Triple-DES block of 96 Bits: An application to colour image encryption

According to international standards, FIPS PUB 146-3, the cryptographic system Triple-Data Encryption Standard (Triple DES) encrypts blocks of 64 bits. However, it isn’t difficult to extend the block to 96-bit encryption, which is called Triple-DES-96. This change includes a modification to Triple-DES cryptosystems that appeared recently as the Advanced Encryption Standard - AES - FIPS PUB 197. Including encryption, file M (with m bits) is achieved in less time than Triple-DES. Developing Triple DES-96, intends to apply the Factorial Theorem that for this particular case tells us that any permutation on an array of 96 positions can be constructed from 3 permutations on arrays of 64 positions. According to Theorem JV, a given number n with 0 ≤ n ≤ 64! - 1 ≈ 1089, can associate a permutation of 64 positions in 63 steps. This allows applying a variable permutation on an array of 96 positions at the start of the third round, using 3 numbers with 0 ≤ n_i ≤ 1089 and for i = 1, 2, 3, instead of using numbers 0 ≤ n ≤ 96 ! - 1 ≈ 10150 for permutations on arrays of 96 positions directly. The algorithm illustrates Triple-DES-96 encryption images in colour, which is carried out without loss of information, that is, does not apply JPEG formats. There is a criterion of how many permutations have to be applied; also a randomness measure of the encrypted image for χ2 value is used.