International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Thomas Holenstein

Publications

Year
Venue
Title
2019
JOFC
The Communication Complexity of Private Simultaneous Messages, Revisited
Private simultaneous message (PSM) protocols were introduced by Feige, Kilian, and Naor (STOC ’94) as a minimal non-interactive model for information theoretic three-party secure computation. While it is known that every function $$f:\{0,1\}^k\times \{0,1\}^k \rightarrow \{0,1\}$$ f : { 0 , 1 } k × { 0 , 1 } k → { 0 , 1 } admits a PSM protocol with exponential communication of $$2^{k/2}$$ 2 k / 2 (Beimel et al., TCC ’14), the best known (non-explicit) lower-bound is $$3k-O(1)$$ 3 k - O ( 1 ) bits. To prove this lower-bound, FKN identified a set of simple requirements, showed that any function that satisfies these requirements is subject to the $$3k-O(1)$$ 3 k - O ( 1 ) lower-bound, and proved that a random function is likely to satisfy the requirements. We revisit the FKN lower-bound and prove the following results: (Counterexample) We construct a function that satisfies the FKN requirements but has a PSM protocol with communication of $$2k+O(1)$$ 2 k + O ( 1 ) bits, revealing a gap in the FKN proof. (PSM lower-bounds) We show that by imposing additional requirements, the FKN argument can be fixed leading to a $$3k-O(\log k)$$ 3 k - O ( log k ) lower-bound for a random function. We also get a similar lower-bound for a function that can be computed by a polynomial-size circuit (or even polynomial-time Turing machine under standard complexity-theoretic assumptions). This yields the first non-trivial lower-bound for an explicit Boolean function partially resolving an open problem of Data, Prabhakaran, and Prabhakaran (Crypto ’14, IEEE Information Theory ’16). We further extend these results to the setting of imperfect PSM protocols which may have small correctness or privacy error. (CDS lower-bounds) We show that the original FKN argument applies (as is) to some weak form of PSM protocols which are strongly related to the setting of Conditional Disclosure of Secrets (CDS). This connection yields a simple combinatorial criterion for establishing linear $$\varOmega (k)$$ Ω ( k ) -bit CDS lower-bounds. As a corollary, we settle the complexity of the inner-product predicate resolving an open problem of Gay, Kerenidis, and Wee (Crypto ’15).
2018
EUROCRYPT
2016
JOFC
2013
TCC
2011
TCC
2010
EUROCRYPT
2009
TCC
2006
TCC
2005
CRYPTO
2004
CRYPTO
2004
EUROCRYPT
2003
EUROCRYPT

Program Committees

TCC 2015
Crypto 2014
TCC 2013
Crypto 2010
TCC 2009