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Time-Frequency Analysis for Second-Order Attacks

  • Pierre Belgarric
  • Shivam Bhasin
  • Nicolas Bruneau
  • Jean-Luc Danger
  • Nicolas Debande
  • Sylvain Guilley
  • Annelie Heuser
  • Zakaria Najm
  • Olivier Rioul
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8419)

Abstract

Second-order side-channel attacks are used to break first-order masking protections. A practical reason which often limits the efficiency of second-order attacks is the temporal localisation of the leaking samples. Several pairs of leakage samples must be combined which means high computational power. For second-order attacks, the computational complexity is quadratic. At CHES ’04, Waddle and Wagner introduced attacks with complexity \(\mathcal {O}(n \log _2 n)\) on traces collected from a hardware cryptographic implementation, where \(n\) is the window size, by working on traces auto-correlation. Nonetheless, the two samples must belong to the same window which is (normally) not the case for software implementations. In this article, we introduce preprocessing tools that improve the efficiency of bi-variate attacks (while keeping a complexity of \(\mathcal {O}(n \log _2 n)\)), even if the two samples that leak are far away one from the other (as in software). We put forward two main improvements. Firstly, we introduce a method to avoid losing the phase information. Next, we empirically notice that keeping the analysis in the frequency domain can be beneficial for the attack. We apply these attacks in practice on real measurements, publicly available under the DPA Contest v4, to evaluate the proposed techniques. An attack using a window as large as 4000 points is able to reveal the key in only 3000 traces.

Keywords

Bi-variate attacks Zero-offset 2O-CPA Discrete Hartley transform Leakage in phase 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pierre Belgarric
    • 1
    • 3
  • Shivam Bhasin
    • 1
  • Nicolas Bruneau
    • 1
    • 4
  • Jean-Luc Danger
    • 1
    • 5
  • Nicolas Debande
    • 1
    • 6
  • Sylvain Guilley
    • 1
    • 5
  • Annelie Heuser
    • 1
  • Zakaria Najm
    • 1
  • Olivier Rioul
    • 2
    • 7
  1. 1.TELECOM-ParisTech, Crypto GroupParisFrance
  2. 2.TELECOM-ParisTech, Digital Communications GroupParisFrance
  3. 3.Orange Labs, Applied Cryptography GroupIssy-les-MoulineauxFrance
  4. 4.STMicroelectronics, AST DivisionRoussetFrance
  5. 5.Secure-IC S.A.S.RennesFrance
  6. 6.SERMA ITSEFPessacFrance
  7. 7.École PolytechniquePalaiseauFrance

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