Paper 2019/1063

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

Behzad Abdolmaleki, Hamidreza Khoshakhlagh, and Daniel Slamanig


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.

Note: Minor updates to definitions.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. IMA CC 2019
UC commitmentsmooth projective hash functionSPHFanonymous credentials
Contact author(s)
behzad abdolmaleki @ ut ee
hamidreza @ cs au dk
daniel slamanig @ ait ac at
2019-10-14: revised
2019-09-21: received
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Creative Commons Attribution


      author = {Behzad Abdolmaleki and Hamidreza Khoshakhlagh and Daniel Slamanig},
      title = {A Framework for {UC}-Secure Commitments from Publicly Computable Smooth Projective Hashing},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1063},
      year = {2019},
      note = {\url{}},
      url = {}
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