In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined. Our results show that these sequences also have high linear complexity.

In this correspondence, we present a simple bit-stream generator. It is a specialization of shrinking generator and a generalization of self-shrinking generator. We call it "generalized self-shrinking generator." The family of such generated sequences has a group structure. The correlation between the sequences is quite good and the sequences themselves are balanced. For each k, 0<k<n, no more than 1/2/sup n-k/ of the sequences have least periods less than 2/sup k/. No more than 1/4 of the sequences have least periods less than 2/sup n-1/. There are two sequences with least periods of 2. There is no sequence with a least period p such that 2<p

Resilient functions play an important role in the art of information security. In this correspondence, we discuss the existence, construction, and enumeration of resilient functions over finite fields. We show that, for each finite field GF(q) with q > 3, we can easily construct a large number of (q, n, 1, n - 1) resilient functions, most of which include mixing terms. We give a general structure for (q, m + 1, m, 1) resilient functions, and present an example which is not of this general structure. We prove that (q, m + 2, m, 2) resilient functions exist for any m such that 12. We prove that (q, m + t, m, t) resilient functions exist for any (m, t) such that 13. By making some simple generalizations of former results, we also provide some new methods for constructing resilient functions.

A fast algorithm is presented for determining the linear complexity and the minimal polynomial of a sequence with period 2p/sup n/ over GF (q), where p and q are odd prime, and q is a primitive root (mod p/sup 2/). The algorithm uses the fact that in this case the factorization of x/sup 2p(n)/-1 is especially simple.

A fast algorithm is presented for determining the linear complexity of a sequence with period p/sup n/ over GF (q), where p is an odd prime, and where q is a prime and a primitive root (mod p/sup 2/).