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A Framework for UC-Secure Commitments from Publicly Computable Smooth Projective Hashing

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Cryptography and Coding (IMACC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11929))

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Abstract

Hash proof systems or smooth projective hash functions (SPHFs) have been proposed by Cramer and Shoup (Eurocrypt’02) and can be seen as special type of zero-knowledge proof system for a language. While initially used to build efficient chosen-ciphertext secure public-key encryption, they found numerous applications in several other contexts. In this paper, we revisit the notion of SPHFs and introduce a new feature (a third mode of hashing) that allows to compute the hash value of an SPHF without having access to neither the witness nor the hashing key, but some additional auxiliary information. We call this new type publicly computable SPHFs (PC-SPHFs) and present a formal framework along with concrete instantiations from a large class of SPHFs.

We then show that this new tool generically leads to commitment schemes that are secure against adaptive adversaries, assuming erasures in the Universal Composability (UC) framework, yielding the first UC secure commitments build from a single SPHF instance. Instantiating our PC-SPHF with an SPHF for labeled Cramer-Shoup encryption gives the currently most efficient non-interactive UC-secure commitment. Finally, we also discuss additional applications to information retrieval based on anonymous credentials being UC secure against adaptive adversaries.

H. Khoshakhlagh—Majority of this work was done while working at the University of Tartu.

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Notes

  1. 1.

    We note that we follow existing literature and thus focus on the size of commitments and openings and exclude the message(s) in the opening information.

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Acknowledgments

This work was supported by the EU’s Horizon 2020 ECSEL Joint Undertaking project SECREDAS under grant agreement n\(\circ \)783119, the Austrian Science Fund (FWF) and netidee SCIENCE project PROFET (grant agreement P31621-N38) and the Estonian Research Council grant PRG49.

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Authors and Affiliations

  1. University of Tartu, Tartu, Estonia

    Behzad Abdolmaleki

  2. Aarhus University, Aarhus, Denmark

    Hamidreza Khoshakhlagh

  3. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

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  1. Behzad Abdolmaleki
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  2. Hamidreza Khoshakhlagh
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  3. Daniel Slamanig
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Correspondence to Behzad Abdolmaleki .

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  1. Royal Holloway, University of London, London, UK

    Martin Albrecht

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Abdolmaleki, B., Khoshakhlagh, H., Slamanig, D. (2019). A Framework for UC-Secure Commitments from Publicly Computable Smooth Projective Hashing. In: Albrecht, M. (eds) Cryptography and Coding. IMACC 2019. Lecture Notes in Computer Science(), vol 11929. Springer, Cham. https://doi.org/10.1007/978-3-030-35199-1_1

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  • DOI: https://doi.org/10.1007/978-3-030-35199-1_1

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