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A New Class of Trapdoor Verifiable Delay Functions

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Foundations and Practice of Security (FPS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13877))

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Abstract

A verifiable delay function (VDF) is a function whose evaluation involves lengthy sequential operations, yet its outcome is publicly verifiable. As an extension, a trapdoor-VDF is a VDF with a shortcut that speeds up the evaluation process. This paper presents a new class of trapdoor-VDFs featuring a large ensemble of trapdoors for each instantiation of the function. This way, a client can randomly choose a private trapdoor from the ensemble, thereby using it to encapsulate a secret to the future as a unique puzzle. To solve the puzzle, the server, which does not know the trapdoor, requires a prescribed number of sequential steps to evaluate the function. Any client can efficiently verify the correctness of the server’s evaluation with zero knowledge of the trapdoor being used. We present an approach for constructing the proposed class of trapdoor-VDFs based on bilinear pairings and a long walk on supersingular isogeny graphs. Finally, we examine the security of our construction under trapdoor-VDF security notions.

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Notes

  1. 1.

    The subgroup \( {G}_{1}^{ E_{} } \) is defined as \( {G}_{1}^{ E_{} } := E_{} [N]\cap \textsf {ker} (\pi +[1])\), whereas, \( {G}_{2}^{ E_{} } := E_{} [N]\cap \textsf {ker} (\pi -[1])\).

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Ahmed Zawia & M. Anwar Hasan

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  1. Ahmed Zawia
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  2. M. Anwar Hasan
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Correspondence to Ahmed Zawia .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Guy-Vincent Jourdan

  2. Université Grenoble Alpes, Grenoble, France

    Laurent Mounier

  3. University of Ottawa, Ottawa, ON, Canada

    Carlisle Adams

  4. University Toulouse III Paul Sabatier, Toulouse, France

    Florence Sèdes

  5. Telecom SudParis, Palaiseau, France

    Joaquin Garcia-Alfaro

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Zawia, A., Hasan, M.A. (2023). A New Class of Trapdoor Verifiable Delay Functions. In: Jourdan, GV., Mounier, L., Adams, C., Sèdes, F., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2022. Lecture Notes in Computer Science, vol 13877. Springer, Cham. https://doi.org/10.1007/978-3-031-30122-3_5

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  • DOI: https://doi.org/10.1007/978-3-031-30122-3_5

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  • Online ISBN: 978-3-031-30122-3

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