A highly adaptive novel symmetric encryption method using the Sylvester equation with an application example for lossless audio compression

This paper presents a novel, highly adaptive, symmetric encryption technique based on the Sylvester equation. A sender encrypts data using two matrices generated by the QR decomposition of a Hankel matrix or, conversely, using a Hankel matrix that is itself composed of a symmetric key sequence. The decrypted information at the receiver is obtained by solving the Sylvester equation. Three theorems are presented that ratify the Sylvester equation and the QR factorization as valid methods for encryption. These schemes do not have any constraints for generating symmetric keys, since a random key sequence is used for this. The huge amount of possible keys makes an exhaustive search the best approach towards breaking the algorithm. Results are shown for lossless audio coding both for encryption and compression. The results display excellent performance.