substitution and transposi- tion to produce consecutive blocks of ciphertext. In such systems an error in transmission usually results in corruption of the whole received block. In all these systems, it is essential that the key is changed frequently; the security of an otherwise satisfactory cryptosystem can be compromised if the key is reused. Specific Cryptosystems Many cryptosystems have been developed, both by government agencies and commercial organizations. The first public standard system was the National Bureau of Standards Data Encryption Standard (DES), which is a block cipher with a 64-bit block length involving both substitution and transposition under the control of a 56-bit key (NBS, 1977). The origi- nal proposal was for a 64-bit key, and there are claims that DES keys have been broken in less than 24 hours and that DES is therefore too insecure for many applications. Triple DES, which consists of applying DES three times in succession, is believed to be secure in practice. DES has now been superseded by the Advanced Encryption Standard (AES), also known as Rijndael (NIST, 2001). AES has a fixed block size of 128 bits and a key size of 128, 192, or 256 bits. The RSA algorithm (Rivest, 1978) is a public-key encryption algorithm in which the recipient publishes an encipherment key, N, consisting of the product of two primes, each of order 10100, together with another number, E. The sender breaks the plaintext into blocks that can be represented by numbers less than N, then encrypts the blocks using a simple modulo-N arithmetic operation involving E. The recipient recovers the plaintext using further simple modulo-N operations that rely on knowledge of the factors of N. The diffi- culty of factoring numbers of order 10200 means that the eavesdropper cannot work out the two factors of N and cannot decrypt the message. Spread-Spectrum Systems Spread spectrum systems (Proakis, 1989; Tsui and Clarkson, 1994) are used in digital com- munications for Combating interference arising from jamming by others, o