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.
In this paper an attack strategy on the Data Encryption Standard (DES) that is different from the existing ones is developed. The attack strategy is based on a theorem proved by the author, called LR theorem. The attack can be done by means of a personal computer, i.e. a Pentium IV based machine. Obviously, more information than a sample of plaintext and ciphertext is required. However, this additional requirement is reduced to a minimum of just 24 bits. The LR theorem uncovers 16 trapdoors of which 2 are of importance. With this knowledge, an attack on Triple-DES can be performed using the aforementioned personal computer. A simple solution to this kind of attack is proposed, preserving the complexity of the Triple-DES, 2<sup>112</sup>.