Abstract
In recent years, many leakage-resilient schemes have been published. These schemes guarantee security against side-channel attacks given bounded leakage of the underlying primitive. However, it is a challenging task to reliably determine these leakage bounds from physical properties.
In this work, we present a novel approach to find reliable leakage bounds for side channels of cryptographic implementations when the input data complexity is limited such as in leakage-resilient schemes. By mapping results from communication theory to the side-channel domain, we show that the channel capacity is the natural upper bound for the mutual information (MI) to be learned from multivariate side-channels with Gaussian noise. It shows that this upper bound is determined by the device-specific signal-to-noise ratio (SNR). We further investigate the case when attackers are capable of measuring the same side-channel leakage multiple times and perform signal averaging. Our results here indicate that the gain in the SNR obtained from averaging is exponential in the number of points of interest that are used from the leakage traces. Based on this, we illustrate how the side-channel capacity gives a tool to compute the minimum attack complexity to learn a certain amount of information from side-channel leakage. We then show that our MI bounds match with reality by evaluating the MI in multivariate Gaussian templates built from practical measurements on an ASIC. We finally use our model to show the security of the keccak-\(f\)[400]-based authenticated encryption scheme Isap on this ASIC against power analysis attacks.
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Notes
- 1.
The constant covariance assumption is invalid in case the covariance carries information as, e.g., in masked implementations. However, leakage-resilient cryptography aims to bound the leakage without the use of countermeasures like masking, and thus noise will typically be independent from the signal.
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Acknowledgements
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 681402) and from the Austrian Research Promotion Agency (FFG) under grant number 845589 (SCALAS).
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Unterluggauer, T. et al. (2018). Leakage Bounds for Gaussian Side Channels. In: Eisenbarth, T., Teglia, Y. (eds) Smart Card Research and Advanced Applications. CARDIS 2017. Lecture Notes in Computer Science(), vol 10728. Springer, Cham. https://doi.org/10.1007/978-3-319-75208-2_6
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