Low c-differential and c-boomerang uniformity of the swapped inverse function
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Authors
Stӑnicӑ, Pantelimon
Subjects
Finite field equations
c-boomerang uniformity
c-differential uniformity
Vectorial Boolean functions
c-boomerang uniformity
c-differential uniformity
Vectorial Boolean functions
Advisors
Date of Issue
2021
Date
Publisher
Elsevier
Language
Abstract
Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a 4-differential uniform permutation function. Recently, in [21] it was shown that this swapped version of the inverse function has boomerang uniformity exactly 10, if n ≡ 0 (mod 6), 8, if n ≡ 3 (mod 6), and 6, if n ≡ 0 (mod 3). Based upon the c-differential and c-boomerang uniformity notions we defined in [16], respectively, [30], in this paper we characterize the c-differential and c-boomerang uniformity for the (0, 1)- swapped inverse function in even characteristic, x2n−2 + x2n−1 + (x + 1)2n−1 on F2n : we show that for all c = 1, the c-differential uniformity is upper bounded by 4 and the c-boomerang uniformity by 5 with both bounds being attained for n ≥ 4
Type
Article
Description
17 USC 105 interim-entered record; under temporary embargo.
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
U.S. Government affiliation is unstated in article text.
Format
13 p.
Citation
Stănică, Pantelimon. "Low c-differential and c-boomerang uniformity of the swapped inverse function." Discrete Mathematics 344.10 (2021): 112543.