Mathematical Model Using LU Decomposition as Cryptographic System

Abstract

Cryptography plays a significant role in protecting privacy and secrecy in modern communications. The paper describes a novel text encrypt and decrypt scheme based on LU Matrix Decomposition, a numerical method. The scheme uses a key in the form of a invertible square matrix in order to encrypt and decrypt the text. It is broken down into lower triangular (L) and upper triangular (U) matrices. The text is reduced to numerical vectors, encrypted through L and U matrix transforms, and thereafter decrypted through their inverses. This method yields a systematic and secure process of encryption based on the intrinsic complexity of calculations in a matrix to secure the cryptographic process. The method is made calculational efficient with the efficient LU decomposition methods available in state-of-the-art numerical toolsets. Practical implementation issues such as block length and padding schemes are considered in order to handle variable text lengths. The paper evaluates the performance and security of the LU matrix crypto system and predicts and how the system would play a viable role in securing information in resource-constrained scenarios. The method demonstrates a singular combination of linear algebra and cryptography and opens the door for other research in inscriptive techniques based on matrices. While the method boasts strong confidentiality and operational efficiency, enhancements should preferably be made in the area of integrity verification and post-quantum security.