Optimality and beyond: The case of 4&amp;#x00D7;4 S-boxes

Picek, Stjepan; Ege, Barış; Papagiannopoulos, Kostas; Batina, Lejla; Jakobović, Domagoj

doi:10.1109/hst.2014.6855573

Cited by 27 publications

(26 citation statements)

References 9 publications

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“…Even if several works have been published on this notion (e.g., [5,11,18,22]), we exhibited several inconsistencies in the definition as well as in the interpretation of the definition that went unnoticed for a long time. We have then conducted an in-depth analysis of the notion which led us to output a revised definition which answers all the issues identified in the previous version.…”

Section: Resultsmentioning

confidence: 86%

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Redefining the transparency order

Chakraborty

Sarkar²,

Maitra

et al. 2016

Des. Codes Cryptogr.

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Abstract. In this paper, we consider the multi-bit Differential Power Analysis (DPA) in the Hamming weight model. In this regard, we revisit the definition of Transparency Order (TO) from the work of Prouff (FSE 2005) and find that the definition has certain limitations. Although this work has been quite well referred in the literature, surprisingly, these limitations remained unexplored for almost a decade. We analyse the definition from scratch, modify it and finally provide a definition with better insight that can theoretically capture DPA in Hamming weight model for hardware implementation with precharge logic. At the end, we confront the notion of (revised) transparency order with attack simulations in order to study to what extent the low transparency order of an s-box impacts the efficiency of a side channel attack against its processing. To the best of our knowledge, this is the first time that such a critical analysis is conducted (even considering the original notion of Prouff). It practically confirms that the transparency order is indeed related to the resistance of the s-box against side-channel attacks, but it also shows that it is not sufficient alone to directly achieve a satisfying level of security. Regarding this point, our conclusion is that the (revised) transparency order is a valuable criterion to consider when designing a cryptographic algorithm, and even if it does not preclude to also use classical countermeasures like masking or shuffling, it enables to improve their effectiveness.

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Section: Resultsmentioning

confidence: 86%

“…However, the linear s-boxes are not acceptable as a secure cryptographic primitive. Further analyses of TO, as defined in [24], have been followed in e.g., [5,11,18,22].…”

Section: Introductionmentioning

confidence: 99%

Redefining the transparency order

Chakraborty

Sarkar²,

Maitra

et al. 2016

Des. Codes Cryptogr.

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“…[1]'de, bir S-kutusunun FGA dayanıklılıgı saydamlık derecesi (SD) kavramı ortaya konularak nicelleştirilmiş ve bu ölçütün geçerliligi SASEBO-GII kartı [2][3][4] ve ATmega163 akıllı kart [5,6] gibi kriptografik cihazlar üzerinde uygulanan birçok implementasyon ile dogrulanmıştır.…”

Section: Introductionunclassified

“…Yakın zamanda gerçekleştirilen bazı çalışmalarda [6,8,9], bir S-kutusunun FGA dayanıklılıgının dogrusal olmama, farksal birbiçimlilik ve cebirsel gibi kriptografik özel-likleri degişmeden afin dönüşümlerle iyileştirilebilecegi tespit edilmiştir. Bir S-kutusunun uzaklık profili FGA dayanıklılıgının göstergesi olarak tanımlandıgında, bütün (genişletilmiş) afin eşdeger S-kutuları arasında ikinci en düşük uzaklıga sahip (mutlak gösterge degeri 8 ve boyutu 4 olan) optimal S-kutularının [10], blokşifre PRINCE [11] için öngörülen 8 S-kutusu yerine kullanılmaları öner-ilmiştir [9].…”

Section: Introductionunclassified

“…Bir S-kutusunun uzaklık profili FGA dayanıklılıgının göstergesi olarak tanımlandıgında, bütün (genişletilmiş) afin eşdeger S-kutuları arasında ikinci en düşük uzaklıga sahip (mutlak gösterge degeri 8 ve boyutu 4 olan) optimal S-kutularının [10], blokşifre PRINCE [11] için öngörülen 8 S-kutusu yerine kullanılmaları öner-ilmiştir [9]. Bununla birlikte, bu S-kutuları SD degerleri bakımından en iyi degillerdir; rasgele arama ve genetik algoritmalar kullanılarak, optimal S-kutularının SD'lerinin bazı afin dönüşümler altında 3.2 ile 3.73 arasında degiştigi gözlenmiştir [6].…”

Section: Introductionunclassified

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Düşük Saydamlık Derecesine Sahip Küçük Büyüklükte S-kutuları

Kavut¹

2017

SDÜ Fen Bil Enst Der

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Özet: Farksal güç analizine (FGA) kendiliginden dayanıklı S-kutularının inşası kriptografide önemli bir problemdir. Prouff tarafından 2004'te ortaya konuldugundan itibaren bir S-kutusunun saydamlık derecesi (SD), FGA karşısında önemli bir gösterge olarak yaygın biçimde kullanılmaktadır. Bu çalışmada ilk olarak, bir S-kutusunun SD'sini degiştirmeyen bazı afin dönüşümler saglanmakta ve bu sonuca dayanarak afin eşdeger olan bütün S-kutuları arasından en düşük SD'yi başaran S-kutularını elde etmek için verimli bir tüketici arama stratejisi verilmektedir.İyi bilinen yapıların boyutu ≤ 6 olan durumları için arama stratejimiz başarıyla uygulanmış ve sonuçlar sunulmuştur.İkinci olarak, boyutun 6 oldugu durum için en dik iniş prensibine dayalı özyineli arama algoritması gerçekleştirilmiş ve bilinen yapılardan daha iyi SD degerleri saglarken aynı zamanda yüksek dogrusal olmama ve düşük farksal birbiçimlilige sahip S-kutuları üretilmiştir. Small Size S-boxes with Low Transparency Order Keywords Differential power analysis (DPA), S-boxes, Transparency order (TO)Abstract: Constructing S-boxes that are inherently resistant against the differential power analysis (DPA) is an important problem in cryptography. Since it was introduced by Prouff in 2004, the transparency order (TO) of an S-box has been commonly used as a significant indicator against the DPA. In this work, we fist provide some affine transformations under which the TO of an S-box remains the same, and based on this result we give an efficient exhaustive search strategy to attain the S-boxes achieving the lowest TO among all the S-boxes which are affine equivalent. For the well-known constructions in dimensions ≤ 6, we apply our search strategy successfully and present the results. Secondly, for dimension 6 we perform the steepest-descent-like iterative search algorithm and generate the S-boxes which, while providing better TOs than those of the known constructions, have high nonlineariy and low differential uniformity.

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A Theoretical Study of Kolmogorov-Smirnov Distinguishers

Heuser

Rioul

Guilley

2014

Constructive Side-Channel Analysis and Secure Design

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In this paper, we carry out a detailed mathematical study of two theoretical distinguishers based on the Kolmogorov-Smirnov (KS) distance. This includes a proof of soundness and the derivation of closedform expressions, which can be split into two factors: one depending only on the noise and the other on the confusion coefficient of Fei, Luo and Ding. This allows one to have a deeper understanding of the relative influences of the signal-to-noise ratio and the confusion coefficient on the distinguisher's performance. Moreover, one is able to directly compare distinguishers based on their closed-form expressions instead of using evaluation metric that might obscure the actual performance and favor one distinguisher over the other. Furthermore, we formalize the link between the confusion coefficient and differential cryptanalysis, which shows that the stronger an S-box is resistant to differential attacks the weaker it is against side-channel attacks, and vice versa.

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Optimality and beyond: The case of 4×4 S-boxes

Cited by 27 publications

References 9 publications

Redefining the transparency order

Redefining the transparency order

Düşük Saydamlık Derecesine Sahip Küçük Büyüklükte S-kutuları

A Theoretical Study of Kolmogorov-Smirnov Distinguishers

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