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The Differential Spectrum of the Power Mapping x p n −3.
- Source :
-
IEEE Transactions on Information Theory . Aug2022, Vol. 68 Issue 8, p5535-5547. 13p. - Publication Year :
- 2022
-
Abstract
- Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^{n}-3}$ over ${\mathbb {F}}_{p^{n}}$ has desirable differential properties, and its differential spectra for $p=2,\,3$ have been determined. In this paper, for any odd prime $p$ , by investigating certain quadratic character sums and some equations over ${\mathbb {F}}_{p^{n}}$ , we determine the differential spectrum of $x^{p^{n}-3}$ with a unified approach. The obtained result shows that for any given odd prime $p$ , the differential spectrum can be expressed explicitly in terms of $n$. Compared with previous results, a special elliptic curve over ${\mathbb {F}}_{p}$ plays an important role in our computation for the general case $p \ge 5$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POWER spectra
*ELLIPTIC curves
*INTEGERS
*WIRELESS communications
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157958016
- Full Text :
- https://doi.org/10.1109/TIT.2022.3162334