Counterexample to the Generalized Belfiore-Solé Secrecy Function Conjecture for l-modular lattices
نویسندگان
چکیده
We show that the secrecy function conjecture that states that the maximum of the secrecy function of an l-modular lattice occurs at 1/ √ l is false, by proving that the 4-modular lattice C = Z⊕ √ 2Z⊕ 2Z fails to satisfy this conjecture. We also indicate how the secrecy function must be modified in the l-modular case to have a more reasonable chance for it to have a maximum at 1/ √ l, and show that the conjecture, modified with this new secrecy function, is true for various 2-modular lattices.
منابع مشابه
Counterexample to the $l$-modular Belfiore-Solé Conjecture
We show that the secrecy function conjecture that states that the maximum of the secrecy function of an l-modular lattice occurs at 1/ √ l is false, by proving that the 4-modular lattice C = Z⊕ √ 2Z⊕ 2Z fails to satisfy this conjecture. We also indicate how the secrecy function must be modified in the l-modular case to have a more reasonable chance for it to have a maximum at 1/ √ l, and show t...
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