International Association
for Cryptologic Research

Linear mappings are crucial components of symmetric ciphers. A special type of linear mappings are

(0,1)-matrices which have been used in symmetric ciphers such as ARIA, E2 and Camellia as diffusion

layers with efficient implementation. Bitwise linear maps are also used in symmetric ciphers such as

SHA family of hash functions and HC family of stream ciphers. In this article, we investigate a special

kind of linear mappings: based upon this study, we propose several linear mappings with only XOR and

rotation operations. The corresponding matrices of these mappings can be used in either the former case

as (0,1)-matrices of maximal branch number or in the latter case as linear mappings with good cryptographic

properties. The proposed mappings and their corresponding matrices can be efficiently implemented both

in software and hardware.