On the Existence of $(10, 2, 7, 488)$ Resilient Functions

Using a heuristic search combined with some algebraic techniques, several examples for 10-variable Boolean functions with nonlinearity 488, algebraic degree 7, and resiliency degree 2 , were constructed. This construction affirmatively answers the open problem about the existence of such functions.

[1]  Subhamoy Maitra,et al.  Further constructions of resilient Boolean functions with very high nonlinearity , 2002, IEEE Trans. Inf. Theory.

[2]  Palash Sarkar,et al.  Nonlinearity Bounds and Constructions of Resilient Boolean Functions , 2000, CRYPTO.

[3]  John A. Clark,et al.  Almost Boolean functions: the design of Boolean functions by spectral inversion , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[4]  Selçuk Kavut,et al.  Search for Boolean Functions With Excellent Profiles in the Rotation Symmetric Class , 2007, IEEE Transactions on Information Theory.

[5]  Amr M. Youssef,et al.  On the existence of (9,3,5,240) resilient functions , 2006, IEEE Transactions on Information Theory.

[6]  Eric Filiol,et al.  Highly Nonlinear Balanced Boolean Functions with a Good Correlation-Immunity , 1998, EUROCRYPT.

[7]  Josef Pieprzyk,et al.  Rotation-Symmetric Functions and Fast Hashing , 1998, J. Univers. Comput. Sci..

[8]  James L. Massey,et al.  A spectral characterization of correlation-immune combining functions , 1988, IEEE Trans. Inf. Theory.

[9]  Josef Pieprzyk,et al.  Fast Hashing and Rotation-Symmetric Functions , 1999 .

[10]  Pantelimon Stanica,et al.  A constructive count of rotation symmetric functions , 2003, Inf. Process. Lett..

[11]  Palash Sarkar,et al.  Construction of nonlinear resilient Boolean functions using "small" affine functions , 2004, IEEE Transactions on Information Theory.

[12]  John A. Clark,et al.  Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion , 2004, Comput. Intell..