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GET_RFC3526_PRIME_8192(3) Library Functions Manual GET_RFC3526_PRIME_8192(3)

get_rfc2409_prime_768, get_rfc2409_prime_1024, get_rfc3526_prime_1536, get_rfc3526_prime_2048, get_rfc3526_prime_3072, get_rfc3526_prime_4096, get_rfc3526_prime_6144, get_rfc3526_prime_8192, BN_get_rfc2409_prime_768, BN_get_rfc2409_prime_1024, BN_get_rfc3526_prime_2048, BN_get_rfc3526_prime_3072, BN_get_rfc3526_prime_4096, BN_get_rfc3526_prime_6144, BN_get_rfc3526_prime_8192
standard moduli for Diffie-Hellmann key exchange

#include <openssl/bn.h>

BIGNUM *
get_rfc2409_prime_768(BIGNUM *bn);

BIGNUM *
get_rfc2409_prime_1024(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_1536(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_2048(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_3072(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_4096(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_6144(BIGNUM *bn);

BIGNUM *
get_rfc3526_prime_8192(BIGNUM *bn);

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);

Each of these functions returns one specific constant Sophie Germain prime number p. The names with the prefix ‘BN_’ are aliases for the names without that prefix.

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=2s2s641+264*2s130π+offset

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-Hellmann key exchange. The first two of these groups are called the First Oakley Group and the Second Oakley Group. Obiviously, all these groups are cyclic groups of order p, respectively, and the numbers returned by these functions are not secrets.

If memory allocation fails, these functions return NULL. That can happen even if bn is not NULL.

BN_mod_exp(3), BN_new(3), BN_set_flags(3), DH_new(3)

RFC 2409, "The Internet Key Exchange (IKE)", defines the Oakley Groups.

RFC 2412, "The OAKLEY Key Determination Protocol", contains additional information about these numbers.

RFC 3526, "More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE)", defines the other six numbers.

get_rfc2409_prime_768(), get_rfc2409_prime_1024(), get_rfc3526_prime_1536(), get_rfc3526_prime_2048(), get_rfc3526_prime_3072(), get_rfc3526_prime_4096(), get_rfc3526_prime_6144(), and get_rfc3526_prime_8192() first appeared in OpenSSL 0.9.8a and have been available since OpenBSD 4.5.

The BN_ aliases first appeared in OpenSSL 1.1.0 and have been available since OpenBSD 6.3.

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.
March 23, 2018 OpenBSD-current