Abstract
This paper proposes a method for constructing permutations on m position arrangements. Our objective is to encrypt color images using advanced encryption standard (AES), using variable permutations means a different one for each 128-bit block in the first round after the x-or operation is applied. Furthermore, this research offers the possibility of knowing the original image when the encrypted figure suffered a failure from either an attack or not. This is achieved by permuting the original image pixel positions before being encrypted with AES variable permutations, which means building a pseudorandom permutation of 250,000 position arrays or more. To this end, an algorithm that defines a bijective function between the nonnegative integer and permutation sets is built. From this algorithm, the way to build permutations on the 0,1,…,m−1 array, knowing m−1 constants, is presented. The transcendental numbers are used to select these m−1 constants in a pseudorandom way. The quality of the proposed encryption according to the following criteria is evaluated: the correlation coefficient, the entropy, and the discrete Fourier transform. A goodness-of-fit test for each basic color image is proposed to measure the bits randomness degree of the encrypted figure. On the other hand, cipher images are obtained in a loss-less encryption way, i.e., no JPEG file formats are used.
Highlights
With the development of communications, the security problem for confidential information has emerged
If l is multiplied by pi, that is, the product l à pi, the result is a transcendental number
This section carried out the results analysis, separated them into two parts, namely, in the first part, the encrypted images randomness used the two-steps procedure in question
Summary
With the development of communications, the security problem for confidential information has emerged. There have appeared several encryption procedures for information, in particular, images.[1] There are some new methods using the Hilbert transform,[2] chaos,[3] the hyper-chaos,[4] or even the advanced encryption standard (AES) cryptosystem[5] with the CBC encryption mode,[6] this way is a sequential encryption. The AES cryptosystem has no problem with any of them yet.[9] the AES key set can reach 2256 elements. The nonlinearity of the AES box is superior to data encryption standard (DES) and triple-DES boxes.[11] there are encryptions for color images using the transformed Fourier,[12] the gyrator and Arnold transforms.[13] in
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