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Paper details

Number 2 - June 2020

Volume 30 - 2020

**Image cipher applications using the elliptical curve and chaos**

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

**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.

**Keywords**

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