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Simple, Fast, Efficient, and Tightly-Secure Non-malleable Non-interactive Timed Commitments

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Public-Key Cryptography – PKC 2023 (PKC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13940))

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Abstract

Timed commitment schemes, introduced by Boneh and Naor (CRYPTO 2000), can be used to achieve fairness in secure computation protocols in a simple and elegant way. The only known non-malleable construction in the standard model is due to Katz, Loss, and Xu (TCC 2020). This construction requires general-purpose zero knowledge proofs with specific properties, and it suffers from an inefficient commitment protocol, which requires the committing party to solve a computationally expensive puzzle.

We propose new constructions of non-malleable non-interactive timed commitments, which combine (an extension of) the Naor-Yung paradigm used to construct IND-CCA secure encryption with a non-interactive ZK proof for a simple algebraic language. This yields much simpler and more efficient non-malleable timed commitments in the standard model.

Furthermore, our constructions also compare favourably to known constructions of timed commitments in the random oracle model, as they achieve several further interesting properties that make the schemes very practical. This includes the possibility of using a homomorphism for the forced opening of multiple commitments in the sense of Malavolta and Thyagarajan (CRYPTO 2019), and they are the first constructions to achieve public verifiability, which seems particularly useful to apply the homomorphism in practical applications.

Peter Chvojka has been partially funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under project PICOCRYPT (grant agreement No. 101001283), a research grant from Nomadic Labs and the Tezos Foundation, the Spanish Government under project PRODIGY (TED2021-132464B-I00), and the Madrid Regional Government under project BLOQUES (S2018/TCS-4339), the last two projects are co-funded by European Union EIE, and NextGenerationEU/PRTR funds. Tibor Jager is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement 802823.

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Notes

  1. 1.

    The choice of Q and T such that \(QT = 2^{64}\) is convenient because it yields \(\lambda = 192\) and [4] provides concrete parameters for this security parameter.

  2. 2.

    Note that [17] \(\textsf{FDec}\) also implicitly checks well-formedness, as it runs a decryption algorithm, which verifies the NIZK proof.

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Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Peter Chvojka

  2. University of Wuppertal, Wuppertal, Germany

    Tibor Jager

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  1. Peter Chvojka
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Correspondence to Peter Chvojka .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Chvojka, P., Jager, T. (2023). Simple, Fast, Efficient, and Tightly-Secure Non-malleable Non-interactive Timed Commitments. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13940. Springer, Cham. https://doi.org/10.1007/978-3-031-31368-4_18

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