New chaotic system: M-map and its application in chaos-based cryptography
Authors:
- Marcin Lawnik,
- Marek Berezowski
Abstract
One of the applications of dynamical systems with chaotic behavior is data encryption. Chaos-based cryptography uses chaotic dynamical systems as the basis for creating algorithms. The present article discusses a new dynamical system called M-map with its analysis: fixed points, bifurcation diagram, Lyapunov exponent, and invariant density. The obtained bifurcation diagram and the plot of the Lyapunov exponent (with a minimum value of ln2 and a maximum value of ln4) suggest that the so-called robust chaos characterizes this map. Moreover, the obtained results are compared with other dynamical systems used in cryptography. Additionally, the article proposes a new image encryption algorithm. It uses, among others, cyclically shifted S-box or saving encrypted pixels on the first or last free space in the cipher-image. The conducted analysis shows that the cipher-images are characterized by an entropy value close to 8, a correlation of adjacent pixels value close to 0, or values of Number of Pixel of Change Rate (NPCR) and Unified Average Changing Intensity (UACI) measures close to 100% and 33%, respectively.
- Record ID
- CUTe0523caafee64578abb49e86b0870fe4
- Publication categories
- ;
- Author
- Journal series
- Symmetry, ISSN , e-ISSN 2073-8994, Monthly
- Issue year
- 2022
- Vol
- 14
- No
- 5
- Pages
- [1-18]
- Article number
- 895
- Other elements of collation
- fot.; rys.; schem.; tab.; wykr.; Bibliografia (na s.) - 16-18; Bibliografia (liczba pozycji) - 48; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 14, Iss. 5, Spec. Iss.
- Substantive notes
- Special Issue: Nonlinear Symmetric Systems and Chaotic Systems in Engineering
- Keywords in English
- discrete dynamical system, logistic map, tent map, sine map, chaos, Lyapunov exponent, image encryption
- ASJC Classification
- ; ; ;
- DOI
- DOI:10.3390/sym14050895 Opening in a new tab
- URL
- https://www.mdpi.com/2073-8994/14/5/895 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 70
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTe0523caafee64578abb49e86b0870fe4/
- URN
urn:pkr-prod:CUTe0523caafee64578abb49e86b0870fe4
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.