The c-differential behavior of the inverse function under the EA-equivalence
Loading...
Authors
Stӑnicӑ, Pantelimon
Geary, Aaron
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
2020-05-30
Date
Publisher
ArXiv
Language
Abstract
While the classical differential uniformity (c = 1) is invariant under the CCZ-equivalence, the newly defined [9] concept of c-differential uniformity, in general is not invariant under EA or CCZ-equivalence, as was observed in [10]. In this paper, we find an intriguing behavior of the inverse function, namely, that adding some appropriate linearized monomials increases the c-differential uniformity significantly, dn for some c. For example, adding the linearized monomial x2 to x2 −2, where d is the largest nontrivial divisor of n, increases the mentioned c-differential uniformity from 2 or 3 (for c ̸= 0) to ≥ 2d + 2, which in the case of AES’ inverse function on F28 is a significant value of 18.
Type
Preprint
Description
Series/Report No
Department
Applied Mathematics (MA)
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
12 p.
Citation
Stanica, Pantelimon, and Aaron Geary. "The $ c $-differential behavior of the inverse function under the $ EA $-equivalence." arXiv preprint arXiv:2006.00355 (2020).
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.