Cryptology ePrint Archive: Report 2021/546

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

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

Abstract: This paper proposes distinguishing and key recovery attacks on the reduced-round versions of the SNOW-V stream cipher. 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-, and 5-round versions with time complexities of \(2^8\), \(2^{16}\), and \(2^{48}\), 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- and 4-round differential distinguishers with time complexities of \(2^{48}\) and \(2^{103}\), 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 observe the best bit-wise differential biases with \(2^{−1.733}\) and \(2^{−17.934}\) in the 4- and 5-round versions, respectively. This is feasible to construct a very practical distinguisher with a time complexity of \(2^{4.466}\) for the 4-round version, and a distinguisher with a time complexity of at least \(2^{36.868}\) for the 5-round version. 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 version with a time complexity of \(2^{153.97}\) and data complexity of \(2^{26.96}\). 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

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

Available format(s): PDF | BibTeX Citation

Version: 20210427:061034 (All versions of this report)

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