Publication:
The c-differential uniformity and boomerang uniformity of two classes of permutation polynomials

Loading...
Thumbnail Image
Authors
Hasan, Sartaj Ul
Pal, Mohit
Stănică, Pantelimon
Subjects
Finite fields
permutation polynomials
c- differential uniformity
boomerang uniformity
perfect and almost perfect c-nonlinearity
Advisors
Date of Issue
2021
Date
Publisher
Naval Postgraduate School; Monterey, California
Language
Abstract
The Difference Distribution Table (DDT) and the differential uniformity play a major role for the design of substitution boxes in block ciphers, since they indicate the func- tion’s resistance against differential cryptanalysis. This concept was extended recently to c-DDT and c-differential uniformity, which have the potential of extending differential cryptanalysis. Recently, a new theoretical tool, the Boomerang Connectivity Table (BCT) and the corresponding boomerang uniformity were introduced to quantify the resistance of a block cipher against boomerang-style attacks. Here we concentrate on two classes (introduced recently) of permutation polynomials over finite fields of even characteristic. For one of these, which is an involution used to construct a 4-uniform permutation, we explicitly determine the c-DDT entries and BCT entries. For the second type of function, which is a differentially 4-uniform function, we give bounds for its c-differential and boomerang uniformities.
Type
Preprint
Description
The article of record as published may be found at http://dx.doi.org/10.1109/TIT.2021.3123104
Series/Report No
Department
Applied Mathematics (MA)
Other Units
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
The research of Sartaj Ul Hasan is partially supported by MATRICS grant MTR/2019/000744 from the Science and Engineering Research Board, Government of India. Pantelimon Stănică acknowledges the sabbatical support from Naval Postgraduate School from September 2020 to July 2021.
Funder
Format
14 p.
Citation
Hasan, Sartaj Ul, Mohit Pal, and Pantelimon Stănică. "The c-differential uniformity and boomerang uniformity of two classes of permutation polynomials." IEEE Transactions on Information Theory 68.1 (2021): 679-691.
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.
Collections