Key derivation algorithms are disclosed. In one key derivation application, a segment of the master key is hashed. Two numbers of derived from another segment of the master key. A universal hash function, using the two numbers, is applied to the result of the hash, from which bits are selected as the derived key. In another embodiment, an encoded counter is combined with segments of the master key. The result is then hashed, from which bits are selected as the derived key.