Commitment and Authentication Systems

In the present paper, we answer a question raised in the paper Constructions and Bounds for Unconditionally Secure Non-Interactive Commitment Schemes, by Blundo et al, 2002, showing that there is a close relation between unconditionally secure commitment schemes and unconditionally secure authentication schemes, and that an unconditionally secure commitment scheme can be built from such an authentication scheme and an unconditionally secure cipher system. To investigate the opposite direction, we define optimal commitment systems and show that these must be resolvable design commitment schemes. Then, a proof is given that the resolvable design commitment schemes are a composition of an authentication system and a cipher system and the conclusion follows that this is the case for all optimal commitment systems. We also show how to build optimal schemes from transversal designs that are easy to build and can be more efficiently implemented than the proposal in the previously cited paper.