Degree optimized resilient Boolean functions from
INRIA, projet CODES
78153 Le Chesnay Cedex, France
To appear in the Proceedings of "IMA conference of
Coding and Cryptography", Cirencester, England, December 2003.
In this paper we present a construction method of degree optimized
resilient Boolean functions with very high nonlinearity.
We present a general construction method valid for any
n greater than 4 and for order of
resiliency less than or equal to n-3.
The construction is based on the
modification of the famous Marioana-McFarland class in a controlled
manner such that the resulting functions will contain some extra terms
of high algebraic degree in its ANF including one term of highest
algebraic degree. Hence, the linear complexity is increased, the
functions obtained reach the Siegentheler's bound
and furthermore the nonlinearity of such a function
in many cases is superior to all previously known
construction methods. This construction method is then
generalized to the case of vectorial resilient functions,
that is for mappings with n input and m output.
This provides functions of very
high algebraic degree almost reaching the Siegenthaler's upper bound.
Boolean Function, Resiliency, Nonlinearity, Algebraic