C Libgcrypt: Unable to check if number is prime using libgcrypt

Question

I am using a libgcrypt function gcry_prime_check to test if the number 3 is a prime number. It turns out 3 is not a prime number according to my the function. What am i doing wrong?

Here is my code

#include <gcrypt.h>
#include <stdio.h>

int main(void)
{

    gcry_mpi_t cript_prime;
    gcry_error_t err;
    char buffer[8] = {0};
    char number[8] = {0};


    printf("%s\n", gcry_check_version ( NULL ) );
    gcry_control( GCRYCTL_INIT_SECMEM, 16384, 0 );

    cript_prime = gcry_mpi_new(16);

    strcpy(number,"3");
    gcry_mpi_scan(&cript_prime,GCRYMPI_FMT_USG,number,sizeof(number),NULL);

    gcry_mpi_print(GCRYMPI_FMT_USG,buffer,sizeof(buffer),NULL,cript_prime);

    printf("The number tested is: %s\n",buffer);

    err = gcry_prime_check(cript_prime,4);

    if(err)
    {
        printf("%s\n",gcry_strerror(err));
    }

    gcry_mpi_release(cript_prime);

    return 0;
}

Here is the output

1.4.4
The number tested is: 3
Number is not prime

Also, a link for a good tutorial on using libgcrypt would be a big bonus. Thanks

EDIT:

Alright, I managed to generate a prime number using gcry_prime_generate and copied the value into number. Turns out it failed the prime check. But when you directly the pass the mpi output from prime generate to the prime check function ... it passes!!

score 1 · Answer 1 · answered Jul 13 '12 at 07:11

1

It's a bug. Like most prime tests, it tests for divisibility by small prime values before moving onto more expensive tests. Unfortunately, if your prime is one of these values, it is reported as being divisible (by itself) - and therefore composite.

Since the focus of libgcrypt is cryptographic applications, such a small prime has no utility. It's sloppy though, and wouldn't take much to rectify.

answered Jul 13 '12 at 07:11

Brett Hale

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But the manual http://www.gnupg.org/documentation/manuals/gcrypt/Prime_002dNumber_002dGenerator-Subsystem-Architecture.html for the prime number generation architecture states the following `The standard sieve algorithm using the primes up to 4999 is used as a quick first check.` – Andy Stow Away Jul 13 '12 at 07:20
Quite. So, I'd wager `4999` is declared composite, and `5003` is declared prime. – Brett Hale Jul 13 '12 at 07:32
I tried 5003, still same result. Will keep trying till probably 9973 – Andy Stow Away Jul 13 '12 at 07:35

score 0 · Answer 2 · edited Jul 13 '12 at 06:34

0

This is the function prototype, it takes a gcry_mpi_t structure and an Integer.

gcry_error_t gcry_prime_check (gcry_mpi_t p, unsigned int flags)

gcry_mpi_t : This type represents an object to hold an MPI.

gcry_mpi_t structures can be allocated using the gcry_mpi_new function

And can be set using the gcry_mpi_set function.

edited Jul 13 '12 at 06:34

Jens Gustedt

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answered Jul 13 '12 at 05:24

Luke

1

hmmm what about the gcry_prime_check(...,**unsigned int flags**) There is no documentation on that. I have tried integers from 0 to 4. All give the same result. – Andy Stow Away Jul 13 '12 at 05:27
1

mpi.h contains a struct definition struct gcry_mpi{ int alloced; /* Array size (# of allocated limbs). */ int nlimbs; /* Number of valid limbs. */ int sign; /* Indicates a negative number and is also used for opaque MPIs to store the length. */ unsigned int flags; /* Bit 0: Array to be allocated in secure memory space.*/ /* Bit 2: the limb is a pointer to some m_alloced data.*/ mpi_limb_t *d; /* Array with the limbs */ };` It seems to only use bit 0 and bit 2, and only for memory management. – Luke Jul 13 '12 at 05:51
Tyrns out the unsigned int flags are not considered at all in the prime_check function definition – Andy Stow Away Jul 13 '12 at 14:24

C Libgcrypt: Unable to check if number is prime using libgcrypt

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