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Clustering Algorithms for Non-profiled Single-Execution Attacks on Exponentiations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 8419)

Abstract

Most implementations of public key cryptography employ exponentiation algorithms. Side-channel attacks on secret exponents are typically bound to the leakage of single executions due to cryptographic protocols or side-channel countermeasures such as blinding. We propose for the first time, to use a well-established class of algorithms, i.e. unsupervised cluster classification algorithms such as the k-means algorithm to attack cryptographic exponentiations and recover secret exponents without any prior profiling, manual tuning or leakage models. Not requiring profiling is of significant advantage to attackers, as are well-established algorithms. The proposed non-profiled single-execution attack is able to exploit any available single-execution leakage and provides a straight-forward option to combine simultaneous measurements to increase the available leakage. We present empirical results from attacking an FPGA-based elliptic curve scalar multiplication using the \(k\)-means clustering algorithm and successfully exploit location-based leakage from high-resolution electromagnetic field measurements to achieve a low remaining brute-force complexity of the secret exponent. A simulated multi-channel measurement even enables an error-free recovery of the exponent.

Keywords

  • Exponentiation
  • Side-channel attack
  • Non-profiled
  • Single-execution
  • Unsupervised clustering
  • Simultaneous measurements
  • EM

Stefan Mangard – This research has been conducted while working for Infineon Technologies AG, Munich, Germany.

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Acknowledgments

This work was partly funded by the German Federal Ministry of Education and Research in the project SIBASE through grant number 01IS13020.

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Correspondence to Johann Heyszl .

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Heyszl, J., Ibing, A., Mangard, S., De Santis, F., Sigl, G. (2014). Clustering Algorithms for Non-profiled Single-Execution Attacks on Exponentiations. In: Francillon, A., Rohatgi, P. (eds) Smart Card Research and Advanced Applications. CARDIS 2013. Lecture Notes in Computer Science(), vol 8419. Springer, Cham. https://doi.org/10.1007/978-3-319-08302-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-08302-5_6

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