Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

01-06-2015 | CHES 2014 | Issue 2/2015

Journal of Cryptographic Engineering 2/2015

Fast evaluation of polynomials over binary finite fields and application to side-channel countermeasures

Journal:
Journal of Cryptographic Engineering > Issue 2/2015
Authors:
Jean-Sébastien Coron, Arnab Roy, Srinivas Vivek
Important notes
A preliminary version of this paper has appeared at CHES 2014.

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 \({\fancyscript{O}}(2^{n/2}/\sqrt{n})\) instead of \({\fancyscript{O}}(2^{n/2})\) proven complexity for the Parity-Split method. We also prove a lower bound of \({{\varOmega }}(2^{n/2}/\sqrt{n})\) 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.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Maschinenbau + Werkstoffe




Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 30 Tage kostenlos.

Literature
About this article

Other articles of this Issue 2/2015

Journal of Cryptographic Engineering 2/2015 Go to the issue

Premium Partner

    Image Credits