Vesselin Velichkov

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Title: Design Strategies for ARX with Provable Bounds: SPARX and LAX

Abstract: We present a general strategy for designing ARX symmetric-key primitives with provable resistance against single-trail differential and linear cryptanalysis. The latter has been a long standing open problem in the area of ARX design. The {\it wide trail design strategy} (WTS), that is at the basis of many S-box based ciphers, including the AES, is not suitable for ARX designs due to the lack of S-boxes in the latter. In this talk we address the mentioned limitation by proposing the \emph{long trail design strategy} (LTS) -- a dual of the WTS that is applicable (but not limited) to ARX constructions. To illustrate its effectiveness, we propose SPARX -- a family of efficient ARX-based block ciphers designed according to the LTS.

As a second contribution we propose another strategy for designing ARX ciphers with provable properties, that is completely independent of the LTS. It is motivated by a challenge proposed earlier by Wallèn and uses the differential properties of modular addition to minimize the maximum differential probability across multiple rounds of a cipher. A new primitive, called LAX, is designed following those principles. LAX partly solves the Wallèn challenge.

This paper has been presented earlier at ASIACRYPT'16. It is joint work with Daniel Dinu, Léo Perrin, Aleksei Udovenko, Johann Großschädl and Alex Biryukov.