int gnutls_x509_privkey_generate2(gnutls_x509_privkey_t key, gnutls_pk_algorithm_t algo, unsigned int bits, unsigned int flags, const gnutls_keygen_data_st * data, unsigned data_size);
The flag GNUTLS_PRIVKEY_FLAG_PROVABLE instructs the key generation process to use algorithms like Shawe-Taylor (from FIPS PUB186-4) which generate provable parameters out of a seed for RSA and DSA keys. On DSA keys the PQG parameters are generated using the seed, while on RSA the two primes. To specify an explicit seed (by default a random seed is used), use the data with a GNUTLS_KEYGEN_SEED type.
Note that when generating an elliptic curve key, the curve can be substituted in the place of the bits parameter using the GNUTLS_CURVE_TO_BITS() macro.
To export the generated keys in memory or in files it is recommended to use the PKCS8 form as it can handle all key types, and can store additional parameters such as the seed, in case of provable RSA or DSA keys. Generated keys can be exported in memory using gnutls_privkey_export_x509(), and then with gnutls_x509_privkey_export2_pkcs8().
If key generation is part of your application, avoid setting the number of bits directly, and instead use gnutls_sec_param_to_pk_bits(). That way the generated keys will adapt to the security levels of the underlying GnuTLS library.
See also gnutls_privkey_generate2().