Cryptology ePrint Archive: Report 2016/984

Design Strategies for ARX with Provable Bounds: SPARX and LAX (Full Version)

Daniel Dinu and Lo Perrin and Aleksei Udovenko and Vesselin Velichkov and Johann Groschdl and Alex Biryukov

Abstract: 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 ARX-based 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.

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 Wallén 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 Wallén challenge.

Category / Keywords: secret-key cryptography / ARX, block ciphers, differential cryptanalysis, linear cryptanalysis, lightweight, wide trail strategy

Original Publication (with major differences): IACR-ASIACRYPT-2016

Date: received 11 Oct 2016

Contact author: leo perrin at uni lu

Available format(s): PDF | BibTeX Citation

Version: 20161015:190931 (All versions of this report)

Short URL: ia.cr/2016/984

Discussion forum: Show discussion | Start new discussion


[ Cryptology ePrint archive ]