = 0; i < 1000; ++i) {
printf ("%6d\r", i);
fflush (stdout);
/* test mp_is_square false negatives */
n = (rand () & 7) + 1;
mp_rand (&a, n);
mp_sqr (&a, &a);
if (mp_is_square (&a, &n) != MP_OKAY) {
printf ("\nfn:mp_is_square() error!");
return EXIT_FAILURE;
}
if (n == 0) {
printf ("\nfn:mp_is_square() bad result!");
return EXIT_FAILURE;
}
/* test for false positives */
mp_add_d (&a, 1, &a);
if (mp_is_square (&a, &n) != MP_OKAY) {
printf ("\nfp:mp_is_square() error!");
return EXIT_FAILURE;
}
if (n == 1) {
printf ("\nfp:mp_is_square() bad result!");
return EXIT_FAILURE;
}
}
printf("\n\n");
// r^2 = n (mod p)
for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
mp_set_int(&a, sqrtmod_prime[i].p);
mp_set_int(&b, sqrtmod_prime[i].n);
if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) {
printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1));
return EXIT_FAILURE;
}
if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) {
printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1));
ndraw(&c, "r");
return EXIT_FAILURE;
}
}
/* test for size */
for (ix = 10; ix < 128; ix++) {
printf ("Testing (not safe-prime): %9d bits \r", ix);
fflush (stdout);
err = mp_prime_random_ex (&a, 8, ix,
(rand () & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng,
NULL);
if (err != MP_OKAY) {
printf ("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits (&a) != ix) {
printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
return EXIT_FAILURE;
}
}
printf("\n");
for (ix = 16; ix < 128; ix++) {
printf ("Testing ( safe-prime): %9d bits \r", ix);
fflush (stdout);
err = mp_prime_random_ex (
&a, 8, ix, ((rand () & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE,
myrng, NULL);
if (err != MP_OKAY) {
printf ("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits (&a) != ix) {
printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
return EXIT_FAILURE;
}
/* let's see if it's really a safe prime */
mp_sub_d (&a, 1, &a);
mp_div_2 (&a, &a);
mp_prime_is_prime (&a, 8, &cnt);
if (cnt != MP_YES) {
printf ("sub is not prime!\n");
return EXIT_FAILURE;
}
}
printf("\n\n");
// test montgomery
printf("Testing: montgomery...\n");
for (i = 1; i <= 10; i++) {
if (i == 10)
i = 1000;
printf(" digit size: %2d\r", i);
fflush(stdout);
for (n = 0; n < 1000; n++) {
mp_rand(&a, i);
a.dp[0] |= 1;
// let's see if R is right
mp_montgomery_calc_normalization(&b, &a);
mp_montgomery_setup(&a, &mp);
// now test a random reduction
for (ix = 0; ix < 100; ix++) {
mp_rand(&c, 1 + abs(rand()) % (2*i));
mp_copy(&c, &d);
mp_copy(&c, &e);
mp_mod(&d, &a, &d);
mp_montgomery_reduce(&c, &a, mp);
mp_mulmod(&c, &b, &a, &c);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); return EXIT_FAILURE; }
/* only one big montgomery reduction */
if (i > 10)
{
n = 1000;
ix = 100;
}
}
}
}
printf("\n\n");
mp_read_radix(&a, "123456", 10);
mp_toradix_n(&a, buf, 10, 3);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 4);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 30);
printf("a == %s\n", buf);
#if 0
for (;;) {
fgets(buf, sizeof(buf), stdin);
mp_read_radix(&a, buf, 10);
mp_prime_next_prime(&a, 5, 1);
mp_toradix(&a, buf, 10);
printf("%s, %lu\n", buf, a.dp[0] & 3);
}
#endif
/* test mp_cnt_lsb */
printf("\n\nTesting: mp_cnt_lsb");
mp_set(&a, 1);
for (ix = 0; ix < 1024; ix++) {
if (mp_cnt_lsb (&a) != ix) {
printf ("Failed at %d, %d\n", ix, mp_cnt_lsb (&a));
return EXIT_FAILURE;
}
mp_mul_2 (&a, &a);
}
/* test mp_reduce_2k */
printf("\n\nTesting: mp_reduce_2k\n");
for (cnt = 3; cnt <= 128; ++cnt) {
mp_digit tmp;
mp_2expt (&a, cnt);
mp_sub_d (&a, 2, &a); /* a = 2**cnt - 2 */
printf ("\r %4d bits", cnt);
printf ("(%d)", mp_reduce_is_2k (&a));
mp_reduce_2k_setup (&a, &tmp);
printf ("(%lu)", (unsigned long) tmp);
for (ix = 0; ix < 1000; ix++) {
if (!(ix & 127)) {
printf (".");
fflush (stdout);
}
mp_rand (&b, (cnt / DIGIT_BIT + 1) * 2);
mp_copy (&c, &b);
mp_mod (&c, &a, &c);
mp_reduce_2k (&b, &a, 2);
if (mp_cmp (&c, &b)) {
printf ("FAILED\n");
return EXIT_FAILURE;
}
}
}
/* test mp_div_3 */
printf("\n\nTesting: mp_div_3...\n");
mp_set(&d, 3);
for (cnt = 0; cnt < 10000;) {
mp_digit r2;
if (!(++cnt & 127))
{
printf("%9d\r", cnt);
fflush(stdout);
}
mp_rand(&a, abs(rand()) % 128 + 1);
mp_div(&a, &d, &b, &e);
mp_div_3(&a, &c, &r2);
if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
printf("\nmp_div_3 => Failure\n");
}
}
printf("\nPassed div_3 testing");
/* test the DR reduction */
printf("\n\nTesting: mp_dr_reduce...\n");
for (cnt = 2; cnt < 32; cnt++) {
printf ("\r%d digit modulus", cnt);
mp_grow (&a, cnt);
mp_zero (&a);
for (ix = 1; ix < cnt; ix++) {
a.dp[ix] = MP_MASK;
}
a.used = cnt;
a.dp[0] = 3;
mp_rand (&b, cnt - 1);
mp_copy (&b, &c);
rr = 0;
do {
if (!(rr & 127)) {
printf (".");
fflush (stdout);
}
mp_sqr (&b, &b);
mp_add_d (&b, 1, &b);
mp_copy (&b, &c);
mp_mod (&b, &a, &b);
mp_dr_setup(&a, &mp),
mp_dr_reduce (&c, &a, mp);
if (mp_cmp (&b, &c) != MP_EQ) {
printf ("Failed on trial %u\n", rr);
return EXIT_FAILURE;
}
} while (++rr < 500);
printf (" passed");
fflush (stdout);
}
#if LTM_DEMO_TEST_REDUCE_2K_L
/* test the mp_reduce_2k_l code */
#if LTM_DEMO_TEST_REDUCE_2K_L == 1
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
mp_2expt(&a, 1024);
mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
mp_sub(&a, &b, &a);
#elif LTM_DEMO_TEST_REDUCE_2K_L == 2
/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */
mp_2expt(&a, 2048);
mp_read_radix(&b,
"1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
16);
mp_sub(&a, &b, &a);
#else
#error oops
#endif
mp_todecimal(&a, buf);
printf("\n\np==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
if (mp_reduce_is_2k_l(&a) != 1) {
printf("mp_reduce_is_2k_l() return 0, should be 1\n");
return EXIT_FAILURE;
}
mp_reduce_2k_setup_l(&a, &d);
/* now do a million square+1 to see if it varies */
mp_rand(&b, 64);
mp_mod(&b, &a, &b);
mp_copy(&b, &c);
printf("Testing: mp_reduce_2k_l...");
fflush(stdout);
for (cnt = 0; cnt < (int)(1UL << 20); cnt++) {
mp_sqr(&b, &b);
mp_add_d(&b, 1, &b);
mp_reduce_2k_l(&b, &a, &d);
mp_sqr(&c, &c);
mp_add_d(&c, 1, &c);
mp_mod(&c, &a, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("mp_reduce_2k_l() failed at step %d\n", cnt);
mp_tohex(&b, buf);
printf("b == %s\n", buf);
mp_tohex(&c, buf);
printf("c == %s\n", buf);
return EXIT_FAILURE;
}
}
printf("...Passed\n");
#endif /* LTM_DEMO_TEST_REDUCE_2K_L */
#else
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
sub_d_n = 0;
/* force KARA and TOOM to enable despite cutoffs */
KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;
for (;;) {
/* randomly clear and re-init one variable, this has the affect of triming the alloc space */
switch (abs(rand()) % 7) {
case 0:
mp_clear(&a);
mp_init(&a);
break;
case 1:
mp_clear(&b);
mp_init(&b);
break;
case 2:
mp_clear(&c);
mp_init(&c);
break;
case 3:
mp_clear(&d);
mp_init(&d);
break;
case 4:
mp_clear(&e);
mp_init(&e);
break;
case 5:
mp_clear(&f);
mp_init(&f);
break;
case 6:
break; /* don't clear any */
}
printf
("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
ret=fgets(cmd, 4095, stdin); if(!ret){_panic(__LINE__);}
cmd[strlen(cmd) - 1] = 0;
printf("%-6s ]\r", cmd);
fflush(stdout);
if (!strcmp(cmd, "mul2d")) {
++mul2d_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
sscanf(buf, "%d", &rr);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_mul_2d(&a, rr, &a);
a.sign = b.sign;
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mul2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "div2d")) {
++div2d_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
sscanf(buf, "%d", &rr);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_div_2d(&a, rr, &a, &e);
a.sign = b.sign;
if (a.used == b.used && a.used == 0) {
a.sign = b.sign = MP_ZPOS;
}
if (mp_cmp(&a, &b) != MP_EQ) {
printf("div2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "add")) {
++add_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_add(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("add %lu failure!\n", add_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
/* test the sign/unsigned storage functions */
rr = mp_signed_bin_size(&c);
mp_to_signed_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mp_signed_bin failure!\n");
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
rr = mp_unsigned_bin_size(&c);
mp_to_unsigned_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp_mag(&c, &d) != MP_EQ) {
printf("mp_unsigned_bin failure!\n");
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "sub")) {
++sub_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_sub(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("sub %lu failure!\n", sub_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "mul")) {
++mul_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_mul(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mul %lu failure!\n", mul_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "div")) {
++div_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&d, buf, 64);
mp_div(&a, &b, &e, &f);
if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
mp_cmp(&d, &f));
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
draw(&f);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "sqr")) {
++sqr_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_copy(&a, &c);
mp_sqr(&c, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sqr %lu failure!\n", sqr_n);
draw(&a);
draw(&b);
draw(&c);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "gcd")) {
++gcd_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_gcd(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("gcd %lu failure!\n", gcd_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "lcm")) {
++lcm_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_lcm(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("lcm %lu failure!\n", lcm_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "expt")) {
++expt_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&d, buf, 64);
mp_copy(&a, &e);
mp_exptmod(&e, &b, &c, &e);
if (mp_cmp(&d, &e) != MP_EQ) {
printf("expt %lu failure!\n", expt_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "invmod")) {
++inv_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&c, buf, 64);
mp_invmod(&a, &b, &d);
mp_mulmod(&d, &a, &b, &e);
if (mp_cmp_d(&e, 1) != MP_EQ) {
printf("inv [wrong value from MPI?!] failure\n");
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
mp_gcd(&a, &b, &e);
draw(&e);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "div2")) {
++div2_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_div_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("div_2 %lu failure\n", div2_n);
draw(&a);
draw(&b);
draw(&c);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "mul2")) {
++mul2_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_mul_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("mul_2 %lu failure\n", mul2_n);
draw(&a);
draw(&b);
draw(&c);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "add_d")) {
++add_d_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
sscanf(buf, "%d", &ix);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_add_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("add_d %lu failure\n", add_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "sub_d")) {
++sub_d_n;
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&a, buf, 64);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
sscanf(buf, "%d", &ix);
ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
mp_read_radix(&b, buf, 64);
mp_sub_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sub_d %lu failure\n", sub_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return EXIT_FAILURE;
}
} else if (!strcmp(cmd, "exit")) {
printf("\nokay, exiting now\n");
break;
}
}
#endif
return 0;
}
