# RSA ALGORITHM IN FRACTIONAL-RATIONAL N-ARY FORMS WHILE ENCRYPTION-DECRYPTION OF MONOCHROME IMAGES

2022;
: pp.11-15
1
Національний університет "Львівська політехніка", кафедра інформаційних технологій видавничої справи
2
Lviv Polytechnic National University
3
Національний університет «Львівська політехніка»

The basis for image protection is the assumption that the image is a stochastic signal. But the image is a specific signal that possesses, in addition to typical informativeness (informativeness of data), also visual informativeness, which brings new challenges to the issue of protection. Therefore, the urgent task is to implement such application of the RSA algorithm that when encrypting an image: – the cryptographic stability of the RSA algorithm did not deteriorate; – achieves full image noise to prevent the use of visual image processing methods. An algorithm for encryption-decryption of monochrome images in fractional-rational forms of order n using the elements of the RSA algorithm is proposed, as the most resistant to unauthorized decryption of signals. The proposed algorithm is applied to images with strictly separated contours. Elements of the RSA algorithm are applied to construct the coefficients of fractional-rational affine transformations. The developed algorithm is inherent in the higher cryptographic stability compared to the ordinary RSA algorithm. The possibilities of using the elements of the RSA algorithm in affine transformations while encrypting and decrypting images are described. The results of encryption modeling for cryptographic transformations of monochrome images of a given dimension are given. Modified models and algorithmic procedures of key formation processes, direct and inverse cryptographic transformations, reduced to mathematical element-by-element operations, have been developed.

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[4] Tsmots I., Riznyk O., Rabyk V., Kynash Y., Kustra N., Logoida M. (2020) Implementation of FPGA-Based Barker's-Like Codes. In: Lytvynenko V., Babichev S., Wójcik W., Vynokurova O., Vyshemyrskaya S., Radetskaya S. (eds) "Lecture Notes in Computational Intelligence and Decision Making". ISDMCI 2019. Advances in Intelligent Systems and Computing, vol 1020. Springer, Cham. doi: 10.1007/978-3-030-26474-1_15.
https://doi.org/10.1007/978-3-030-26474-1_15
[5] Rafael C. Gonzalez, Richard E. Woods, "Digital Image Processing", published by Prentice Hall Upper Saddle River, New Jersey, 07456, http://sdeuoc.ac.in /sites/default /files/sde_videos.pdf
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https://doi.org/10.23939/istcmtm2020.04.025
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https://doi.org/10.1016/j.procs.2019.11.059
[8] B. Girod "The information theoretical significance of spatial and temporal masking in video signals", Proc. of the SPIE Symposium on Electronic Imaging.1989.-Vol. 1077.- P.178-187, https://typeset.io/papers/the-informationtheoretical-significance-of-spa....
[9] Majid Rabbani, Rajan Joshi. "An overview of the JPEG2000 still image compression standard", Eastman Kodak Company, Rochester, NY 14650, USA, Signal Processing: Image Communication. - 2002. - Vol. 17. - P. 3-48, https://scirp.org/reference/referencespapers.aspx?referenceid =727652
https://doi.org/10.1016/S0923-5965(01)00024-8
[10] S. X. Liao and M. Pawlak On image analysis by moments, IEEE Transaction on Pattern Analysis and Machine Intelligence. - 1996. - 18, No 3. - P. 254-266, https://ieeexplore.ieee.org/document/485554
https://doi.org/10.1109/34.485554
[11] E.M. Haacke, R.W. Brown, M.R. Thompson and R. Venkatesan. Magnetic Resonance Imagin: Physical Principles and Sequence Design. John Wiley & Sons, New York, 1999, https://www.wiley.com/ensg/Magnetic+ Resonance+Imaging:+Physical+Principles+and+Sequence +Design,+2nd+Edition-p-9780471720850
[12] J.T. Kajiya. The rendering equation. Computer Graphics, 20: 143-150, 1986, https://dl.acm.org/doi/10.1145/ 15886.15902
https://doi.org/10.1145/15886.15902
[13] M. Sarfraz. Introductory Chapter: On Digital Image Processing. 2020, DOI: 10.5772 intechopen.92060, https://www.intechopen.com/chapters/71817
https://doi.org/10.5772/intechopen.92060
[14] Ehsan Samei, Donald J Peck, Projection X‐ray Imaging, Hendee's Physics of Medical Imaging, 10.1002 9781118671016, (217-242), (2019), https://onlinelibrary. wiley.com/doi/10.1002/9781118671016.ch6
https://doi.org/10.1002/9781118671016.ch6
[15] Michael Vollmer, Klaus‐Peter Mollmann, Fundamentals of Infrared Thermal Imaging, Infrared Thermal Imaging, 10.1002 9783527693306, (1-106), (2017), https://www. wiley.com/enus/Infrared+Thermal+Imaging:+Fundamenta ls,+Research+and+Applications,+2nd+Edition-p9783527413515
https://doi.org/10.1002/9783527693306.ch1
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https://doi.org/10.1109/ICISCT.2017.8188589
[17] Wagh, D. P., Fadewar, H. S., & Shinde, G. N. (2020). Biometric Finger Vein Recognition Methods for Authentication. In Computing in Engineering and Technology, pp. 45-53. DOI: 10.1007/978-981-32-9515-5_5.
https://doi.org/10.1007/978-981-32-9515-5_5