Paper 2018/1159
Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions
Sihem Mesnager, Kwang Ho Kim, and Myong Song Jo
Abstract
To determine the dimension of null space of any given linearized
polynomial is one of vital problems in finite field theory, with
concern to design of modern symmetric cryptosystems. But, the known
general theory for this task is much far from giving the exact
dimension when applied to a specific linearized polynomial. The
first contribution of this paper is to give a better general method
to get more precise upper bound on the root number of any given
linearized polynomial. We anticipate this result would be applied as
a useful tool in many research branches of finite field and
cryptography. Really we apply this result to get tighter estimations
of the lower bounds on the second order nonlinearities of general
cubic Boolean functions, which has been being an active research
problem during the past decade, with many examples showing great
improvements. Furthermore, this paper shows that by studying the
distribution of radicals of derivatives of a given Boolean functions
one can get a better lower bound of the second-order nonlinearity,
through an example of the monomial Boolean function
Note: The list of references was not compiled.
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean FunctionsNonlinearityLinearized PolynomialRoot Number
- Contact author(s)
- smesnager @ univ-paris8 fr
- History
- 2018-12-04: last of 2 revisions
- 2018-12-03: received
- See all versions
- Short URL
- https://ia.cr/2018/1159
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2018/1159, author = {Sihem Mesnager and Kwang Ho Kim and Myong Song Jo}, title = {Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions}, howpublished = {Cryptology {ePrint} Archive, Paper 2018/1159}, year = {2018}, url = {https://eprint.iacr.org/2018/1159} }