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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 1-2/2017

23-07-2016

Redefining the transparency order

Authors: Kaushik Chakraborty, Sumanta Sarkar, Subhamoy Maitra, Bodhisatwa Mazumdar, Debdeep Mukhopadhyay, Emmanuel Prouff

Published in: Designs, Codes and Cryptography | Issue 1-2/2017

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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 (\(\mathsf {TO}\)) 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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Appendix
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Footnotes
1
Such a model is used in CPA, together with the key hypothesis K, to compute the predictions that are correlated to each point of the traces \({\varvec{T}}_x\) (see [4] for a detailed presentation of the CPA).
 
2
This should correspond to a maximum level of security.
 
3
We recall that the correlation coefficient between two random variables U and V can be soundly estimated from respectively N observations \((u_i)_i\) and \((v_i)_i\) of U and V by \(\rho (U,V) \simeq (N\sum _i u_iv_i - \sum _i u_iv_i) / (\sqrt{N\sum _i u_i^2 - (\sum _i u_i)^2}\sqrt{N\sum _i v_i^2 - (\sum _i v_i)^2})\).
 
4
Those s-boxes correspond to the two opposite extrema in terms of \(\mathsf {TO}\).
 
5
These standard deviations correspond to j % of the mean \(\mathsf {H}(y)\) when y ranges uniformly over \({\mathbb {F}}_2^4\) and \(j\in \{0,10,20,30,40,50\}\).
 
6
The number of repetitions is 1000.
 
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Metadata
Title
Redefining the transparency order
Authors
Kaushik Chakraborty
Sumanta Sarkar
Subhamoy Maitra
Bodhisatwa Mazumdar
Debdeep Mukhopadhyay
Emmanuel Prouff
Publication date
23-07-2016
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 1-2/2017
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-016-0250-3

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