Abstract
The family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on \(\mathbb{Z}_{2}^{n}\) by the support of a bent function is a strongly regular graph \(srg(v,k,\lambda,\mu)\), with \(\lambda=\mu\). In this note we list the parameters of such Cayley graphs. Moreover, it is given a condition on \((n,m)\)-bent functions \(F=(f_1,\ldots,f_m)\), involving the support of their components \(f_i\), and their \(n\)-ary symmetric differences.
Reference9 articles.
1. A. J. Menezes, P. van Oorschot, S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997.
2. M. Matsui, Linear cryptanalysis method for DES cypher, EUROCRYPT93, LNCS 765, Springer, 1994, pp. 386-397.
3. E. Biham, A. Shamir, Differential cryptanalysis of DES-like cryptosystems, Journal of Cryptology, 1991, 4, pp. 3-72.
4. A. Bernasconi, B. Codenotti, Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem, IEEE Transactions on Computers, 1999, 48(3), pp. 345-351.
5. A. Bernasconi, B. Codenotti, J. M. VanderKam, A Characterization of Bent Functions in terms of Strongly Regular Graphs, IEEE Transactions on Computers, 2001, 50(9), pp. 984-985.