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- W2397087910 abstract "In this paper, we show that the secrecy function conjecture that states that the maximum of the secrecy function of an $l$ -modular lattice occurs at $1/sqrt {l}$ is false, by proving that the four-modular lattice $ C^{(4)}= mathbb {Z}oplus sqrt {2} mathbb {Z}oplus 2 mathbb {Z}$ fails to satisfy this conjecture. After this, we indicate how the secrecy function must be modified in the $l$ -modular case to provide a more meaningful comparison for $l$ -modular lattices, and show that this new secrecy function indeed has a maximum at $1/sqrt {l}$ for various two-modular lattices and for $ C^{(4)}$ . We conjecture that this must hold true for all $l$ -modular lattices." @default.
- W2397087910 created "2016-06-24" @default.
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- W2397087910 date "2016-08-01" @default.
- W2397087910 modified "2023-10-09" @default.
- W2397087910 title "Counterexample to the Generalized Belfiore–Solé Secrecy Function Conjecture for <inline-formula> <tex-math notation=LaTeX>$l$ </tex-math> </inline-formula>-Modular Lattices" @default.
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- W2397087910 doi "https://doi.org/10.1109/tit.2016.2573826" @default.
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