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Fault and Power Analysis Attack Protection Techniques for Standardized Public Key Cryptosystems

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Hardware Security and Trust

Abstract

Implementation—physical attacks like side channel and fault injection attacks constitute a realistic problem for all security applications. Standardized public key cryptography implementations like RSA and Elliptic Curve cryptography (ECC) schemes are very vulnerable to easy-to-mount such attacks. Focus point of those attacks is the RSA/ECC cryptographic primitives of modular exponentiation or scalar multiplication respectively. There exist a very wide variety of implementation attacks on the above two cryptographic primitives so designing appropriate countermeasures is not a straightforward process. In this book chapter, we view RSA and ECC cryptographic primitives in a unified way and introduce a side channel and fault injection attack countermeasure approach that is applicable to both schemes. To achieve that, we describe and analyze the existing implementation attack ecosystem and propose an algorithm that is applicable to both modular exponentiation and scalar multiplication and is capable of providing broad resistance. The proposed approach is based on Montgomery Power Ladder which is extended in order to provide strong randomization through multiplicative/additive blinding of the RSA/ECC sensitive information. This randomization is realized in such a way that in each round of the algorithm the involved random element is propagated and expanded according to the algorithmic computation flow. In the proposed concept, faults are detected through an appropriate mechanism (fault detection) at the end of all computations by exploiting mathematical coherency between intermediate values in the algorithmic flow. Through the above countermeasure techniques, the proposed algorithm can provide protection against a wide range of “horizontal” and “vertical” side channel attacks as well as fault injection attacks, thus, acting as an all-in-one protection framework for RSA/ECC schemes.

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Notes

  1. 1.

    Chinese Remainder Theorem.

  2. 2.

    A weak elliptic curve is a curve that can be cryptanalyzed easily.

  3. 3.

    Note that \(\overline{e}\) is logical NOT of e and that \(e+\overline{e}=2^t-1\).

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Acknowledgements

This work is supported by EU COST action IC1204 “Trustworthy Manufacturing and Utilization of Secure Devices (TRUDEVICE)”.

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Authors and Affiliations

  1. Computer Informatics Engineering Department, Technological Educational Institute of Western, Antirion, Greece

    Apostolos P. Fournaris

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  1. Apostolos P. Fournaris
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Correspondence to Apostolos P. Fournaris .

Editor information

Editors and Affiliations

  1. Computer & Informatics Engineering Department, Technological Educational Institute of Western Greece, Antirrio, Greece

    Nicolas Sklavos

  2. INESC-ID, IST, University of Lisbon, Lisbon, Portugal

    Ricardo Chaves

  3. UMR 5506 - CC 477, LIRMM - CNRS / University of Montpellier, Montpellier, France

    Giorgio Di Natale

  4. ALaRI Institute, University of Lugano, Lugano, Switzerland

    Francesco Regazzoni

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Fournaris, A.P. (2017). Fault and Power Analysis Attack Protection Techniques for Standardized Public Key Cryptosystems. In: Sklavos, N., Chaves, R., Di Natale, G., Regazzoni, F. (eds) Hardware Security and Trust. Springer, Cham. https://doi.org/10.1007/978-3-319-44318-8_5

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  • DOI: https://doi.org/10.1007/978-3-319-44318-8_5

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  • Online ISBN: 978-3-319-44318-8

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