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International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2017: Progress in Cryptology – LATINCRYPT 2017 pp 401–414Cite as

Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11368))

Abstract

In an \(\ell \) out of n threshold scheme, \(\ell \) out of n members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and further used to retrieve a user’s secret key. We combine the notions of threshold scheme and kleptographic attack to construct the first \(\ell \) out of n threshold kleptographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models.

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Notes

  1. 1.

    A black-box is a device, process or system, whose inputs and outputs are known, but its internal structure or working is not known or accessible to the user (e.g. tamper proof devices).

  2. 2.

    that implements the mechanisms to recover the secrets.

  3. 3.

    We refer the reader to [29].

  4. 4.

    We refer the reader to [12] for a description of AES.

  5. 5.

    at least 2048 bits, better 3072 bits.

  6. 6.

    at least 192 bits, better 256 bits.

  7. 7.

    If V knows his secret key, he is able to detect a SETUP mechanism using its description and parameters (found by means of reverse engineering a black-box, for example).

  8. 8.

    We refer the reader to Sect. 5.

  9. 9.

    We refer the reader to the full version of the paper [32].

  10. 10.

    that uses \(y_M\).

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Acknowledgments

The author would like to thank Adrian Atanasiu, Alejandro Hevia, Tanja Lange, Diana Maimuţ and Ferucio Laurenţiu Ţiplea, and the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Computer Science, “Al.I.Cuza” University of Iaşi, 700506, Iaşi, Romania

    George Teşeleanu

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  1. George Teşeleanu
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Correspondence to George Teşeleanu .

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Editors and Affiliations

  1. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Tanja Lange

  2. University of Haifa, Haifa, Israel

    Orr Dunkelman

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Teşeleanu, G. (2019). Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures. In: Lange, T., Dunkelman, O. (eds) Progress in Cryptology – LATINCRYPT 2017. LATINCRYPT 2017. Lecture Notes in Computer Science(), vol 11368. Springer, Cham. https://doi.org/10.1007/978-3-030-25283-0_21

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