Cryptography is the study of mathematical techniques for information security. The security of information to maintain its confidentiality, integrity and availability has become a major issue today. Since security is the main concern in data communication, encryption algorithm carry an important part of it. The art or science encompasses the principles 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.
Key words: Finite field, Logical XNOR operator, Plain text, Cipher text, Key rhotrix
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