On the secrecy gain of $\ell$-modular lattices

Esa V. Vesalainen; Anne-Maria Ernvall-Hytönen

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arXiv · 1708.09239

On the secrecy gain of $\ell$-modular lattices

Esa V. Vesalainen·Anne-Maria Ernvall-Hytönen

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Abstract

We show that for every $\ell>1$, there is a counterexample to the $\ell$-modular secrecy function conjecture by Oggier, Solé and Belfiore. These counterexamples all satisfy the modified conjecture by Ernvall-Hytönen and Sethuraman. Furthermore, we provide a method to prove or disprove the modified conjecture for any given $\ell$-modular lattice rationally equivalent to a suitable amount of copies of $\mathbb{Z}\oplus \sqrt{\ell}\,\mathbb{Z}$ with $\ell \in \{3,5,7,11,23\}$. We also provide a variant of the method for strongly $\ell$-modular lattices when $\ell\in \{6,14,15\}$.

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Esa V. Vesalainen, Anne-Maria Ernvall-Hytönen. 2017-09-11. On the secrecy gain of $\ell$-modular lattices. https://arxiv.org/abs/1708.09239

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