Efficient UC commitment extension with homomorphism for free (and applications)

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

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

5 Citations (Scopus)


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
Subtitle of host publication25th International Conference on the Theory and Application of Cryptology and Information Security Kobe, Japan, December 8–12, 2019 Proceedings, Part II
EditorsSteven D. Galbraith, Shiho Moriai
Place of PublicationCham Switzerland
Number of pages30
ISBN (Electronic)9783030346218
ISBN (Print)9783030346201
Publication statusPublished - 2019
Externally publishedYes
EventInternational Conference on the Theory and Application of Cryptology and Information Security 2019 - Kobe, Japan
Duration: 8 Dec 201912 Dec 2019
Conference number: 25th
https://link.springer.com/book/10.1007/978-3-030-34621-8 (Proceedings)
https://asiacrypt.iacr.org/2019/ (Website)

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Conference on the Theory and Application of Cryptology and Information Security 2019
Abbreviated titleASIACRYPT 2019
Internet address

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