A Cryptographic Technique Involving Finite Fields and Logical Operators

Abstract
Objectives: The aim of this study is to propose a new encryption/ decryption technique which involves logical operators and finite field.

Methods/statistical analysis: The study proposes a new method for encrypting/decrypting messages which use logical operator XOR and finite field. The method involves sharing common keys between sender and receiver. Then converting plain text into ASCII values bit-form. XORing this with random matrix and then using finite field GF (2^5) for converting it into polynomial elements. These elements are then used for creating cipher text. Decrypting process is reverse of encrypting process.

Findings: The technique uses 6×6 matrix form for encrypting messages which can be very difficult to crack with known plain text attacks. The use of XOR operations displaces bits in matrix which makes it difficult to break by brute force technique.

Application/improvements: The technique is useful in areas where sensitive information is to be transferred like banking, military services. If the private key has got into third-party hands, the damage can be huge. To overcome this, the proposed algorithm can be used by randomizing the keys used for encrypting the messages which will provide different keys for encrypting different data blocks.

Keywords: Encryption, Decryption, Finite Fields, Logical Operator XOR