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Side-Channel Analysis of Multiplications in GF(2128)

Application to AES-GCM
  • Sonia Belaïd
  • Pierre-Alain Fouque
  • Benoît Gérard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8874)

Abstract

In this paper, we study the side-channel security of the field multiplication in GF(2 n ). We particularly focus on GF(2128) multiplication which is the one used in the authentication part of \(\mathsf{AES}\textrm{-}\mathsf{GCM}\) but the proposed attack also applies to other binary extensions. In a hardware implementation using a 128-bit multiplier, the full 128-bit secret is manipulated at once. In this context, classical DPA attacks based on the divide and conquer strategy cannot be applied. In this work, the algebraic structure of the multiplication is leveraged to recover bits of information about the secret multiplicand without having to perform any key-guess. To do so, the leakage corresponding to the writing of the multiplication output into a register is considered. It is assumed to follow a Hamming weight/distance leakage model. Under these particular, yet easily met, assumption we exhibit a nice connection between the key recovery problem and some classical coding and Learning Parities with Noise problems with certain instance parameters. In our case, the noise is very high, but the length of the secret is rather short. In this work we investigate different solving techniques corresponding to different attacker models and eventually refine the attack when considering particular implementations of the multiplication.

Keywords

Field Multiplication Authenticated Encryption \(\mathsf{AES}\textrm{-}\mathsf{GCM}\) Side-Channel 

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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Sonia Belaïd
    • 1
    • 2
  • Pierre-Alain Fouque
    • 3
    • 4
  • Benoît Gérard
    • 5
  1. 1.École normale supérieureParisFrance
  2. 2.Thales Communications & SecurityGennevilliersFrance
  3. 3.Université de Rennes 1RennesFrance
  4. 4.Institut Universitaire de FranceFrance
  5. 5.DGA–MI and IRISARennesFrance

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