Paper 2018/174 Original: eprint.iacr.org/2018/174 ↗

A New Framework for Finding Nonlinear Superpolies in Cube Attacks against Trivium-Like Ciphers

Abstract

In this paper, we study experimental cube attacks against Trivium-like ciphers and we focus on improving nonlinear superpolies recovery. We first present a general framework in cube attacks to test nonlinear superpolies, by exploiting a kind of linearization technique. It worth noting that, in the new framework, the complexities of testing and recovering nonlinear superpolies are almost the same as those of testing and recovering linear superpolies. To demonstrate the effectiveness of our new attack framework, we do extensive experiments on Trivium, Kreyvium, and TriviA-SC-v2 respectively. We obtain several linear and quadratic superpolies for the 802-round Trivium, which is the best experimental results against Trivium regarding the number of initialization rounds. For Kreyvium, it is shown that the probability of finding a quadratic superpoly using the new framework is twice as large as finding a linear superpoly. Hopefully, this new framework would provide some new insights on cube attacks against NFSR-based ciphers, and in particular make nonlinear superpolies potentially useful in the future cube attacks.