Paper 2025/1836

On the Security of LOL-MINI and LOL-DOUBLE against Correlation Attacks

Abstract

LOL (League of Legends) is a general framework for designing blockwise stream ciphers to achieve higher software performance in 5G/6G. Following this framework, stream ciphers LOL-MINI and LOL-DOUBLE are proposed, each with a 256-bit key. This paper focuses on analyzing their security against correlation attacks. Additionally, we propose an observation on constructing linear approximation trails. The repeated linear approximations in trails may not only increase the number of active S-boxes but also make the correlations of corresponding approximations zero. We propose a new rule to address this situation and develop multiple correlation attacks. Furthermore, we use theoretical cryptanalysis to lower the time complexity of aggregation and construct multiple linear approximations efficiently. For LOL-MINI, we construct approximately $2^{32.17}$ linear approximations with absolute correlations ranging from $2^{-118.38}$ to $2^{-127}$. We launch the developed multiple correlation attack on LOL-MINI with a time complexity of $2^{250.56}$, a data complexity of $2^{250}$, a memory complexity of $2^{250}$ and a success probability of 99.4$\%$. For LOL-DOUBLE, there similarly exist approximately ${{2}^{22.86}}$ linear approximations with absolute correlations ranging from $2^{-147.23}$ to $2^{-156}$. It is worth noting that our results do not violate the declaration of LOL-MINI since the maximum length of keystreams for a single pair of key and IV is less than $2^{64}$.