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BN_GET_RFC3526_PRIME_8192(3) FreeBSD Library Functions Manual NAME BN_get_rfc2409_prime_768, BN_get_rfc2409_prime_1024, BN_get_rfc3526_prime_1536, 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-Hellman key exchange SYNOPSIS #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); DESCRIPTION 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^s - 2^(s - 64) - 1 + 2^64 * {[2^(s - 130) <pi>] + 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-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. SEE ALSO BN_mod_exp(3), BN_new(3), BN_set_flags(3), DH_new(3) STANDARDS 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. HISTORY BN_get_rfc2409_prime_768(), BN_get_rfc2409_prime_1024(), BN_get_rfc3526_prime_1536(), BN_get_rfc3526_prime_2048(), BN_get_rfc3526_prime_3072(), BN_get_rfc3526_prime_4096(), BN_get_rfc3526_prime_6144(), and BN_get_rfc3526_prime_8192() first appeared in OpenSSL 1.1.0 and have been available since OpenBSD 6.3. The same functions without BN_ prefix first appeared in OpenSSL 0.9.8a and OpenBSD 4.5; they were removed in OpenBSD 7.4. 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. FreeBSD 14.1-RELEASE-p8 July 20, 2023 FreeBSD 14.1-RELEASE-p8