Counterexample to the Generalized Belfiore–Solé Secrecy Function Conjecture for -Modular Lattices

摘要

In this paper, we show that the secrecy function conjecture that states that the maximum of the secrecy function of an -modular lattice occurs at is false, by proving that the four-modular lattice fails to satisfy this conjecture. After this, we indicate how the secrecy function must be modified in the -modular case to provide a more meaningful comparison for -modular lattices, and show that this new secrecy function indeed has a maximum at for various two-modular lattices and for . We conjecture that this must hold true for all -modular lattices.