A Study of Logical Exclusive Operations and Linear Transformations in Cryptography: Achieving a Good Avalanche Effect in Cryptography

Abstract

In the present study the message is encrypted in blocks and each data block is encrypted in 8rounds. In each round different linear transformations are applied on different elements of the datablock. These linear transformations are sub-key dependent. The sub-key of each round is derived fromthe session key of that particular data block. The session key of each data block is generated from themaster key (secret key) agreed upon by the communicating parities before communicating themessages. Between two successive linear transformation operations Exclusive-OR (XOR) operation isapplied on each element with its nearest four neighbors in the matrix array to ensure good avalanche. Inthe key scheduled algorithm proposed in this study different keys are used for encrypting different datablocks which are called session keys generated from the master key (secret key between the sender andthe receiver) and the key used for the encryption of each round is different and is derived from thesession key of the corresponding block which is called the sub key. As different keys are used forencrypting different data blocks cipher is less vulnerable to passive attacks. The binary bits of eachelement of the message matrix M in each round are rotated right in the encryption of the message. Therotation is not fixed rotation. The number of rotations of the bits of each element of the matrix M dependson the sub key of that particular round of encryption. Logical XOR operation is performed on eachelement between two successive rotation operations with all its nearest neighboring elements. Hence,the identical characters in the plain text are mapped to different cipher characters even though they arein the same text block or in different text blocks. So, cipher text is not easily amenable to cryptanalysis.Even the change of a single character of the message changes almost the entire cipher block, i.e., to saythat the proposed algorithm of this study has achieved a good avalanche effect.