Abstract
In this study, a well-known chaotic
transformation namely Arnold’s CAT map is used to extend 2-dimensional mapping
to a higher dimension. This extension is achieved by means of the planar
extension and Multinacci series. The demonstration of a 3-dimensional Arnold’s
CAT map is performed by RGB component substitution of a colored image. For this
purpose, the colored image is converted from a standard RGB space into an
intensity-hue-saturation (IHS) space. Consequently, both Chebyshev and Hadamard
map is employed for encryption of the intensity component. Besides, CAT map is
engaged to encrypt the hue and saturation components. According to the results,
the proposed method has a great potential to be an efficient tool for data
encryption.
References
- Reference1. Masuda N. and Aihara K., "Cryptosystems with discretized chaotic maps," IEEE Trans. on Circuits and Systems - I: Fundamental Theory and Applications, 2002, vol. 49, no. 1, page(s): 28-40. DOI: 10.1109/81.974872.Reference2. V. Arnold and A. Avez, "Ergodic Problems of Classical Mechanics," Benjamin, 1968. DOI:10.1002/zamm.19700500721.Reference3. F. Svanstrom, "Properties of a generalized Arnold’s discrete cat map," 2014.Reference4. R.L. Devaney, "An Introduction to Chaotic Dynamical Systems," Second Edition, Addison-Wesley, 1987. DOI: 10.1063/1.2820117.Reference5. Brugia O., Filipponi P., Mazzarella F., "Applications of Fibonacci Numbers," Springer, 1991. DOI: 10.1007/978-94-011-3586-3-7.Reference6. J. Rosen, Z. Scherr, B. Weiss, and M. E. Zieve, "Chebyshev mappings of finite fields," Amer. Math. Monthly, 119(2):151-155, 2012.Reference7. K. J. Horadam, "Hadamard Matrices and Their Applications," Princeton University Press, ISBN: 9780691119212, 2007.Reference8. S. S. Agaian, "Hadamard Matrices and Their Applications," Springer, ISBN: 978-3-540-16056-4. DOI: 10.1007/BFb0101073, 1985.Reference9. Q. Guo, Z. Liu, S. Liu, "Color image encryption by using Arnold and discrete fractional random transforms in IHS space," Optics and Lasers in Engineering, 48,1174–1181, 2010.Reference10. R.C. Gonzalez, R.E.Woods, "Digital Image Processing," Second Edition, ISBN:0-201-11026-1, 1987.
Abstract
Bu çalışmada, 2 boyutlu dönüşümü daha yüksek bir
boyuta genişletmek için Arnold’ın CAT dönüşümü olarak bilinen kaotik
bir dönüşüm kullanılmıştır. Bu boyut artırma
işlemi düzlemsel genişleme ve Multinacci serisi ile elde
edilir. 3 boyutlu bir Arnold’ın CAT dönüşümünün gösterimi, renkli bir
görüntünün RGB bileşen değişimi ile gerçekleştirilir. Bu amaçla, renkli görüntü
standart bir RGB uzayından yoğunluk-ton-doygunluk (IHS) aralığına
dönüştürülür. Sonuç olarak, hem Chebyshev hem de Hadamard dönüşümü, yoğunluk
bileşeninin şifrelenmesi için kullanılmaktadır. Ayrıca, ton haritası ve
doygunluk bileşenlerini şifrelemek için CAT
dönüşümü kullanılmıştır. Elde edilen sonuçlara göre, önerilen
yöntem veri şifreleme için etkin bir yöntem olma potansiyeline sahiptir.
References
- Reference1. Masuda N. and Aihara K., "Cryptosystems with discretized chaotic maps," IEEE Trans. on Circuits and Systems - I: Fundamental Theory and Applications, 2002, vol. 49, no. 1, page(s): 28-40. DOI: 10.1109/81.974872.Reference2. V. Arnold and A. Avez, "Ergodic Problems of Classical Mechanics," Benjamin, 1968. DOI:10.1002/zamm.19700500721.Reference3. F. Svanstrom, "Properties of a generalized Arnold’s discrete cat map," 2014.Reference4. R.L. Devaney, "An Introduction to Chaotic Dynamical Systems," Second Edition, Addison-Wesley, 1987. DOI: 10.1063/1.2820117.Reference5. Brugia O., Filipponi P., Mazzarella F., "Applications of Fibonacci Numbers," Springer, 1991. DOI: 10.1007/978-94-011-3586-3-7.Reference6. J. Rosen, Z. Scherr, B. Weiss, and M. E. Zieve, "Chebyshev mappings of finite fields," Amer. Math. Monthly, 119(2):151-155, 2012.Reference7. K. J. Horadam, "Hadamard Matrices and Their Applications," Princeton University Press, ISBN: 9780691119212, 2007.Reference8. S. S. Agaian, "Hadamard Matrices and Their Applications," Springer, ISBN: 978-3-540-16056-4. DOI: 10.1007/BFb0101073, 1985.Reference9. Q. Guo, Z. Liu, S. Liu, "Color image encryption by using Arnold and discrete fractional random transforms in IHS space," Optics and Lasers in Engineering, 48,1174–1181, 2010.Reference10. R.C. Gonzalez, R.E.Woods, "Digital Image Processing," Second Edition, ISBN:0-201-11026-1, 1987.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | August 31, 2019 |
| Published in Issue | Year 2019 |