A new chosen IV statistical distinguishing framework to attack symmetric ciphers, and its application to ACORN-v3 and Grain-128a

Abstract

We propose a new attack framework based upon cube testers and d-monomial test. The d-monomial test is a general framework for comparing the ANF of the symmetric cipher’s output with ANF of a random Boolean function. In the d-monomial test, the focus is on the frequency of the special monomial in the ANF of Boolean functions, but in the proposed framework, the focus is on the truth table. We attack ACORN-v3 and Grain-128a and demonstrate the efficiency of our framework. We show how it is possible to apply a distinguishing attack for up to 670 initialization rounds of ACORN-v3 and 171 initialization rounds of Grain-128a using our framework. The attack on ACORN-v3 is the best practical attack (and better results can be obtained by using more computing power such as cube attacks). One can apply distinguishing attacks to black box symmetric ciphers by the proposed framework, and we suggest some guidelines to make it possible to improve the attack by analyzing the internal structure of ciphers. The framework is applicable to all symmetric ciphers and hash functions. We discuss how it can reveal weaknesses that are not possible to find by other statistical tests. The attacks were practically implemented and verified.