Cryptology ePrint Archive: Report 2019/1063

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

Behzad Abdolmaleki and Hamidreza Khoshakhlagh and Daniel Slamanig

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.

Category / Keywords: cryptographic protocols / UC commitment, smooth projective hash function, SPHF, anonymous credentials

Original Publication (in the same form): IMA CC 2019

Date: received 19 Sep 2019, last revised 14 Oct 2019

Contact author: behzad abdolmaleki at ut ee, hamidreza at cs au dk, daniel slamanig at ait ac at

Available format(s): PDF | BibTeX Citation

Note: Minor updates to definitions.

Version: 20191014:090359 (All versions of this report)

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