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

Ignacio Cascudo, Ivan Damgård, Bernardo David, Rafael Dowsley, Nico Döttling, Irene Giacomelli

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review


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. 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. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete eciency and oering new insights into the sucient conditions for obtaining homomorphic UC commitments. 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 ecient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.
Original languageEnglish
Title of host publication Advances in Cryptology – ASIACRYPT 2019 : 25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, December 8–12, 2019, Proceedings, Part II
EditorsSteven Galbraith, Shiho Moriai
Publication date22 Nov 2019
ISBN (Print)978-3-030-34620-1
ISBN (Electronic)978-3-030-34621-8
Publication statusPublished - 22 Nov 2019
EventAsiacrypt 2019 -
Duration: 8 Dec 201912 Dec 2019


ConferenceAsiacrypt 2019
SeriesLecture Notes in Computer Science


  • Commitments
  • Universal Composability
  • Homomorphism
  • Multiparty Computation
  • Provable Security


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