Characters, Weil sums and c-differential uniformity with an application to the perturbed Gold function
Loading...
Authors
Stănică, Pantelimon
Riera, Constanza
Tkachenko, Anton
Subjects
Boolean and p-ary functions
c-differentials
differential uniformity
perfect and almost perfect c-nonlinearity
perturbations
c-differentials
differential uniformity
perfect and almost perfect c-nonlinearity
perturbations
Advisors
Date of Issue
2020-09-17
Date
September 17, 2020
Publisher
ArXiv
Language
Abstract
Building upon the observation that the newly defined [12] concept of c-differential uniformity is not invariant under EA or CCZ-equivalence [13], we showed in [22] that adding some appropriate linearized monomials increases the c-differential uniformity of the inverse
function, significantly, for some c. We continue that investigation here.
First, by analyzing the involved equations, we find bounds for the uniformity of the Gold function perturbed by a single monomial, exhibiting the discrepancy we previously observed on the inverse function.
Secondly, to treat the general case of perturbations via any linearized
polynomial, we use characters in the finite field to express all entries
in the c-Differential Distribution Table (DDT) of an (n, n)-function on
the finite field Fpn , and further, we use that method to find explicit
expressions for all entries of the c-DDT of the perturbed Gold function
(via an arbitrary linearized polynomial).
Type
Preprint
Description
Series/Report No
Department
Applied Mathematics
Computer Science (CS)
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
22 p.
Citation
Stănică, Pantelimon, Constanza Riera, and Anton Tkachenko. "Characters, Weil sums and c-differential uniformity with an application to the perturbed Gold function." Cryptography and Communications (2021): 1-17.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.