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Enhancing Side-Channel Analysis of Binary-Field Multiplication with Bit Reliability

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Topics in Cryptology - CT-RSA 2016 (CT-RSA 2016)

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Abstract

At Africacrypt 2010, Medwed et al. presented Fresh Re-Keying as a countermeasure to protect low-cost devices against side-channel analysis. They propose to use binary-field multiplication as a re-keying function. In this paper, we present a new side-channel attack on this construction (and multiplication in general). By using template attacks and the simple algebraic structure of multiplication, the problem of key recovery can be casted to the well known Learning Parity with Noise problem (LPN). However, instead of using standard LPN solving algorithms, we present a method which makes extensive use of bit reliabilities derived from side-channel information. It allows us to decrease the attack runtime in cases with low-to-medium error probabilities. In a practical experiment, we can successfully attack a protected 8-bit Fresh Re-Keying implementation by Medwed et al. using only 512 traces.

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Notes

  1. 1.

    This method is only of limited use in a standard DPA, where the device uses a fixed key, as it strictly limits the number of observable plaintexts per key byte.

  2. 2.

    This assumes that there is no reshuffling between key addition and S-box processing.

  3. 3.

    This is not entirely correct for the attack of [1], in which each sampled error rate is applied to n samples instead of a single one. We neglect this minor difference.

  4. 4.

    Beware that due to the strong dependency on the quality of the samples and the exponential complexity, the runtime can still vary greatly for a certain trace count.

  5. 5.

    For the plaintext, we only consider leakage during the key addition. The initial operand fetching was ignored, as this can be implemented without leaking the shuffling position.

  6. 6.

    In fact, Belaïd et al. [15] present an attack on an 8-bit implementation using this approach. However, they do not consider the shuffling countermeasure and use Hamming-weight filtering instead of S-box templates.

  7. 7.

    Note that we already used our S-box templates and bit-wise filtering for this estimation. When using the extreme Hamming weight method proposed in [1] (on 8-bit data), then the expected error and thus runtime increases.

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Acknowledgements

figure a

The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 644052 (HECTOR). Furthermore, this work has been supported by the Austrian Research Promotion Agency (FFG) under grant number 845589 (SCALAS). We would also like to thank Benoît Gérard and Jean-Gabriel Kammerer for answering questions regarding their work and for providing the source code used for their runtime estimation.

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  1. Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology, Inffeldgasse 16a, 8010, Graz, Austria

    Peter Pessl & Stefan Mangard

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  1. Peter Pessl
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  2. Stefan Mangard
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Correspondence to Peter Pessl .

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  1. NEC Cloud Systems Research Laboratories, Kawasaki, Japan

    Kazue Sako

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Pessl, P., Mangard, S. (2016). Enhancing Side-Channel Analysis of Binary-Field Multiplication with Bit Reliability. In: Sako, K. (eds) Topics in Cryptology - CT-RSA 2016. CT-RSA 2016. Lecture Notes in Computer Science(), vol 9610. Springer, Cham. https://doi.org/10.1007/978-3-319-29485-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-29485-8_15

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