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

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