Single and Multiple Error Detection and Correction using Redundant Residue Number System for Cryptographic and Stenographic Schemes

Abstract

The possibility of errors being propagated during the encoding process of cryptographic and steganographic schemes is real due to the introduction of noise by ciphering the data from stage to stage. This real possibility therefore requires that an efficient scheme is proposed such that if after the decoding process the accurate information is not discovered, then it can be employed to detect and correct any errors in the system. The Residue Number System (RNS) by its nature is fault tolerant since an error in one digit position does not affect other digit positions; but the Redundant Residue Number System (RRNS) had been used over the years to effectively detect and correct errors. In this paper, we propose an efficient scheme that can detect and correct both single and multiple errors after and/or during computation and/or transmission provided the redundant moduli are sufficient enough. A theoretical analysis of the performance of the proposed scheme show it will be a better choice for detecting and correcting computational and transmission errors to existing similar state-of-the-art schemes.