Design, Analysis of Security and Cryptanalysis of Message Authentication Codes

Abstract

This thesis is a compilation of various message authentication codes having beyond the birthday bound (BBB) security. Kicking off with preliminary development in chapter 1, it proceeds to introduce the nEHtM (nonce-based Enhanced Hash-then-Mask) MAC in chapter 2, which is BBB-secure when nonce misuse occurs, through the concept of faulty nonces. The construction is based on a single block cipher, used on the inputs after they undergo a domain-separation. Next, chapter 3 tackles the security and cryptanalysis of MAC constructions that use pseudorandom permutations as primitives by introducing the construction PDMMAC (Permutation-based Davies-Meyer MAC) and its variants. The work on obtaining pseudorandom functions from PRPs by [53] lead to our exploration of PRP-based MACs, and one of our constructions was inspired by the DWCDM of [62]. This was instrumental in the search for an inverse-free permutation-based MAC with a single instance of permutation. This is addressed in chapter 4 through the p-EDM (permutation-based Encrypted Davies-Meyer), which follows the trend of constructing n-bit to n-bit PRFs by summing smaller constructions such as the Even-Mansour and the Davies-Meyer, like the SoEM and SoKAC constructions of [53] and the PDMMAC and variant constructions of [47] before it. The BBB security is again tight. Two interesting treatments of the DbHtS construction [61] can be found in chapters 5 and 6. A permutation-based version, dubbed p-DbHtS (permutation- based Double-block Hash-then-Sum) is proven to possess BBB security and a matching attack provided. Finally, a block cipher-based version of the original construction is shown to have BBB security in the multi-user setting for underlying hash functions that are constructed without the use of block Ciphers. Furthermore, each chapter extends Patarin’s Mirror Theory to provide partial bounds for solutions to a system of affine bivariate equations and non-equations satisfying certain conditions.