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Symmetric Algorithms II
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
In every encompassing, the two words on the left are used as input to the g functions. (One of them is swapped by 8 bits first.) The g function consists of 32-bit general key-dependent Sand boxes and linear MDS matrix. The consequences of the two g functions are common using a Pseudo Hadamard Transform (PHT), and two keywords are extra. These two consequences are then XORed into the words on the right (one of which is left shift by 1 bit first, the further is rotated right afterward). The left and right are divided into two parts and swapped for further rounds. At the end of all 16 rounds, four words are Exclusive ORed with four keywords to generate the final ciphertext. Thus, 16 bytes of plaintext p0 … p15 are the first tear into four words P0 … P3 of 32 bits apiece by means of the little-endian gathering.
A Review on Evolution of Symmetric Key Block Ciphers and Their Applications
Published in IETE Journal of Education, 2020
AES block cipher uses 4×4 circulant MDS matrix and the realized function is called Mix Column. In this, each of the 32 bit output bits is a linear function of some of the input bits. The following 4×4 matrix is the diffusion matrix used to multiply with 32-bit input considered as 4 bytes a0,a1, a2 and a3 to get the 4-byte output b0,b1,b2,b3. Note that the entries in the matrix are bytes written in HEX form (as two nibbles). The output of the Mix Column operation is as follows: Note that the bytes are treated as polynomials in GF(2). A byte p = p7p6p5p4p3p2p1p0 is considered as the polynomial Note that p7,p6, … ., p0 are all bits. Similarly, the {03} corresponds to the byte 00000011 = x+1. The multiplication of ai with another polynomial needs to be reduced modulo the irreducible polynomial , This is possible by noting that and so on up to x14. Some exercises on Galois field multiplications need to be given to the students.