TY - JOUR
T1 - Image Cipher Applications Using the Elliptical Curve and Chaos
AU - Silva-Garciá, Víctor Manuel
AU - Flores-Carapia, Rolando
AU - Rquez, Carlos Renteriá Má
AU - Luna-Benoso, Bejamín
AU - Chimal-Eguiá, Juan Carlos
N1 - Publisher Copyright:
© 2020 Víctor Manuel Silva-Garciá et al., published by Sciendo 2020.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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.
AB - 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.
KW - chaos
KW - discrete Fourier transform
KW - elliptic curve
KW - entropy
KW - image ciphering
UR - http://www.scopus.com/inward/record.url?scp=85090298325&partnerID=8YFLogxK
U2 - 10.34768/amcs-2020-0029
DO - 10.34768/amcs-2020-0029
M3 - Artículo
AN - SCOPUS:85090298325
SN - 1641-876X
VL - 30
SP - 377
EP - 391
JO - International Journal of Applied Mathematics and Computer Science
JF - International Journal of Applied Mathematics and Computer Science
IS - 2
ER -