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.

A New Approach to Detecting and Correcting Single and Multiple Errors in Wireless Sensor Networks

“…The performance of the proposed error detection and correction algorithm is evaluated primarily in terms of computational time -number of iterations needed to recovers a message. Compared to exiting schemes [21,27,37] and [29], the scheme inhere offers fewest iterations to recover an original transmitted. In the worstcase scenario, the algorithm in this work requires (the codes length) trials to decode an integer value equivalent of a signal that has been transmitted over a sensing network.…”

“…A careful look at Table 5, show the most recent error correction method presented by [21] requires trials to detect and correct both single and multiple errors that may be contained in a transmitted data. This is same as the works of [16] for single error correction; but better than the schemes presented in [37,29] and [27].…”

“…Fig. 3 below compares the error handling scheme in [21] and the proposed scheme for = 4 and varying . The scheme in [21] presents a single hardware implementation for both forward and reverse conversion; while the proposed scheme here provides only an architecture for forward conversion.…”

“…The scheme in [18] is applicable to multiple error detection and correction but the procedures use of the mixed radix method may slow the encoding process. In recent past, RRNS has been applied to achieve fault tolerance in communication systems for reliable transmission; data encryption and compression; and in cryptographic and stenographic schemes [20,21]. The high degree of computational parallelism and carry-free operations inherent in the system offers new avenue for energy efficiency, for example in sensor nodes, data security, increased data transfer rate, and better data storage.…”

“…RNS also offers some useful properties for error detection and correction in computerized systems. These and many of its inherent features helps in building fault tolerant systems required of many data communications systems including in digital filtering, convolution, Discrete Cosine Transform, communication engineering, cryptography, image processing and speech processing and stenography schemes [32,33,21,22]. Others beneficiary areas of application of RNS are; direct digital frequency synthesis, Discrete Fourier Transform and Fast Fourier Transform [3].…”