On Actively-Secure Elementary MPC Reductions

Benny Applebaum, Aarushi Goel*

*Corresponding author for this work

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


We introduce the notion of elementary MPC reductions that allow us to securely compute a functionality f by making a single call to a constant-degree “non-cryptographic” functionality g without requiring any additional interaction. Roughly speaking, “non-cryptographic” means that g does not make use of cryptographic primitives, though the parties can locally call such primitives. Classical MPC results yield such elementary reductions in various cases including the setting of passive security with full corruption threshold t< n (Yao, FOCS’86; Beaver, Micali, and Rogaway, STOC’90), the setting of full active security against a corrupted minority t< n/ 2 (Damgård and Ishai, Crypto’05), and, for NC1 functionalities, even for the setting of full active (information-theoretic) security with full corruption threshold of t< n (Ishai and Kushilevitz, FOCS’00). This leaves open the existence of an elementary reduction that achieves full active security in the dishonest majority setting for all efficiently computable functions. Our main result shows that such a reduction is unlikely to exist. Specifically, the existence of a computationally secure elementary reduction that makes black-box use of a PRG and achieves a very weak form of partial fairness (e.g., that holds only when the first party is not corrupted) would allow us to realize any efficiently-computable function by a constant-round protocol that achieves a non-trivial notion of information-theoretic passive security. The existence of the latter is a well-known 3-decade old open problem in information-theoretic cryptography (Beaver, Micali, and Rogaway, STOC’90). On the positive side, we observe that this barrier can be bypassed under any of the following relaxations: (1) non-black-box use of a pseudorandom generator; (2) weaker security guarantees such as security with identifiable abort; or (3) an additional round of communication with the functionality g.

Original languageEnglish
Title of host publicationTheory of Cryptography - 19th International Conference, TCC 2021, Proceedings
EditorsKobbi Nissim, Brent Waters, Brent Waters
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages33
ISBN (Print)9783030904586
StatePublished - 2021
Event19th International Conference on Theory of Cryptography, TCC 2021 - Raleigh, United States
Duration: 8 Nov 202111 Nov 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13042 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Theory of Cryptography, TCC 2021
Country/TerritoryUnited States


Dive into the research topics of 'On Actively-Secure Elementary MPC Reductions'. Together they form a unique fingerprint.

Cite this