On the Secrecy Gain of $\ell$-Modular Lattices

DOI10.1137/17M1154187zbMath1447.11077arXiv1708.09239MaRDI QIDQ4569569

Esa V. Vesalainen, Anne-Maria Ernvall-Hytönen

Publication date: 25 June 2018

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09239

zbMATH Keywords

latticestheta-functionssecrecy gain\(\ell\)-modular lattices\(\vartheta\)-functionssecrecy function conjecture

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Dedekind eta function, Dedekind sums (11F20) Authentication, digital signatures and secret sharing (94A62) Relations with coding theory (11H71)

Related Items (3)

Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies ⋮ Extremal determinants of Laplace-Beltrami operators for rectangular tori ⋮ On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of \(\vartheta_{4}\)

Cites Work

• Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions
• 2- and 3-modular lattice wiretap codes in small dimensions
• The shadow theory of modular and unimodular lattices
• Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis
• Counterexample to the Generalized Belfiore–Solé Secrecy Function Conjecture for <inline-formula> <tex-math notation="LaTeX">$l$ </tex-math> </inline-formula>-Modular Lattices
• A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions
• On a Conjecture by Belfiore and Solé on Some Lattices
• The Wire-Tap Channel

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