Core Concepts
The author explores the relationship between bent functions and strongly regular graphs, highlighting their significance in cryptography.
Abstract
The content delves into the connection between bent functions and strongly regular graphs in the realm of cryptography. Bent functions, known for their importance in encryption, are discussed alongside Cayley graphs defined by these functions. The article provides insights into the parameters of such Cayley graphs and sheds light on (n, m)-bent functions. It also touches upon the concept of linear cryptanalysis techniques and the quest for non-linear functions to enhance security against attacks. Moreover, it explores how bent functions are characterized in terms of strongly regular graphs, emphasizing their unique properties. The discussion extends to vectorial bent functions and symmetric differences, offering a comprehensive view of these cryptographic elements. Additionally, the article presents examples of strongly regular graphs defined by bent functions across different dimensions, showcasing their diverse parameters.
Stats
The i-th eigenvalue λi of the Cayley graph is given by λi = X x∈Zn 2 (-1)Trn 1 (b(i)x)f(x) = 2nf ∗(b(i)).
The largest spectral coefficient is λ0 = 2nf ∗(b(0)) = |Ωf| with multiplicity 2n-dim⟨Ωf⟩.
If Gf is connected, f has a spectral coefficient equal to -λ0 if and only if its Walsh spectrum is symmetric with respect to 0.