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

  • Behzad AbdolmalekiEmail author
  • Hamidreza Khoshakhlagh
  • Daniel Slamanig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11929)


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.



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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Behzad Abdolmaleki
    • 1
    Email author
  • Hamidreza Khoshakhlagh
    • 2
  • Daniel Slamanig
    • 3
  1. 1.University of TartuTartuEstonia
  2. 2.Aarhus UniversityAarhusDenmark
  3. 3.AIT Austrian Institute of TechnologyViennaAustria

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