Welcome to the resource topic for 2004/276
Title:
Improving the algebraic immunity of resilient and nonlinear functions and constructing bent functions
Authors: C. Carlet
Abstract:The currently known constructions of Boolean functions with
high nonlinearities, high algebraic degrees and high resiliency
orders do not seem to permit achieving
sufficiently high algebraic
immunities.
We introduce a construction of Boolean functions, which builds a new function from three
known ones. Assuming that the three functions have some
resiliency order, nonlinearity and algebraic degree, as well as their sum modulo 2, the constructed function
has the same resiliency order and can have the same nonlinearity, but
has potentially better
algebraic degree and algebraic immunity. The set of classical constructions together
with this new one (and with a simpler derived one, having the same advantages) permit now to obtain functions achieving all necessary criteria
for being used in the pseudo-random generators in stream ciphers.\
We also apply this construction to obtain bent functions from known ones.
ePrint: https://eprint.iacr.org/2004/276
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