Construction and Comparison of Authentication Codes

Abstract

One of the main problems we want to address is the fact that in the construction theory of authentication codes, the expression “new code” is used all the time, while it is almost never shown that the obtained codes indeed are new, or even what the notion “new” means to begin with. In this paper, we formally define authentication codes and introduce a comparison method for them, using the notion of isomorphism and the invariant isomorphism group. We then define operations in this framework which enable us to “multiply” and “add” arbitrary authentication codes, regardless of how they are initially constructed. We obtain (nonisomorphic) codes with easily calculated parameters, a large number of which are new.