Abstract
Side-channel attacks exploit physical characteristics of implementations of cryptographic algorithms in order to extract sensitive information such as the secret key. These physical attacks are among the most powerful attacks against real-world crypto-systems. In recent years, there has been a number of proposals how to increase the resilience of ciphers against side-channel attacks. One class of proposals concentrates on the intrinsic resilience of ciphers and more precisely their S-boxes. A number of properties has been proposed such as the transparency order, the confusion coefficient and the modified transparency order. Although results with those properties confirm that they are (to some extent) related with the S-box resilience, there is still much to be investigated. There, the biggest drawback stems from the fact that even S-boxes with the best possible values of those properties have only slightly improved side-channel resistance. In this paper, we propose to construct small sized S-boxes based on the results of the measurements of the actual physical attacks. More precisely, we model our S-boxes to be as resilient as possible against non-profiled and profiled physical attacks. Our results highlight that we can design \(4\times 4\) and \(5\times 5\) S-boxes that possess increased resistance against various real-world attacks.
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Notes
- 1.
\((2^n)!\) if we only consider permutations.
- 2.
Note that in general case of a fitness function it is possible to sacrifice one parameter in order to boost another. However, in our case it is impossible to sacrifice the nonlinearity \(N_{F}\) in order to improve the success rate due to the fact that \(N_{F} \in \mathbb {N}\) and \(\mathsf {SR} \in \mathbb {R}\) and \(0< \mathsf {SR} < 1\). In other words the minimal step in values of \(N_{F}\) is 1, while 1 is the maximum increase that the \(\mathsf {SR}\) can get, thus, the whole \(\mathsf {fitness}\) will decrease if \(N_{F}\) decreases while boosting the \(\mathsf {SR}\).
- 3.
A small amount of noise is necessary in order to avoid numerical issues during template attacks.
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Acknowledgments
L. Lerman is funded by the Brussels Institute for Research and Innovation (Innoviris) for the SCAUT project. S. Picek was supported in part by Croatian Science Foundation under the project IP-2014-09-4882.
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Lerman, L., Veshchikov, N., Picek, S., Markowitch, O. (2017). On the Construction of Side-Channel Attack Resilient S-boxes. In: Guilley, S. (eds) Constructive Side-Channel Analysis and Secure Design. COSADE 2017. Lecture Notes in Computer Science(), vol 10348. Springer, Cham. https://doi.org/10.1007/978-3-319-64647-3_7
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