On Computational Shortcuts for Information-Theoretic PIR

Hong, Matthew M.; Ishai, Yuval; Kolobov, Victor I.; Lai, Russell W. F.

doi:10.1007/978-3-030-64375-1_18

Cited by 3 publications

(2 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As far as we know, there is no research on how we improve a protocol in domain-restricted setting in the literature of general secure computation. On the other hand, in the literature of private information retrieval (PIR) [13], Hong et al [14] showed that the computation cost can be reduced when a database has a structure, that is, the domain of a database is restricted.…”

Section: Restriction Of Domainmentioning

confidence: 99%

Correlated Randomness Reduction in Domain-Restricted Secure Two-Party Computation

HIWATASHI,

NUIDA

2024

IEICE Trans. Fundamentals

View full text Add to dashboard Cite

Secure two-party computation is a cryptographic tool that enables two parties to compute a function jointly without revealing their inputs. It is known that any function can be realized in the correlated randomness (CR) model, where a trusted dealer distributes input-independent CR to the parties beforehand. Sometimes we can construct more efficient secure two-party protocol for a function g than that for a function f , where g is a restriction of f . However, it is not known in which case we can construct more efficient protocol for domain-restricted function. In this paper, we focus on the size of CR. We prove that we can construct more efficient protocol for a domain-restricted function when there is a "good" structure in CR space of a protocol for the original function, and show a unified way to construct a more efficient protocol in such case. In addition, we show two applications of the above result: The first application shows that some known techniques of reducing CR size for domain-restricted function can be derived in a unified way, and the second application shows that we can construct more efficient protocol than an existing one using our result.

show abstract

Section: Restriction Of Domainmentioning

confidence: 99%

Correlated Randomness Reduction in Domain-Restricted Secure Two-Party Computation

HIWATASHI,

NUIDA

2024

IEICE Trans. Fundamentals

View full text Add to dashboard Cite

show abstract

“…Extremal set theory deals with determining the size of set-systems that satisfy certain restrictions. It is one of the most rapidly developing areas in combinatorics, with applications in various other branches of mathematics and theoretical computer science, including functional analysis, probability theory, circuit complexity, cryptography, coding theory, probabilistic methods, discrete geometry, linear algebra, spectral graph theory, ergodic theory, and harmonic analysis [38,39,107,106,112,319,196,278,276,255,45,307,297,132,149,160]. For more details on extremal set theory, we refer the reader to the book by Gerbner and Patkos [139]; for probabilistic arguments/proofs, see the books by Bollobás [52] and Spencer [284].…”

Section: Maximally Cover-free At Most T-intersecting K-uniform Familiesmentioning

confidence: 99%

Star-specific Key-homomorphic PRFs from Linear Regression and Extremal Set Theory

Sehrawat¹,

Yeo²,

Vassilyev³

2022

Preprint

View full text Add to dashboard Cite

We introduce a novel method to derandomize the learning with errors (LWE) problem by generating deterministic yet sufficiently independent LWE instances, that are constructed via special linear regression models. We also introduce star-specific key-homomorphic (SSKH) pseudorandom functions (PRFs), which are defined by the respective sets of parties that construct them. We use our derandomized variant of LWE to construct a SSKH PRF family. The sets of parties constructing SSKH PRFs are arranged as star graphs with possibly shared vertices, i.e., some pair of sets have non-empty intersections. We reduce the security of our SSKH PRF family to the hardness of LWE. To establish the maximum number of SSKH PRFs that can be constructed -by a set of parties -in the presence of passive/active and external/internal adversaries, we prove several bounds on the size of maximally cover-free at most t-intersecting k-uniform family of sets H, where the three properties are defined as:For the same purpose, we define and compute the mutual information between different linear regression hypotheses that are generated via overlapping training datasets.

show abstract