### view libtommath/bn_mp_prime_is_prime.c @ 1938:77bc00dcc19fdefaulttipmainmaster

Bump version to 2022.82
author Matt Johnston Fri, 01 Apr 2022 14:43:27 +0800 1051e4eea25a
line wrap: on
line source
```#include "tommath_private.h"
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */

/* portable integer log of two with small footprint */
static unsigned int s_floor_ilog2(int value)
{
unsigned int r = 0;
while ((value >>= 1) != 0) {
r++;
}
return r;
}

mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
{
mp_int  b;
int     ix, p_max = 0, size_a, len;
mp_bool res;
mp_err  err;

/* default to no */
*result = MP_NO;

/* Some shortcuts */
/* N > 3 */
if (a->used == 1) {
if ((a->dp == 0u) || (a->dp == 1u)) {
*result = MP_NO;
return MP_OKAY;
}
if (a->dp == 2u) {
*result = MP_YES;
return MP_OKAY;
}
}

/* N must be odd */
if (MP_IS_EVEN(a)) {
return MP_OKAY;
}
/* N is not a perfect square: floor(sqrt(N))^2 != N */
if ((err = mp_is_square(a, &res)) != MP_OKAY) {
return err;
}
if (res != MP_NO) {
return MP_OKAY;
}

/* is the input equal to one of the primes in the table? */
for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
*result = MP_YES;
return MP_OKAY;
}
}
#ifdef MP_8BIT
/* The search in the loop above was exhaustive in this case */
if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
return MP_OKAY;
}
#endif

/* first perform trial division */
if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
return err;
}

/* return if it was trivially divisible */
if (res == MP_YES) {
return MP_OKAY;
}

/*
Run the Miller-Rabin test with base 2 for the BPSW test.
*/
if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
return err;
}

if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
/*
Rumours have it that Mathematica does a second M-R test with base 3.
Other rumours have it that their strong L-S test is slightly different.
It does not hurt, though, beside a bit of extra runtime.
*/
b.dp++;
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}

/*
* Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
* slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
* bases 2, 3 and t random bases.
*/
#ifndef LTM_USE_ONLY_MR
if (t >= 0) {
/*
* Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
* MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
* integers but the necesssary analysis is on the todo-list).
*/
#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
err = mp_prime_frobenius_underwood(a, &res);
if ((err != MP_OKAY) && (err != MP_ITER)) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#else
if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#endif
}
#endif

/* run at least one Miller-Rabin test with a random base */
if (t == 0) {
t = 1;
}

/*
Only recommended if the input range is known to be < 3317044064679887385961981

It uses the bases necessary for a deterministic M-R test if the input is
smaller than  3317044064679887385961981
The caller has to check the size.
TODO: can be made a bit finer grained but comparing is not free.
*/
if (t < 0) {
/*
Sorenson, Jonathan; Webster, Jonathan (2015).
"Strong Pseudoprimes to Twelve Prime Bases".
*/
/* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
goto LBL_B;
}

if (mp_cmp(a, &b) == MP_LT) {
p_max = 12;
} else {
goto LBL_B;
}

if (mp_cmp(a, &b) == MP_LT) {
p_max = 13;
} else {
err = MP_VAL;
goto LBL_B;
}
}

/* we did bases 2 and 3  already, skip them */
for (ix = 2; ix < p_max; ix++) {
mp_set(&b, s_mp_prime_tab[ix]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
}
}
/*
Do "t" M-R tests with random bases between 3 and "a".
See Fips 186.4 p. 126ff
*/
else if (t > 0) {
/*
* The mp_digit's have a defined bit-size but the size of the
* array a.dp is a simple 'int' and this library can not assume full
* compliance to the current C-standard (ISO/IEC 9899:2011) because
* it gets used for small embeded processors, too. Some of those MCUs
* have compilers that one cannot call standard compliant by any means.
* Hence the ugly type-fiddling in the following code.
*/
size_a = mp_count_bits(a);
mask = (1u << s_floor_ilog2(size_a)) - 1u;
/*
Assuming the General Rieman hypothesis (never thought to write that in a
comment) the upper bound can be lowered to  2*(log a)^2.
E. Bach, "Explicit bounds for primality testing and related problems,"
Math. Comp. 55 (1990), 355-380.

size_a = (size_a/10) * 7;
len = 2 * (size_a * size_a);

E.g.: a number of size 2^2048 would be reduced to the upper limit

floor(2048/10)*7 = 1428
2 * 1428^2       = 4078368

That number is smaller than 2^28, the default bit-size of mp_digit.
*/

/*
How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.

The function mp_rand() goes to some length to use a cryptographically
good PRNG. That also means that the chance to always get the same base
in the loop is non-zero, although very low.
If the BPSW test and/or the addtional Frobenious test have been
performed instead of just the Miller-Rabin test with the bases 2 and 3,
a single extra test should suffice, so such a very unlikely event
will not do much harm.

To preemptivly answer the dangling question: no, a witness does not
need to be prime.
*/
for (ix = 0; ix < t; ix++) {
/* mp_rand() guarantees the first digit to be non-zero */
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
/*
* Reduce digit before casting because mp_digit might be bigger than
* an unsigned int and "mask" on the other side is most probably not.
*/
fips_rand = (unsigned int)(b.dp & (mp_digit) mask);
#ifdef MP_8BIT
/*
* One 8-bit digit is too small, so concatenate two if the size of
* unsigned int allows for it.
*/
if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
fips_rand <<= MP_SIZEOF_BITS(mp_digit);
fips_rand |= (unsigned int) b.dp;
}
#endif
if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
len = INT_MAX / MP_DIGIT_BIT;
} else {
len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
}
/*  Unlikely. */
if (len < 0) {
ix--;
continue;
}
/*
* As mentioned above, one 8-bit digit is too small and
* although it can only happen in the unlikely case that
* an "unsigned int" is smaller than 16 bit a simple test
* is cheap and the correction even cheaper.
*/
#ifdef MP_8BIT
/* All "a" < 2^8 have been caught before */
if (len == 1) {
len++;
}
#endif
if ((err = mp_rand(&b, len)) != MP_OKAY) {
goto LBL_B;
}
/*
* That number might got too big and the witness has to be
* smaller than "a"
*/
len = mp_count_bits(&b);
if (len >= size_a) {
len = (len - size_a) + 1;
if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
goto LBL_B;
}
}
/* Although the chance for b <= 3 is miniscule, try again. */
if (mp_cmp_d(&b, 3uL) != MP_GT) {
ix--;
continue;
}
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
}
}

/* passed the test */
*result = MP_YES;
LBL_B:
mp_clear(&b);
return err;
}

#endif
```