Linear authentication codes: Bounds and constructions

Abstract

In this paper, we consider a new class of unconditionally secure authentication codes, called linear authentication code (or linear A-code). We show that a linear A-code can be characterised by a family of subspaces of a vector space over a finite field. We then derive an upper bound on the size of source space when other parameters of the systems, that is the size of the key space and the authenticator space, and the deception probability, are fixed. We give constructions that are asymptotically close to the bound and show application of these codes in constructing distributed authentication systems.