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Exploitable Fault Space Characterization: A Complementary Approach

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Automated Methods in Cryptographic Fault Analysis

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Abstract

Consider the problem of estimating the success rate of an attacker for a given fault location. Intuitively, the success rate indicates the likeliness of an attack for returning the key bits within a practical computational bound. It is a quantity worth estimating as it helps in choosing cipher constructs and sub-operations showing a certain amount of robustness against fault attacks. In this chapter, we present a framework, which can estimate quantities like success rate and can provide new insights into the cipher structures in the context of fault attacks. The main idea is to utilize the exact encoding of algebraic fault attacks (AFA) for exploring the fault space without getting affected by its prohibitive time complexity. We propose a machine learning (ML) based speedup strategy to make the AFA suitable for characterizing huge fault spaces statistically. This statistical approach is found to be extremely informative for cipher designers and evaluators.

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Notes

  1. 1.

    A block cipher is nothing but a Boolean function, and for every Boolean function, we can have such an algebraic representation. In fact, this representation is a normal form known as algebraic normal form (ANF).

  2. 2.

    In this chapter, we shall present a quantification of the fault space size. It is worth mentioning that ExpFault handles the fault space by means of abstraction, which makes the fault space exploration problem rather scalable.

  3. 3.

    The fault values and the plaintext values are not explicitly considered (i.e., abstracted) in ExpFault. The fault space size becomes relatively reasonable to be exhausted without these two parameters. The flip side of this abstraction is that ExpFault returns the best case attack complexity (from attacker’s perspective) for certain ciphers like PRESENT.

  4. 4.

    However, it is worth mentioning that, by assigning some of the correct key bits in the equation system, a cipher evaluator can also handle the cases where key extraction by means of a fault is partial.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

    Sayandeep Saha, Sikhar Patranabis, Debdeep Mukhopadhyay & Pallab Dasgupta

  2. Temasek Laboratories, Nanyang Technological University, Singapore, Singapore

    Dirmanto Jap & Shivam Bhasin

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  1. Sayandeep Saha
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  2. Dirmanto Jap
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  5. Shivam Bhasin
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  6. Pallab Dasgupta
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Correspondence to Sayandeep Saha .

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Editors and Affiliations

  1. Underwriters Laboratories, Singapore, Singapore

    Jakub Breier

  2. Acronis, Singapore, Singapore

    Xiaolu Hou

  3. Temasek Laboratories, Nanyang Technological University, Singapore, Singapore

    Shivam Bhasin

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Saha, S., Jap, D., Patranabis, S., Mukhopadhyay, D., Bhasin, S., Dasgupta, P. (2019). Exploitable Fault Space Characterization: A Complementary Approach. In: Breier, J., Hou, X., Bhasin, S. (eds) Automated Methods in Cryptographic Fault Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-11333-9_3

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  • DOI: https://doi.org/10.1007/978-3-030-11333-9_3

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  • Print ISBN: 978-3-030-11332-2

  • Online ISBN: 978-3-030-11333-9

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