Paper 2021/1059

Revisiting cryptanalysis on ChaCha from Crypto 2020 and Eurocrypt 2021

Sabyasachi Dey and Chandan Dey and Santanu Sarkar and Willi Meier

Abstract

ChaCha has been one of the prominent ARX designs of the last few years because of its use in several systems. The cryptanalysis of ChaCha involves a differential attack which exploits the idea of Probabilistic Neutral Bits (PNBs). For a long period, the single-bit distinguisher in this differential attack was found up to 3 rounds. At Crypto $2020$, Beierle et. al. introduced for the first time single bit distinguishers for $3.5$ rounds, which contributed significantly in regaining the flow of research work in this direction. This discovery became the primary factor behind the huge improvement in the key recovery attack complexity in that work. This was followed by another work at Eurocrypt 2021, where a single bit distinguisher of $3.5$-th round helped to produce a 7-round distinguisher of ChaCha and a further improvement in key recovery. In the first part of this paper, we provide the theoretical framework for the distinguisher given by Beierle et. al. We mathematically derive the observed differential correlation for the particular position where the output difference is observed at $3.5$ rounds. Also, Beierle et. al. mentioned the issue of the availability of proper IVs to produce such distinguishers, and pointed out that not all keys have such IVs available. Here we provide a theoretical insight of this issue. Next we revisit the work of Coutinho et. al. (Eurocrypt 2021). Using Differential-Linear attacks against ChaCha, they claimed distinguisher and key recovery with complexities $2^{218}$ and $2^{228.51}$ respectively. We show that the differential correlation for $3.5$ rounds is much smaller than the claim of Coutinho et. al. This makes the attack complexities much higher than their claim.