[Resource Topic] 2023/1803: Design of a Linear Layer Optimised for Bitsliced 32-bit Implementation

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Design of a Linear Layer Optimised for Bitsliced 32-bit Implementation

Authors: Gaëtan Leurent, Clara Pernot


The linear layer of block ciphers plays an important role in their security.
In particular, ciphers designed following the wide-trail strategy use the branch number of the linear layer to derive bounds on the probability of linear and differential trails.
At FSE 2014, the LS-design construction was introduced as a simple and regular structure to design bitsliced block ciphers. It considers the internal state as a bit matrix, and applies alternatively an identical S-Box on all the columns, and an identical L-Box on all the lines. Security bounds are derived from the branch number of the L-Box.
In this paper, we focus on bitsliced linear layers inspired by the LS-design construction and the Spook AEAD algorithm. We study the construction of bitsliced linear transformations with efficient implementations using XORs and rotations (optimized for bitsliced ciphers implemented on 32-bit processors), and a high branch number.
In order to increase the density of the activity patterns, the linear layer is designed on the whole state, rather than using multiple parallel copies of an L-Box.
Our main result is a linear layer for 128-bit ciphers with branch number 21, improving upon the best 32-bit transformation with branch number 12, and the one of Spook with branch number 16.

ePrint: https://eprint.iacr.org/2023/1803

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