## Cryptology ePrint Archive: Report 2021/546

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

Jin Hoki and Takanori Isobe and Ryoma Ito and 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 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.

Category / Keywords: secret-key cryptography / SNOW, Stream cipher, 5G · Integral attack, Differential attack, Probabilistic Neutral Bits (PNB)

Original Publication (with major differences): ACISP 2021

Date: received 24 Apr 2021, last revised 15 May 2021

Contact author: takanori isobe at ai u-hyogo ac jp, itorym at nict go jp

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/546

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