Welcome to the resource topic for 2024/1163
Title:
On the Number of Restricted Solutions to Constrained Systems and their Applications
Authors: Benoît Cogliati, Jordan Ethan, Ashwin Jha, Mridul Nandi, Abishanka Saha
Abstract:In this paper, we formulate a special class of systems of linear equations over finite fields and derive lower bounds on the number of solutions adhering to some predefined restrictions. We then demonstrate the applications of these lower bounds to derive tight PRF security (up to 2^{3n/4} queries) for single-keyed variants of the Double-block Hash-then-Sum (DBHtS) paradigm, specifically PMAC+ and LightMAC+. Additionally, we show that the sum of r independent copies of the Even-Mansour cipher is a secure PRF up to 2^{\frac{r}{r+1}n} queries.
ePrint: https://eprint.iacr.org/2024/1163
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