AAβ public key cryptosystem - A new practical asymmetric implementation based on the square root problem

This paper aims to provide a practical implementation one of a probabilistic cipher proposed by M.R.K. Ariffin, M.A. Asbullah and N.A. Abu called as AA_β. We provide details on designing and implementing the AA_β algorithm. Furthermore, to support our understanding by providing a statistical analysis of times taken to implement the key generation, encryption and decryption algorithm for the key sizes 3072, 6144, 9216 and 12288 bits for message spaces of 4n where n = 512, 1024, 1536 and 2048 bits. We show the working of the AA_β algorithm purely from a practical standpoint to justify if it is practically implementable even for large data sets operating on large key sizes.