TY - GEN
T1 - Homomorphic Secret Sharing for Multipartite and General Adversary Structures Supporting Parallel Evaluation of Low-Degree Polynomials
AU - Eriguchi, Reo
AU - Nuida, Koji
N1 - Funding Information:
This research was partially supported by JSPS KAKENHI Grant Numbers JP20J20797 and 19H01109, JST CREST JPMJCR19F6 and JPMJCR14D6, and Ministry of Internal Affairs and Communications SCOPE Grant Number 182103105.
Publisher Copyright:
© 2021, International Association for Cryptologic Research.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-030-92075-3_7
DO - 10.1007/978-3-030-92075-3_7
M3 - Conference contribution
AN - SCOPUS:85121931089
SN - 9783030920746
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 191
EP - 221
BT - Advances in Cryptology – ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part 2
A2 - Tibouchi, Mehdi
A2 - Wang, Huaxiong
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021
Y2 - 6 December 2021 through 10 December 2021
ER -