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
Identifiers
NPS Report Number
Sponsors
Funding
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.