An encryption system comprises a pseudo-random number generator (KS) for generating a long pseudo-random sequence (S) from a shorter encryption key (K) and, if necessary, a nonce value (N), and a mixing function (MX) for combining the sequence with a plaintext message (P) on a block-by-block basis, where successive blocks (S(i)) of 128 bits of the sequence are combined with successive 64-bit blocks of plaintext (P(i)) to produce successive 64-bit blocks of ciphertext. The blockwise use of a long pseudo-random sequence preserves the advantages of a block cipher in terms of data confidentiality and data integrity, as well as benefiting from the speed advantages of a stream cipher.