We describe a software-e cient encryption algorithm named SEAL 3.0. Computational cost on a modern 32-bit processor is about 4 clock cycles per byte of text. The cipher is a pseudorandom function family: under control of a key ( rst pre-processed into an internal table) it stretches a 32-bit position index into a long, pseudorandom string. This string can be used as the keystream of a Vernam cipher. Key words. Cryptography, Encryption, Fast encryption, Pseudorandom function family, Software encryption, Stream cipher. To appear in J. of Cryptology. Full version of 16]. Last revised September 18, 1997.