SPARX: A Family of ARX-based Lightweight Block Ciphers Provably Secure Against Linear and Differential Attacks

Daniel Dinu, Léo Perrin, Aleksei Udovenko, Vesselin Velichkov, Johann Großschädl, Alex Biryukov

Research output: Contribution to conferencePaperpeer-review


We present, for the first time, 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 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 paper we address the mentioned limitation by proposing the long trail design strategy (LTS) – a dual of the WTS that is applicable (but not limited) to ARX constructions. In contrast to the WTS, that prescribes the use of small and efficient S-boxes at the expense of heavy linear layers with strong mixing properties, the LTS advocates the use of large (ARX-based) S-Boxes together with sparse linear layers. With the help of the so-called long-trail argument, a designer can bound the maximum differential and linear probabilities for any number of rounds of a cipher built according to the LTS.

To illustrate the effectiveness of the new strategy, we propose Sparx – a family of ARXbased block ciphers designed according to the LTS. Sparx has 32-bit ARX-based S-boxes and has provable bounds against differential and linear cryptanalysis. In addition, Sparx is very efficient on a number of embedded platforms. Its optimized software implementation ranks in the top 6 of the most software-efficient ciphers along with Simon, Speck, Chaskey, LEA and RECTANGLE.
Original languageEnglish
Number of pages21
Publication statusPublished - 2016
EventNIST Lightweight Cryptography Workshop 2016 - Gaithersburg, United States
Duration: 17 Oct 201618 Oct 2016


WorkshopNIST Lightweight Cryptography Workshop 2016
Country/TerritoryUnited States
Internet address

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