Homomorphic Secret Sharing for Multipartite and General Adversary Structures Supporting Parallel Evaluation of Low-Degree Polynomials

Reo Eriguchi, Koji Nuida

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Homomorphic secret sharing (HSS) for a function f allows input parties to distribute shares for their private inputs and then locally compute output shares from which the value of f is recovered. HSS can be directly used to obtain a two-round multiparty computation (MPC) protocol for possibly non-threshold adversary structures whose communication complexity is independent of the size of f. In this paper, we propose two constructions of HSS schemes supporting parallel evaluation of a single low-degree polynomial and tolerating multipartite and general adversary structures. Our multipartite scheme tolerates a wider class of adversary structures than the previous multipartite one in the particular case of a single evaluation and has exponentially smaller share size than the general construction. While restricting the range of tolerable adversary structures (but still applicable to non-threshold ones), our schemes perform ℓ parallel evaluations with communication complexity approximately ℓ/ log ℓ times smaller than simply using ℓ independent instances. We also formalize two classes of adversary structures taking into account real-world situations to which the previous threshold schemes are inapplicable. Our schemes then perform O(m) parallel evaluations with almost the same communication cost as a single evaluation, where m is the number of parties.

Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part 2
EditorsMehdi Tibouchi, Huaxiong Wang
PublisherSpringer Science and Business Media Deutschland GmbH
Pages191-221
Number of pages31
ISBN (Print)9783030920746
DOIs
Publication statusPublished - 2021
Event27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021 - Virtual, Online
Duration: Dec 6 2021Dec 10 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13091 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021
CityVirtual, Online
Period12/6/2112/10/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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