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Design Strategies for ARX with Provable Bounds: SPARX and LAX
Dinu, Dumitru-Daniel; Perrin, Léo Paul; Udovenko, Aleksei et al.
2016In Cheon, Jung Hee; Takagi, Tsuyoshi (Eds.) Advances in Cryptology --- ASIACRYPT 2016, 22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, December 4-8, 2016, Proceedings, Part I
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Keywords :
ARX; Block Ciphers; Differential Cryptanalysis; Linear Cryptanalysis; Lightweight Cryptography; Wide-Trail Strategy
Abstract :
[en] 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 Wallen 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 Wallen challenge.
Disciplines :
Computer science
Author, co-author :
Dinu, Dumitru-Daniel ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Perrin, Léo Paul ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Udovenko, Aleksei  ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)
Velichkov, Vesselin ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Computer Science and Communications Research Unit (CSC)
Groszschädl, Johann ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Biryukov, Alex ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
External co-authors :
no
Language :
English
Title :
Design Strategies for ARX with Provable Bounds: SPARX and LAX
Publication date :
December 2016
Event name :
22nd Annual International Conference on the Theory and Applications of Cryptology and Information Security (ASIACRYPT 2016)
Event place :
Hanoi, Vietnam
Event date :
from 04-12-2016 to 08-12-2016
Audience :
International
Main work title :
Advances in Cryptology --- ASIACRYPT 2016, 22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, December 4-8, 2016, Proceedings, Part I
Editor :
Cheon, Jung Hee
Takagi, Tsuyoshi
Publisher :
Springer Verlag
ISBN/EAN :
978-3-662-53887-6
Collection name :
Lecture Notes in Computer Science, volume 10031
Pages :
484-513
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
FnR Project :
FNR4009992 - Applied Cryptography For The Internet Of Things, 2012 (01/07/2013-30/06/2016) - Alex Biryukov
Funders :
FNR - Fonds National de la Recherche [LU]
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