2014/09/10 by Anne-Maria Ernvall-Hytönen, Ernvall-Hytönen, Anne-Maria, B. A. Sethuraman +1
Computer Science · #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #Cryptography and Data Security #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1409.3188
openalex publication_date 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^(4) = ℤ ⊕ √(2)ℤ ⊕ 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 odd 2-modular lattices.