Belfiore–Solé secrecy function conjecture for formally unimodular lattices

Let Λ\Lambda be a formally unimodular lattice, and let ΞΛ(τ)\Xi_{\Lambda}(\tau) denote its secrecy function and ξΛ\xi_{\Lambda} its maximum value. Belfiore–Solé secrecy function conjecture. The secrecy function achieves its maximum at τ=1\tau=1, i.e.,

ξΛ=ΞΛ(1).\xi_{\Lambda}=\Xi_{\Lambda}(1).

This conjecture concerns the weak secrecy symmetry point of formally unimodular lattices and is the lattice version of the secrecy gain conjecture introduced by Belfiore and Solé.

Sources & referencesView supporting material

Primary source

Maiara F. Bollauf, Hsuan-Yin Lin and Øyvind Ytrehus, “Formally Unimodular Packings for the Gaussian Wiretap Channel”, arXiv:2206.14171 (2023).

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