libressl-BN_get_rfc3526_prime_81923
Standard moduli for diffie-hellman key exchange
Usage
Crypto Library (libcrypto, -lcrypto)
#include <openssl/bn.h>
BIGNUM *
BN_get_rfc2409_prime_768(BIGNUM *bn);
BIGNUM *
BN_get_rfc2409_prime_1024(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_1536(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_2048(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_3072(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_4096(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_6144(BIGNUM *bn);
BIGNUM *
BN_get_rfc3526_prime_8192(BIGNUM *bn);
Overview
Each of these functions returns one specific constant Sophie Germain prime number p.
If bn is NULL, a new BIGNUM object is created and returned. Otherwise, the number is stored in *bn and bn is returned.
All these numbers are of the form
p = 2 sup s - 2 sup left ( s - 64 right ) - 1 + 2 sup 64 * left { left [ 2 sup left ( s - 130 right ) pi right ] + offset right } delim $$
where s is the size of the binary representation of the number in bits and appears at the end of the function names. As long as the offset is sufficiently small, the above form assures that the top and bottom 64 bits of each number are all 1.
The offsets are defined in the standards as follows:
| size s | offset |
| 768 = 3 * 2^8 | 149686 |
| 1024 = 2 * 2^9 | 129093 |
| 1536 = 3 * 2^9 | 741804 |
| 2048 = 2 * 2^10 | 124476 |
| 3072 = 3 * 2^10 | 1690314 |
| 4096 = 2 * 2^11 | 240904 |
| 6144 = 3 * 2^11 | 929484 |
| 8192 = 2 * 2^12 | 4743158 |
For each of these prime numbers, the finite group of natural numbers smaller than p, where the group operation is defined as multiplication modulo p, is used for Diffie-Hellman key exchange. The first two of these groups are called the First Oakley Group and the Second Oakley Group. Obviously, all these groups are cyclic groups of order p, respectively, and the numbers returned by these functions are not secrets.
Return values
If memory allocation fails, these functions return NULL. That can happen even if bn is not NULL.
Caveats
As all the memory needed for storing the numbers is dynamically allocated, the BN_FLG_STATIC_DATA flag is not set on the returned BIGNUM objects. So be careful to not change the returned numbers.