<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to generate 15 keys to encrypt images where each key is the image size. These keys are calculated using an elliptic curve with a constant zero value. The proposed curve is non-singular, non-supersingular, nor trace one. Chaos is employed to find a generating element in a cyclic subgroup and it is produced using the logistic map equation. In addition, a 16 × 16 substitution box is constructed using both chaos and an algorithm that defines a bijective function. The following tools are used in order to measure the degree of randomness of the encrypted figures: entropy, correlation, the discrete Fourier transform and a goodness-of-fit test with the chi-square distribution. Furthermore, an image size variable permutation is applied in the first round, and its inverse in the fourteenth.</p></abstract>

A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to generate 15 keys to encrypt images where each key is the image size. These keys are calculated using an elliptic curve with a constant zero value. The proposed curve is non-singular, non-supersingular, nor trace one. Chaos is employed to find a generating element in a cyclic subgroup and it is produced using the logistic map equation. In addition, a 16 × 16 substitution box is constructed using both chaos and an algorithm that defines a bijective function. The following tools are used in order to measure the degree of randomness of the encrypted figures: entropy, correlation, the discrete Fourier transform and a goodness-of-fit test with the chi-square distribution. Furthermore, an image size variable permutation is applied in the first round, and its inverse in the fourteenth.

Image cipher applications using the elliptical curve and chaos

Higher School of Computing, National Polytechnic Institute (IPN)

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Image cipher applications using the elliptical curve and chaos"}

A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to...

Image cipher applications using the elliptical curve and chaos

Published Online: Jul 04, 2020

Page range: 377 - 391

Received: Sep 10, 2018

Accepted: Nov 06, 2019

DOI: https://doi.org/10.34768/amcs-2020-0029

Keywords
elliptic curve, chaos, entropy, discrete Fourier transform, image ciphering

© 2020 Víctor Manuel Silva-García et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Image cipher applications using the elliptical curve and chaos

Published Online: Jul 04, 2020

Page range: 377 - 391

Received: Sep 10, 2018

Accepted: Nov 06, 2019

DOI: https://doi.org/10.34768/amcs-2020-0029

Keywordselliptic curve, chaos, entropy, discrete Fourier transform, image ciphering

© 2020 Víctor Manuel Silva-García et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
elliptic curve, chaos, entropy, discrete Fourier transform, image ciphering