The Exact Security of PMAC with Two Powering-Up Masks

PMAC is a rate-1, parallelizable, block-cipher-based message authentication code (MAC), proposed by Black and Rogaway (EUROCRYPT 2002). Improving the security bound is a main research topic for PMAC. In particular, showing a tight bound is the primary goal of the research, since Luykx et al.’s paper (EUROCRYPT 2016). Regarding the pseudo-random-function (PRF) security of PMAC, a collision of the hash function, or the difference between a random permutation and a random function offers the lower bound Ω(q2/2n) for q queries and the block cipher size n. Regarding the MAC security (unforgeability), a hash collision for MAC queries, or guessing a tag offers the lower bound Ω(q2m /2n + qv/2n) for qm MAC queries and qv verification queries (forgery attempts). The tight upper bound of the PRF-security O(q2/2n) of PMAC was given by Gaži et el. (ToSC 2017, Issue 1), but their proof requires a 4-wise independent masking scheme that uses 4 n-bit random values. Open problems from their work are: (1) find a masking scheme with three or less random values with which PMAC has the tight upper bound for PRF-security; (2) find a masking scheme with which PMAC has the tight upper bound for MAC-security.In this paper, we consider PMAC with two powering-up masks that uses two random values for the masking scheme. Using the structure of the powering-up masking scheme, we show that the PMAC has the tight upper bound O(q2/2n) for PRF-security, which answers the open problem (1), and the tight upper bound O(q2m /2n + qv/2n) for MAC-security, which answers the open problem (2). Note that these results deal with two-key PMACs, thus showing tight upper bounds of PMACs with single-key and/or with one powering-up mask are open problems

Multi User Security of LightMAC and LightMAC_Plus

In FSE\u2716, Luykx et al. have proposed $\textsf{LightMAC}$ that provably achieves a query length independent PRF security bound. To be precise, the construction achieves security roughly in the order of $O(q^2/2^n)$, when instantiated with two independently keyed $n$-bit block ciphers and $q$ is the total number of queries made by the adversary. Subsequently, in ASIACRYPT\u2717, Naito proposed a beyond-birthday-bound variant of the $\textsf{LightMAC}$ construction, dubbed as \textsf{LightMAC_Plus}, that is built on three independently keyed $n$-bit block ciphers and achieves $2n/3$-bits PRF security. Security analyses of these two constructions have been conducted in the single-user setting, where we assume that the adversary has the access to a single instance of the construction. In this paper, we investigate, for the first time, the security of the $\textsf{LightMAC}$ and the \textsf{LightMAC_Plus} construction in the context of multi-user setting, where we assume that the adversary has access to more than one instances of the construction. In particular, we have shown that $\textsf{LightMAC}$ remains secure roughly up to $2^{n/2}$ construction queries and $2^k$ ideal-cipher queries in the ideal-cipher model and \textsf{LightMAC_Plus} maintains security up to approximately $2^{2n/3}$ construction queries and $2^{2k/3}$ ideal-cipher queries in the ideal-cipher model, where $n$ denotes the block size and $k$ denotes the key size of the block cipher

Critical Perspectives on Provable Security: Fifteen Years of Another Look Papers

We give an overview of our critiques of “proofs” of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata