A cryptographic key is provided for cryptographically processing information. A first key is generated according to a key generator scheme. A key space of the first key is reduced in accordance with a key space reduction scheme. The reduced key space is distributed over a larger key space in accordance with a one-way key space distribution function to provide the cryptographic key. The cryptographic key has an associated first work factor for a person without knowledge of the key space distribution function, and an associated second work factor which is less than the first work factor for a person with knowledge of the key space distribution function. Information is cryptographically processed using the cryptographic key, and a new key is generated at a rate of R keys per second to provide a desired protection factor P=W/RZ for a cryptographic system having a lifetime Z.