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Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-Channel Countermeasures

  • Jean-Sébastien Coron
  • Arnab Roy
  • Srinivas Vivek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8731)

Abstract

We describe a new technique for evaluating polynomials over binary finite fields. This is useful in the context of anti-DPA countermeasures when an S-box is expressed as a polynomial over a binary finite field. For n-bit S-boxes our new technique has heuristic complexity \({\cal O}(2^{n/2}/\sqrt{n})\) instead of \({\cal O}(2^{n/2})\) proven complexity for the Parity-Split method. We also prove a lower bound of \({\Omega}(2^{n/2}/\sqrt{n})\) on the complexity of any method to evaluate n-bit S-boxes; this shows that our method is asymptotically optimal. Here, complexity refers to the number of non-linear multiplications required to evaluate the polynomial corresponding to an S-box.

In practice we can evaluate any 8-bit S-box in 10 non-linear multiplications instead of 16 in the Roy-Vivek paper from CHES 2013, and the DES S-boxes in 4 non-linear multiplications instead of 7. We also evaluate any 4-bit S-box in 2 non-linear multiplications instead of 3. Hence our method achieves optimal complexity for the PRESENT S-box.

Keywords

Full Rank Block Cipher Polynomial Evaluation Random Polynomial Template Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • Arnab Roy
    • 1
    • 2
  • Srinivas Vivek
    • 1
  1. 1.University of LuxembourgLuxembourg
  2. 2.Technical University of DenmarkDenmark

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