Journal of Cryptographic Engineering

, Volume 4, Issue 2, pp 107–121 | Cite as

Achieving side-channel high-order correlation immunity with leakage squeezing

  • Claude Carlet
  • Jean-Luc Danger
  • Sylvain Guilley
  • Houssem Maghrebi
  • Emmanuel Prouff
Regular Paper


This article deeply analyzes high-order (HO) Boolean masking countermeasures against side-channel attacks in contexts where the shares are manipulated simultaneously and the correlation coefficient is used as a statistical distinguisher. The latter attacks are sometimes referred to as zero-offset high-order correlation power analysis (HO-CPA). In particular, the main focus is to get the most out of a single mask (i.e., for masking schemes with two shares). The relationship between the leakage characteristics and the attack efficiency is thoroughly studied. Our main contribution is to link the minimum attack order (called HO-CPA immunity) to the amount of information leaked. Interestingly, the HO-CPA immunity can be much larger than the number of shares in the masking scheme. This is made possible by the leakage squeezing. It is a variant of the Boolean masking where masks are recoded relevantly by bijections. This technique and others from the state-of-the-art (namely leak-free masking and wire-tap codes) are overviewed, and put in perspective.


High-order masking High-order correlation power analysis (HO-CPA) High-order CPA immunity (\(\mathsf {HCI}\)Mutual information metric (MIM) Leakage squeezing 



The authors are grateful to Shivam Bhasin for providing the estimation of the signal-to-noise ratio on FPGAs. We also thank Thanh-Ha Le and Maël Berthier from Safran-Morpho for interesting discussions regarding the use of cumulants in the development of the mutual information in the presence of strong noise. The interaction with them was a key for the rigorous demonstration of Theorem 1. Besides, this work, originating from IACR Cryptology ePrint Archive 2011/520 [32] and from a presentation at CRYPTARCHI 2012 [26], has greatly improved after the numerous fruitful exchanges with the anonymous reviewers. This work has been partly supported by the French National Research Agency (ANR), under Grant ANR-09-SEGI-013 (ARPEGE project SecReSoC, “Secured Reconfigurable System on Chip”).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Claude Carlet
    • 1
  • Jean-Luc Danger
    • 2
    • 3
  • Sylvain Guilley
    • 3
    • 4
  • Houssem Maghrebi
    • 4
    • 5
  • Emmanuel Prouff
    • 6
  1. 1.LAGA, UMR 7539, CNRS, Department of MathematicsUniversity of Paris VIII and University of Paris XIIISaint-Denis CedexFrance
  2. 2.Department COMELECInstitut MINES-TELECOM/TELECOM-ParisTech, CNRS LTCI (UMR 5141) Paris Cedex 13France
  3. 3.Secure-IC S.A.S.RennesFrance
  4. 4.Department COMELECInstitut MINES-TELECOM/TELECOM-ParisTech, CNRS LTCI (UMR 5141) ParisFrance
  5. 5.Morpho-SafranOsnyFrance
  6. 6.Agence Nationale de la Sécurité des Systèmes d’InformationParis 07 SPFrance

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