Image encryption based on chaos, elliptic curve, dynamic S-boxes and variable permutations

Abstract

The proposed algorithm called Image encryption based on chaos, elliptic curve, dynamic S-boxes and variable permutations (IECC) is a symmetric cryptosystem for encrypting bmp images, in this case 512 × 512 pixel figures are used for testing. This algorithm consists of 15 rounds with a different S-box for each round and each set of S-boxes is different for each image encryption. Based on the above, a permutation is applied before the first round, additionally, in round 15 the inverse permutation of the first round intervenes. Both the S-boxes and the permutations are built using the E. Lorenz equations, which obtain solutions with two different points of the elliptic curve chosen randomly in each process. To measure the resistance to differential attack of the proposed cryptosystem, the following measurements are carried out: Number of Pixels Change Rate - NPCR, Unified Average Changing Intensity - UACI. Also, taking into account that the generation of the boxes is dynamic, the algebraic attack is avoided; furthermore, with this symmetric cryptosystem it is possible to distribute keys and sign, since an asymmetric system is used in its construction. On the other hand, four types of noise are applied to the encrypted images to evaluate the resistance of the encryption algorithm to this type of attack. Ten instruments are used to measure the quality of encryption; namely: entropy, correlation, discrete Fourier transform, NPCR, UACI, Avalanche Criteria - AC, contrast, energy, homogeneity and a goodness of fit test is proposed using the χ2 distribution.