A stream cipher cryptosystem includes a keystream generator receiving a key and providing a keystream. A cryptographic combiner combines a first binary data sequence and the keystream with two non-associative operations to provide a second binary data sequence. In encryption operations, the cryptographic combiner is an encryption combiner and the first binary data sequence is a plaintext binary data sequence and the second binary data sequence is a ciphertext binary data sequence. In decryption operations, the cryptographic combiner is a decryption combiner and the first binary data sequence is a ciphertext binary data sequence and the second binary data sequence is a plaintext binary data sequence.