As part of a cryptographic protocol, or in addition to it, a computer may participate in a cryptographic key generation protocol. The cryptographic key generation protocol may be such that it generates a set of bits sufficient for a cryptographic key and, also, one or more additional bits. The cryptographic protocol may have one or more parameters, and the parameters of the cryptographic protocol may be varied as a function of the additional bits generated by the cryptographic key generation protocol. The cryptographic protocol may specify a set of one or more cryptographic key sizes. An overkey may be generated that is at least one bit greater than the set of cryptographic key sizes specified by the cryptographic protocol. The parameters of the cryptographic protocol may then be varied as a function of some subset of bits of the overkey. Cryptography-based security may thus be enhanced.