General Group Authentication Codes and Their Relation to "Unconditionally-Secure Signatures"

Strong notions of security for unconditionally secure digital signature schemes (USDS) were recently proposed where security is defined based on notions of security in computationally–secure digital signatures. The traditional area of unconditionally secure authentication, however, is that of “authentication codes” (A–codes). Relations between primitives is central to cryptographic research. To this end, we develop a novel “general group–based A–code” framework which includes known types of group A–codes and their extensions, including the newly proposed USDS, and also allows other models to be systematically described and analysed. In particular, information theoretic analysis of these codes can be applied to USDS, establishing fundamental bounds on USDS parameters. A second contribution herein is a modular algebraic method of synthesising group codes from simpler A–codes, such that security of the group code follows directly from the component codes. We demonstrate our approach by constructing and analysing a USDS satisfying the ‘strongest security notion’.