Lecture notes in computer science

Lattice-Based, More General Anti-leakage Model and Its Application in Decentralization

Xiaokang Dai, Jingwei Chen, Wenyuan Wu, Yong Feng

Published Jan 1, 2024• 2 citations

Publisher

DOI: 10.1007/978-981-97-5028-3_3

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Lecture notes in computer science

Lattice-Based, More General Anti-leakage Model and Its Application in Decentralization

Xiaokang Dai, Jingwei Chen, Wenyuan Wu, Yong Feng

Published Jan 1, 2024• 2 citations

Publisher

DOI: 10.1007/978-981-97-5028-3_3

Related papers

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Lecture notes in computer scienceJan 1, 20240 citations

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Springer eBooksJan 1, 202016 citations

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Abstract In the case of standard LWE samples

({\textbf {A}},{\textbf {b = sA + e}})

( A , b = sA + e ) ,

{\textbf {A}}

A is typically uniformly over

\mathbb {Z}_q^{n \times m}

Z q n × m . Under the

\textsf {DLWE}

DLWE assumption, the conditional distribution of

{\textbf {s}}|({\textbf {A}}, {\textbf {b}})

s | ( A , b ) and

{\textbf {s}}

s is expected to be consistent. However, in the case where an adversary chooses

{\textbf {A}}

A adaptively, the disparity between the two entities may be larger. In this work, our primary focus is on the quantification of the Average Conditional Min-Entropy

\tilde{H}_\infty ({\textbf {s}}|{\textbf {sA + e}})

H ~ ∞ ( s | sA + e ) of

{\textbf {s}}

s , where

{\textbf {A}}

A is chosen by the adversary. Brakerski and Döttling answered the question in one case: they proved that when

{\textbf {s}}

s is uniformly chosen from

\mathbb {Z}_q^n

Z q n , it holds that

\tilde{H}_\infty ({\textbf {s}}|{\textbf {sA + e}}) \varpropto \rho _\sigma (\varLambda _q({\textbf {A}}))

H ~ ∞ ( s | sA + e ) ∝ ρ σ ( Λ q ( A