New cryptanalysis of LowMC with algebraic techniques

Abstract

LowMC is a family of block ciphers proposed by Albrecht et al. at EUROCRYPT 2015, which is tailored specifically for FHE and MPC applications. At ToSC 2018, a difference enumeration attack was given for the cryptanalysis of low-data instances of full LowMCv2 with few applied S-boxes per round. Recently at CRYPTO 2021, an efficient algebraic technique was proposed to attack 4-round LowMC adopting a full S-box layer. Following these works, we present a new difference enumeration attack framework, which is based on our new observations on the LowMC S-box, to analyze LowMC instances with a full S-box layer. As a result, with only 3 chosen plaintexts, we can attack 4-round LowMC instances which adopt a full S-box layer with block size of 129, 192, and 255 bits, respectively. We show that all these attacks have either a lower time complexity or a higher success probability than those reported in the CRYPTO paper.