Abstract: This abstract discusses a stream cipher based on a simple one-dimensional cellular automaton. The cellular automaton consists of a circular register with N cells, each having value ai equal to 0 or 1. The values are updated synchronously in discrete time steps according to the rule ai? = ai-1 XOR (ai OR ai+1), (1a) or, equivalently, ai? = (ai-1 + ai + ai+1 + aiai+1) mod 2. (1b) The initial state of the register is used as a seed or key. The values a(i) attained by a particular cell through time can then serve as a random sequence. Ciphertext C can be obtained from binary plaintext P as usual according to Ci = Pi XOR a(i); the plaintext can be recovered by repeating the same operation, but only if the sequence a(i) is known.

Abstract: The complexity of a finite sequence as defined by Lempel and Ziv is advocated as the basis of a test for cryptographic algorithms. Assuming binary data and block enciphering, it is claimed that the difference (exclusive OR sum) between the plaintext vector and the corresponding ciphertext vector should have high complexity, with very high probability. We may refer to this as plaintext/ciphertext complexity. Similarly, we can estimate an "avalanche" or ciphertext/ ciphertext complexity. This is determined by changing the plaintext by one bit and computing the complexity of the difference of the corresponding ciphertexts. These ciphertext vectors should appear to be statistically independent and thus their difference should have high complexity with very high probability. The distribution of complexity of randomly selected binary blocks of the same length is used as a reference. If the distribution of complexity generated by the cryptographic algorithm matches well with the reference distribtion, the algorithm passes the complexity test. For demonstration, the test is applied to modulo multiplication and to successive rounds (iterations) of the DES encryption algorithm. For DES, the plaintext/ ciphertext complexity test is satisfied by the second round, but the avalanche complexity test takes four to five rounds before a good fit is obtained.

Abstract: In many single-key, symmetric or conventional cryptosystems the elements of a finite field can be regarded as the characters of a plaintext and ciphertext alphabet. Some properties of polynomials or polynomial functions on finite fields can be used for constructing cryptosystems. This note demonstrates by way of examples that great care has to be taken in choosing polynomials for enciphering and deciphering. Often complex looking polynomial functions induce very simple permutations of the elements of a finite field and therefore are not suitable for the construction of cryptosystems. Also an indication is given of some further areas of research in algebraic cryptography.

Abstract: A new method for realizing public-key cryptosystem is proposed in this paper. Three plaintext messages are transformed into three cryptograms in this method. Message authentication is easily realized by this method. Y≡Ax mod P is used as a one-way function, where P is prime.