Multiple Rows Mixers and Hsilu - A Family of Linear Layers and A Permutation with Fewer XORs

Xiaobin Yu; Meicheng Liu

Paper 2025/1960

Multiple Rows Mixers and Hsilu - A Family of Linear Layers and A Permutation with Fewer XORs

Xiaobin Yu, State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, People’s Republic of China, School of Cyber Security, University of Chinese Academy of Sciences, Beijing, People’s Republic of China

Meicheng Liu, State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, People’s Republic of China, School of Cyber Security, University of Chinese Academy of Sciences, Beijing, People’s Republic of China

Abstract

Over the past decades, extensive research has been conducted on lightweight cryptographic primitives. The linear layer plays an important role in their security. In this paper, we propose a family of linear layers consisting of XORs and rotations, which is called multiple rows mixers (MRM). It is a family designed for LS-type ciphers, but mixing elements from several rows. We investigate the impact of the linear layers on the 3-round trail weight of permutations and explore the properties of the inverse of the linear layers with a low XOR count. We employ a generic and extensible approach to determine the parameters of MRM. This approach can automatically generate linear layers that meet the requirements of a given branch number. By applying these design principles and methods, we derive a linear layer that has a dimension of 5 × 64, a differential branch number of 12, a linear branch number of 5 and a computational cost of 2.6 XOR operations per bit. MRM is not limited to fixed dimension and can be extended to other dimensions. In addition, we present a concrete instantiation of a 320-bit permutation using a more efficient instance of MRM, named Hsilu. Its non-linear layer employs the χ operating on columns. Compared with the permutations of Gaston and NIST lightweight standard Ascon, the round function of Hsilu requires fewer XOR operations. Hsilu exhibits competitive security and performance with Ascon and Gaston. We demonstrate that the best-found 3-round differential and linear trails of Hsilu have much higher weights than those of Ascon. Hsilu outperforms Gaston and Ascon in terms of both software and hardware performance.

Note: This is a revised version of the published paper. We have corrected the mistakes in the proof in Section 5.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: A minor revision of an IACR publication in TOSC 2026
DOI: 10.46586/tosc.v2025.i2.166-191
Keywords: Linear layer Permutations Design Branch number Multiple Rows Mixer Hsilu Lightweight
Contact author(s): yuxiaobin @ iie ac cn
liumeicheng @ iie ac cn
History: 2025-10-20: approved; 2025-10-20: received; See all versions
Short URL: https://ia.cr/2025/1960
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1960,
      author = {Xiaobin Yu and Meicheng Liu},
      title = {Multiple Rows Mixers and Hsilu - A Family of Linear Layers and A Permutation with Fewer {XORs}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1960},
      year = {2025},
      doi = {10.46586/tosc.v2025.i2.166-191},
      url = {https://eprint.iacr.org/2025/1960}
}