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prime_is_prime: remove obsolete restriction on PRIME_SIZE #273

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Merged
merged 1 commit into from
May 24, 2019
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prime_is_prime: remove obsolete restriction on PRIME_SIZE #273

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44 changes: 3 additions & 41 deletions bn_mp_prime_is_prime.c
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Original file line number Diff line number Diff line change
Expand Up @@ -137,41 +137,12 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
}

/*
abs(t) extra rounds of M-R to extend the range of primes it can find if t < 0.
Only recommended if the input range is known to be < 3317044064679887385961981

It uses the bases for a deterministic M-R test if input < 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.

Not for cryptographic use because with known bases strong M-R pseudoprimes can
be constructed. Use at least one M-R test with a random base (t >= 1).

The 1119 bit large number

80383745745363949125707961434194210813883768828755814583748891752229742737653\
33652186502336163960045457915042023603208766569966760987284043965408232928738\
79185086916685732826776177102938969773947016708230428687109997439976544144845\
34115587245063340927902227529622941498423068816854043264575340183297861112989\
60644845216191652872597534901

has been constructed by F. Arnault (F. Arnault, "Rabin-Miller primality test:
composite numbers which pass it.", Mathematics of Computation, 1995, 64. Jg.,
Nr. 209, S. 355-361), is a semiprime with the two factors

40095821663949960541830645208454685300518816604113250877450620473800321707011\
96242716223191597219733582163165085358166969145233813917169287527980445796800\
452592031836601

20047910831974980270915322604227342650259408302056625438725310236900160853505\
98121358111595798609866791081582542679083484572616906958584643763990222898400\
226296015918301

and it is a strong pseudoprime to all forty-six prime M-R bases up to 200

It does not fail the strong Bailley-PSP test as implemented here, it is just
given as an example, if not the reason to use the BPSW-test instead of M-R-tests
with a sequence of primes 2...n.

TODO: can be made a bit finer grained but comparing is not free.
*/
if (t < 0) {
t = -t;
Expand Down Expand Up @@ -200,15 +171,6 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
}
}

/* for compatibility with the current API (well, compatible within a sign's width) */
if (p_max < t) {
p_max = t;
}

if (p_max > MP_PRIME_SIZE) {
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, ltm_prime_tab[ix]);
Expand Down
6 changes: 1 addition & 5 deletions doc/bn.tex
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Expand Up @@ -2018,11 +2018,7 @@ \section{Primality Testing}

One Miller-Rabin tests with a random base will be run automatically, so by setting $t$ to a positive value this function will run $t + 1$ Miller-Rabin tests with random bases.

If $t$ is set to a negative value the test will run the deterministic Miller-Rabin test for the primes up to
$3317044064679887385961981$. That limit has to be checked by the caller. If $-t > 13$ than $-t - 13$ additional rounds of the
Miller-Rabin test will be performed but note that $-t$ is bounded by $1 \le -t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number
of primes in the prime number table (by default this is $256$) and the first 13 primes have already been used. It will return
\texttt{MP\_VAL} in case of$-t > PRIME\_SIZE$.
If $t$ is set to a negative value the test will run the deterministic Miller-Rabin test for the primes up to $3317044064679887385961981$. That limit has to be checked by the caller.

If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero.

Expand Down