Image cipher applications using the elliptical curve and chaos

• Autorzy: Silva-García Víctor Manuel , Flores-Carapia Rolando , Rentería-Márquez Carlos , Luna-Benoso Bejamín , Chimal-Eguía Juan Carlos

Identyfikatory

DOI

10.34768/amcs-2020-0029

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

elliptic curve; chaos; discrete Fourier transform; image ciphering

PL

krzywa eliptyczna; chaos; dyskretna transformata Fouriera

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 2
• Strony: 377--391
• Opis fizyczny: Bibliogr. 42 poz., rys., tab.

Twórcy

autor

Silva-García Víctor Manuel

• Center for Innovation and Technological Development, National Polytechnic Institute (IPN), Av. Juan de Dios Bátiz S/N, Nueva Industrial Vallejo, 07738 Gustavo A. Madero, Ciudad de México, Mexico

autor

Flores-Carapia Rolando

• Center for Innovation and Technological Development, National Polytechnic Institute (IPN), Av. Juan de Dios Bátiz S/N, Nueva Industrial Vallejo, 07738 Gustavo A. Madero, Ciudad de México, Mexico

autor

Rentería-Márquez Carlos

• Higher School of Physics and Mathematics, National Polytechnic Institute (IPN), Building 9, Av Instituto Politécnico Nacional, San Pedro Zacatenco, Nueva Industrial Vallejo, 07738 Gustavo A. Madero, Ciudad de M´exico, Mexico

autor

Luna-Benoso Bejamín

• Higher School of Computing, National Polytechnic Institute (IPN), Av. Juan de Dios Bátiz S/N, Nueva Industrial Vallejo, 07738 Ciudad de México, Mexico

autor

Chimal-Eguía Juan Carlos

• Computation Research Center, National Polytechnic Institute (IPN), Av. Juan de Dios Bátiz Esq. Miguel Othón de Mendizábal S/N, Nueva Industrial Vallejo, 07738 Gustavo A. Madero, Ciudad de México, Mexico

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).