Paper 2021/546

Distinguishing and Key Recovery Attacks on the Reduced-Round SNOW-V and SNOW-Vi

Jin Hoki, Takanori Isobe, Ryoma Ito, Fukang Liu, and Kosei Sakamoto

Abstract

This paper presents distinguishing and key recovery attacks on the reduced-round SNOW-V and SNOW-Vi, which are stream ciphers proposed for standard encryption schemes for the 5G mobile communication system. First, we construct a Mixed-Integer Linear Programming (MILP) model to search for integral characteristics using the division property, and find the best integral distinguisher in the 3-, 4-, 5-round SNOW-V, and 5-round SNOW-Vi with time complexities of \(2^{8}\), \(2^{16}\), \(2^{48}\), and \(2^{16}\), respectively. Next, we construct a bit-level MILP model to efficiently search for differential characteristics, and find the best differential characteristics in the 3- and 4-round versions. These characteristics lead to the 3-round differential distinguishers for SNOW-V and SNOW-Vi with time complexities of \(2^{17}\) and \(2^{12}\) and the 4-round differential distinguishers for SNOW-V and SNOW-Vi with time complexities of \(2^{97}\) and \(2^{39}\), respectively. Then, we consider single-bit and dual-bit differential cryptanalysis, which is inspired by the existing study on Salsa and ChaCha. By carefully choosing the IV values and differences, we can construct practical bit-wise differential distinguishers for the 4-round SNOW-V, 4-, and 5-round SNOW-Vi with time complexities of \(2^{4.466}\), \(2^{1.000}\), and \(2^{14.670}\), respectively. Finally, we improve the existing differential attack based on probabilistic neutral bits, which is also inspired by the existing study on Salsa and ChaCha. As a result, we present the best key recovery attack on the 4-round SNOW-V and SNOW-Vi with time complexities of \(2^{153.97}\) and \(2^{233.99}\) and data complexities of \(2^{26.96}\) and \(2^{19.19}\), respectively. Consequently, we significantly improve the existing best attacks in the initialization phase by the designers.