Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

  • Ignacio Cascudo, IMDEA Software Institute
  • ,
  • Ivan Damgård
  • Bernardo David, IT-Universitetet i Kobenhavn
  • ,
  • Nico Döttling, Helmholtz Center for Information Security
  • ,
  • Rafael Dowsley, Bar-Ilan University
  • ,
  • Irene Giacomelli, Protocol Labs, Inc.

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment, while the previous best constructions require oblivious transfer. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.

Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
EditorsSteven D. Galbraith, Shiho Moriai
Number of pages30
Publication year2019
ISBN (print)9783030346201
Publication statusPublished - 2019
Event25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019 - Kobe, Japan
Duration: 8 Dec 201912 Dec 2019


Conference25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019
SeriesLecture Notes in Computer Science

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