Algebraic Methods in Side-Channel Collision Attacks and Practical Collision Detection

  • Andrey Bogdanov
  • Ilya Kizhvatov
  • Andrey Pyshkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5365)


This paper presents algebraic collision attacks, a new powerful cryptanalytic method based on side-channel leakage which allows for low measurement counts needed for a successful key recovery in case of AES. As opposed to many other side-channel attacks, these techniques are essentially based on the internal structure of the attacked cryptographic algorithm, namely, on the algebraic properties of AES. Moreover, we derived the probability distributions of Euclidean distance for collisions and non-collisions. On this basis, a statistical framework for finding the instances of side-channel traces leaking most key information in collision attacks is proposed.

Additionally to these theoretical findings, the paper also contains a practical evaluation of these side-channel collision attacks for a real-world microcontroller platform similar to many smart card ICs. To our best knowledge, this is the first real-world study of collision attacks based on generalized internal collisions. We also combined our methods with ternary voting [1] which is a recent multiple-differential collision detection technique using profiling, where neither plaintexts, ciphertexts nor keys have to be known in the profiling stage.


Side-channel attacks collision attacks algebraic cryptanalysis multiple-differential collision attacks ternary voting AES DPA 


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  1. 1.
    Bogdanov, A.: Multiple-differential side-channel collision attacks on AES. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 30–44. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Chari, S., Rao, J.R., Rohatgi, P.: Template attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 51–62. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Lemke-Rust, K.: Models and Algorithms for Physical Cryptanalysis. PhD thesis, Ruhr University Bochum (2007)Google Scholar
  5. 5.
    Schramm, K., Leander, G., Felke, P., Paar, C.: A collision-attack on AES: Combining side channel- and differential-attack. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 163–175. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Bogdanov, A.: Improved side-channel collision attacks on AES. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 84–95. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Cid, C., Murphy, S., Robshaw, M.: Algebraic Aspects of the Advanced Encryption Standard. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  8. 8.
    Charvet, X., Pelletier, H.: Improving the DPA attack using wavelet transform. In: NIST Physical Security Testing Workshop (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andrey Bogdanov
    • 1
  • Ilya Kizhvatov
    • 2
  • Andrey Pyshkin
    • 3
  1. 1.Horst Görtz Institute for Information SecurityRuhr-University BochumGermany
  2. 2.University of LuxembourgLuxembourg
  3. 3.Technical University DarmstadtGermany

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