In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation. We tabulate these parameters. We also compare the discrete logarithm problem in the group of circulant matrices with the discrete logarithm problem in finite...

We show that recursive circulant G(cd m ; d) is hamiltonian decomposable. Recursive circulant is a graph proposed for an interconnection structure of multicomputer networks in [8]. The result is not only a partial answer to the problem posed by Alspach that every connected Cayley graph over an abelian group is hamiltonian decomposable, but also an extension of Micheneau's that recursive circula...

In this note, we give a characterization of the adjacency matrix of the line digraph of a regular digraph and we discuss a generalization.On the light of the characterization given, we remark that the underlying digraph of a coined quantum random walk is the line digraph of a regular digraph. 1. A characterization of the adjacency matrix of the line digraph of a regular digraph 1.1. Set-up. The...

In this paper we rst review the basic computational properties of per-manents, and then address some problems concerning permanents of (0; 1) circulant matrices. In particular we analyze their role at the boundary between computational tractability and intractability, showing that (i) a generic circulant matrix contains large arbitrary submatrices, a fact which casts some doubt on the tractabil...

Recursive circulant graphs G(N; d) have been introduced in 1994 by Park and Chwa PC94] as a new topology for interconnection networks. Recursive circulant graphs G(N; d) are circu-lant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2 k ; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better param...

Let n be any fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most fi...