Analyzing the Probability of Key Recovery in the Differential Attacks Against ChaCha

The stream cipher ChaCha has been subjected to differential linear cryptanalysis since 2008. Aumasson et al. (2008) laid the groundwork for this attack, employing the concept of probabilistically neutral bits for key recovery. Subsequently, various enhancements have been made to this attack over the last few decades. These improvements are essentially refinements to the probabilistically neutral bit-based attack approach. Despite the proposed modifications in these improvements, which increase attack complexity, the consequential changes in the associated probability of key recovery have not been thoroughly examined. A comprehensive analysis of the probability of key recovery is lacking in all attacks within this domain. No systematic process is available in the existing works for analyzing the probability of key recovery. This paper addresses this gap by proposing a method for estimating the probability of key recovery in these attacks. Employing this method, we calculate an estimated interval for the probability of key recovery for both the original idea presented by Aumasson et al. (2008) and the subsequent modifications to this idea. This analysis allows us to understand the variations in probability associated with these modifications.