Construction of cryptographic scheme of finite field using logical operators on rhotrices

Abstract

Cryptography is the study of mathematical techniques for information security. The secu-
rity of information to maintain its confidentiality, integrity, and availability has become
a major issue today. Since security is the main concern in data communication, encryp-
tion algorithm carries an important part of it. The art or science encompasses the prin-
ciples and methods of transforming an intelligible message into unintelligible, and then
retransforming the message back into its original form for more security. The sequence
of numbers generated by a Linear Feed Back Shift Register or its XNOR counterpart is
used especially in military cryptography. In this study, we encode and decode messages
using rhotrices and logical operators on Galois finite field. The application of rhotrices in
cryptographic systems using logical operators on Galois finite field prove to be one of the
most secured and constructive method that prevent public or third parties from reading
or getting access to data transmission over an insecure channel.