Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lecture notes in computer science

Breaking the Circuit Size Barrier for Secure Computation Under Quasi-Polynomial LPN

Geoffroy Couteau, Pierre Meyer

Published Jan 1, 2021• 21 citations
Publisher
DOI
10.1007/978-3-030-77886-6_29

Related papers

Large Scale, Actively Secure Computation from LPN and Free-XOR Garbled Circuits

Aner Ben-Efraim, Kelong Cong, Eran Omri +3 more

Lecture notes in computer science•Jan 1, 2021•22 citations

How To Play Almost Any Mental Game Over The Net - Concurrent Composition via Super-Polynomial Simulation

Boaz Barak, Amit Sahai

We construct a secure protocol for any multi-party functionality that remains secure (under a relaxed definition of security) when executed concurrently with multiple copies of itself and other protocols. We stress that we do not use any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security, introduced by Prabhakaran and Sahai (STOC ’04), is obtained by allowing the idealmodel simulator to run in quai-polynomial (as opposed to polynomial) time. Quasi-polynomial simulation suffices to ensure security for most applications of multi-party computation. Furthermore, Lindell (FOCS ’03, TCC ’ 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions. That is, existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations that are secure with respect to circuits of quasi-polynomial size. We introduce a new technique: “protocol condensing”. That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and

Electronic colloquium on computational complexity•Jan 1, 2005•0 citations

Two-Round Maliciously Secure Computation with Super-Polynomial Simulation

Amit Agarwal, James Bartusek, Vipul Goyal +2 more

Lecture notes in computer science•Jan 1, 2021•4 citations

How To Play Almost Any Mental Game Over The Net - Concurrent Composition via Super-Polynomial Simulation

Boaz Barak, Amit Sahai

We construct a secure protocol for any multiparty functionality that remains secure (under a relaxed definition of security introduced by Prabhakaran and Sahai (STOC '04)) when executed concurrently with multiple copies of itself and other protocols, without any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security is obtained by allowing the ideal-model simulator to run in quasipolynomial (as opposed to polynomial) time. Quasipolynomial simulation suffices to ensure security for most applications of multiparty computation. Furthermore, Lindell (FOCS '03, TCC' 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions (i.e., existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations which are secure with respect to circuits of quasi-polynomial size). We introduce a new technique: "protocol condensing". That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and then transforming it into a protocol with polynomial communication and computation, that still inherits the strong security properties of the original protocol. Our result is obtained by combining this technique with previous techniques of Canetti, Lindell, Ostrovsky, and Sahai (STOC '02) and Pass (STOC '04).

Annual Symposium on Foundations of Computer Science•Nov 15, 2005•109 citations

Breaking the minsky-papert barrier for constant-depth circuits

Alexander A. Sherstov

The threshold degree of a Boolean function f is the minimum degree of a real polynomial p that represents f in sign: f(x) ≡ sgn p(x). In a seminal 1969 monograph, Minsky and Papert constructed a polynomial-size constant-depth {∧, ∨)-circuit in n variables with threshold degree Ω(n1/3). This bound underlies some of today's strongest results on constant-depth circuits. It has been an open problem (O'Donnell and Servedio, STOC 2003) to improve Minsky and Papert's bound to nΩ(1)+1/3.

ACM Symposium on Theory of Computing (STOC)•May 31, 2014•15 citations

Secure Computation and Its Diverse Applications

Yuval Ishai

Lecture notes in computer science•Jan 1, 2010•1 citation
We construct a secure protocol for any multi-party functionality that remains secure (under a relaxed definition of security) when executed concurrently with multiple copies of itself and other protocols. We stress that we do not use any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security, introduced by Prabhakaran and Sahai (STOC ’04), is obtained by allowing the idealmodel simulator to run in quai-polynomial (as opposed to polynomial) time. Quasi-polynomial simulation suffices to ensure security for most applications of multi-party computation. Furthermore, Lindell (FOCS ’03, TCC ’ 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions. That is, existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations that are secure with respect to circuits of quasi-polynomial size. We introduce a new technique: “protocol condensing”. That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and
We construct a secure protocol for any multiparty functionality that remains secure (under a relaxed definition of security introduced by Prabhakaran and Sahai (STOC '04)) when executed concurrently with multiple copies of itself and other protocols, without any assumptions on existence of trusted parties, common reference string, honest majority or synchronicity of the network. The relaxation of security is obtained by allowing the ideal-model simulator to run in quasipolynomial (as opposed to polynomial) time. Quasipolynomial simulation suffices to ensure security for most applications of multiparty computation. Furthermore, Lindell (FOCS '03, TCC' 04) recently showed that such a protocol is impossible to obtain under the more standard definition of polynomial-time simulation by an ideal adversary. Our construction is the first such protocol under reasonably standard cryptographic assumptions (i.e., existence of a hash function collection that is collision resistent with respect to circuits of subexponential size, and existence of trapdoor permutations which are secure with respect to circuits of quasi-polynomial size). We introduce a new technique: "protocol condensing". That is, taking a protocol that has strong security properties but requires super-polynomial communication and computation, and then transforming it into a protocol with polynomial communication and computation, that still inherits the strong security properties of the original protocol. Our result is obtained by combining this technique with previous techniques of Canetti, Lindell, Ostrovsky, and Sahai (STOC '02) and Pass (STOC '04).
The threshold degree of a Boolean function f is the minimum degree of a real polynomial p that represents f in sign: f(x) ≡ sgn p(x). In a seminal 1969 monograph, Minsky and Papert constructed a polynomial-size constant-depth {∧, ∨)-circuit in n variables with threshold degree Ω(n1/3). This bound underlies some of today's strongest results on constant-depth circuits. It has been an open problem (O'Donnell and Servedio, STOC 2003) to improve Minsky and Papert's bound to nΩ(1)+1/3.