Redundant Residue Number System Research Articles

Investigating the Applicability of Nested Secret Share for Drone Fleet Photo Storage

Military drones can be used for surveillance or spying on enemies. They, however, can be either destroyed or captured, therefore photos contained inside them can be lost or revealed to the attacker. A possible solution to solve such a problem is to adopt Secret Share (SS) techniques to split photos into several sections/chunks and distribute them among a fleet of drones. The advantages of using such a technique are two folds. Firstly, no single drone contains any photo in its entirety; thus even when a drone is captured, the attacker cannot discover any photos. Secondly, the storage requirements of drones can be simplified, and thus cheaper drones can be produced for such missions. In this scenario, a fleet of drones consists of t+r drones, where t (threshold) is the minimum number of drones required to reconstruct the photos, and r (redundancy) is the maximum number of lost drones the system can tolerate. The optimal configuration of t+r is a formidable task. This configuration is typically rigid and hard to modify in order to fit the requirements of specific missions. In this work, we addressed such an issue and proposed the adoption of a flexible Nested Secret Share (NSS) technique. In our experiments, we compared two of the major SS algorithms (Shamir's schema and the Redundant Residue Number System (RRNS)) with their Two-Level NSS (2NSS) variants to store/retrieve photos. Results showed that Redundant Residue Number System (RRNS) is more suitable for a drone fleet scenario.

DNA Arithmetic with Error Correction.

DNA design approaches are expected to play an important role in the future design of non-silicon-based computers. However, one of the main challenges for its mass fabrication is the considerable error rate. This paper presents a DNA computing system based on the Redundant Residue Number system (RRNS) that has elegant fault-tolerance features. The proposed method is the first to introduce the sticker model into DNA Arithmetic based on RRNS. The ability of error detection and correction are advantages of the proposed computing system. Moreover, the proposed arithmetic method can operate on large DNA-represented numbers, since RNS split them into smaller numbers. The implementation of arithmetic operations on these small numbers decreases the probability of failure in DNA operations.

Enhancing data protection with a distributed storage system based on the redundant residue number system

AbstractBig data becomes the key for ubiquitous computing and intelligence, and Distributed Storage Systems (DSS) are widely used in large-scale data centers or in the cloud for efficient data management. However, the data on stored are likely to be unavailable due to hardware failures and cyberattacks, e.g. DDoS. Maximum Distance Separable (MDS) codes are commonly used for the recovery of faulty storage nodes or unavailable data. However, the recovery of data nodes usually involves access to multiple nodes, which introduces significant communication overheads to the DSS. In this paper, a new DSS based on the Redundant Residue Number System (RRNS) is proposed, where efficient recovery is enabled by applying the second version of Chinese Remainder Theorem (CRT-II). The complexity and network traffic of the proposed data protection scheme is analyzed theoretically and compared with that of traditional MDS based DSSs. Experimental results show that the proposed DSS achieves lower encoding complexity, lower recovery complexity and lower network traffic than the MDS based schemes. Although the proposed data protection scheme introduces computation overheads for the case on which there are no failing nodes, its complexity is still lower for scenarios with frequent data updates. In addition, the proposed scheme introduces additional advantages in terms of security and storage flexibility.

Optimized reverse converters with multibit soft error correction support at 7nm technology

Residue number system (RNS) speeds up digital signal processing systems involving dominant addition and multiplication. Addition and multiplication are accelerated further and performed with a balanced performance on one-hot coded (OHC) residue digits. However, the high complexity of the RNS reverse converter (RC) may kill the performance gain. This paper proposes a high-speed and scalable RNS-RC for both regular and one-hot RNS. For redundant RNS (RRNS), an RRNS-RC is proposed, which based on majority-voting between OHC residue digits, corrects multibit soft errors occurring in a single residue channel. With pass-transistor logic and low-power FinFETs, the proposed RCs are optimized. The simulated RRNS-RC corrected 98.5% of soft errors, while consuming 7, 6.2 and 0.4% of the system's area, leakage power and dynamic power, respectively. As compared to the leading lookup table RC in the literature, RNS-RC exhibited 10.3X, 4.4X and 1.8X savings in area, average power, and delay, respectively.

Enhanced cipher text-policy attribute-based encryption and serialization on media cloud data

Purpose There are various system techniques or models which are used for access control by performing cryptographic operations and characterizing to provide an efficient cloud and in Internet of Things (IoT) access control. Particularly in cloud computing environment, there is a large-scale distribution of these traditional symmetric cryptographic techniques. These symmetric cryptographic techniques use the same key for encryption and decryption processes. However, during the execution of these phases, they are under the problems of key distribution and management. The purpose of this study is to provide efficient key management and key distribution in cloud computing environment. Design/methodology/approach This paper uses the Cipher text-Policy Attribute-Based Encryption (CP-ABE) technique with proper access control policy which is used to provide the data owner’s control and share the data through encryption process in Cloud and IoT environment. The data are shared with the the help of cloud storage, even in presence of authorized users. The main method used in this research is Enhanced CP-ABE Serialization (E-CP-ABES) approach. Findings The results are measured by means of encryption, completion and decryption time that showed better results when compared with the existing CP-ABE technique. The comparative analysis has showed that the proposed E-CP-ABES has obtained better results of 2373 ms for completion time for 256 key lengths, whereas the existing CP-ABE has obtained 3129 ms of completion time. In addition to this, the existing Advanced Encryption Standard (AES) scheme showed 3449 ms of completion time. Originality/value The proposed research work uses an E-CP-ABES access control technique that verifies the hidden attributes having a very sensitive dataset constraint and provides solution to the key management problem and access control mechanism existing in IOT and cloud computing environment. The novelty of the research is that the proposed E-CP-ABES incorporates extensible, partially hidden constraint policy by using a process known as serialization procedure and it serializes to a byte stream. Redundant residue number system is considered to remove errors that occur during the processing of bits or data obtained from the serialization. The data stream is recovered using the Deserialization process.

Teaching redundant residue number system for electronics and computer students

This paper describes a study for teaching number system in a computer arithmetic course and addresses the existing gap in the current course by focusing on the characteristics of applications. A redundant residue number system (RRNS) is an efficient and innovative number system that inherits the interesting properties of both residue number system (RNS) and redundant number systems. It breaks the operands into residues by considering a moduli-set and then signifies the residues by a redundant representation. So, by limiting the carry propagation chain inside and outside the moduli, RRNS proposes more efficient arithmetic units which could be employed in digital signal processing (DSP) applications. Despite the applicability of RRNS, there is not well-organized teaching on RRNS covering the recent achievements. Besides, there is an important question for students and researchers what is the most appropriate number representation for each application category? In this paper, we present a step-by-step education process for RRNS that includes basic concepts of RNS and the redundant number system. Then we address characteristics of different applications that RRNS is suitable to be employed for them. So, the method gives a well-organized proceeding to computer arithmetic designers and students.

Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Модификация алгоритма обнаружения и локализации ошибки в системе остаточных классов

This article presents the design of the modified error detection and localization algorithm in the Residue Number System (RNS). Classical redundant RNS with one control modulus can detect one error but not localize it. Two control moduli are used to localize a single error. Presented algorithm can achieve an error correction with a single control modulus transmitted over a reliable communication channel. The proposed approach was verified using Verilog on ASIC in RTL and physical synthesis tool Cadence Genus Synthesis Solution. It significantly reduces the area of the hardware implementation increasing the packing density and more efficient use of silicon resource. It slightly increases the running time compared with the classical algorithm. Distributed data storage was developed to study efficiency of the proposed algorithm.

Algorithm for Constructing Modular Projections for Correcting Multiple Errors Based on a Redundant Residue Number System Using Maximum Likelihood Decoding

Algorithm for Constructing Modular Projections for Correcting Multiple Errors Based on a Redundant Residue Number System Using Maximum Likelihood Decoding

Effective Error Control Scheme in Real-Time Wireless Sensor Networks

Wireless Sensor Networks (WSNs) subsist on network of huge numbers of hubs that are distributed in unfriendly environments used for habitat monitoring and to observe changes in phenomena. These hubs are susceptible to faults such as energy exhaustion, hardware glitches, communication link errors, malicious attacks, which may lead to errors in message delivery. However, these systems are typically utilized to convey vital information in remote places. Thus, efficient error identification and correction is thereby required in order to maintain the accuracy of the received message. This paper aimed at designing high speed reverse converter for effective error control codes using Redundant Residue Number System in order to enhance the accuracy of messages delivered for real-time WSNs. In order to attain a greater error correction, a reverse converter which was based on Mixed Radix Conversion was designed for the moduli set {2n+1-1, 2n, 2n-1}. In addition to this moduli, an extra redundant moduli set{2n+1+3, 22n - 3} is also designed for higher correctness. For correction and identification of corrupted values in the original data, maximum likelihood was used. The results obtained show that the suggested moduli set offers low energy utilization and consistency of the received message in real time WSNs.

Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

In this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from Oleft (k^{2}right ) to Oleft (kright ) with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.

Security algorithms for distributed storage system for E-health application over wireless body area network

Wireless body area networks (WBANs) are an upcoming technology for achieving effective healthcare. The security and privacy of patient-related data are two essential aspects of WBAN system security. Storing data on a single server is simple but may lead to a single point of failure (whether a typical failure or a failure due to security attacks). In this paper, enhanced security and privacy of patient information and E-health systems based on distributed storage systems (DSSs) are developed using public-key cryptography to store patient information. The storage of data and the security requirements (such as confidentiality, reliability, authentication, and dynamic integrity) are simultaneously distributed among individual nodes throughout the network. The patient data are encrypted using the redundant residue number system (RRNS) technique, which depends on a library of moduli in the encrypting process to generate residues. Three algorithms were implemented to decode the RRNS: the Chinese Remainder Theorem (CRT), Base Extension (BEX) with mixed radix conversion, and the new Chinese Remainder Theorem I (CRT I). The results of a system prototype implementation showed that whenever the value of the moduli was a big prime number, the coding efficiency became large, and the time to send a message decreased by 2 s. The performance of the algorithms was expressed in terms of execution time and cyclomatic complexity (CC). The results showed that the CRT I was 1 s faster than the other decoding algorithms and took around 2.5 s to decode the RRNS. The CRT had a low CC of 15, whereas the MRC and CRT I had a CC of 45 and 40, respectively. The main operation phases of the proposed system are described.

Residue Number System Fade Mitigation Technique with Error Detection and Correction on a Satellite Communication Link

Rain fade is the loss of signal power at the receiver of a telecommunication system mainly due to absorption and scattering caused by rain in the transmission medium, especially at frequencies above 10 GHz. In order to combat the loss of the signal power at the receiver, there is the need to employ rain fade mitigation techniques. Consequently, researchers have been studying how rain affects the signal in different geographical locations as well as proposing some mitigation techniques. Power control is one of the mitigation techniques that have been proposed. But this technique has some associated challenges. Increasing the power will lead to an increase in cost of transmission which will eventually be passed on to the consumer thereby making satellite services expensive. It requires high power in uplink and downlink which increases the burden either on user terminal or satellite payload. Also, because of health concerns there is a limit to the amount of power that can be radiated to the ground and this is governed by international agreements. Another power management drawback in using this technique is that, uplink power control is not efficient in directing the added power to only the ground station experiencing path attenuation, because the additional power is distributed to all locations within the satellite antenna coverage area. In this paper, we address the power control challenges, by leveraging on the inherent properties of Residue Number System (RNS) and Redundant Residue Number System (RRNS) to propose an RNS architecture using the moduli set {2²ⁿ⁺¹-1, 2²ⁿ -1, 2²ⁿ, 2⁴ⁿ⁺¹ -1, 2²ⁿ +1} that can mitigate rain fade in the satellite link as well as detect and correct multiple errors. In digital communication systems, the bit energy, e_b, is the most important parameter in determining the communications link performance. Numerical analysis shows that the proposed scheme performs better than the traditional method as indicated in the high energy per bit value obtained in the proposed system in comparison with the traditional method, all other things being equal.

Scalable Data Storage Design for Nonstationary IoT Environment With Adaptive Security and Reliability

Internet-of-Things (IoT) environment has a dynamic nature with high risks of confidentiality, integrity, and availability violations. The loss of information, denial of access, information leakage, collusion, technical failures, and data security breaches are difficult to predict and anticipate in advance. These types of nonstationarity are one of the main issues in the design of the reliable IoT infrastructure capable of mitigating their consequences. It is not sufficient to propose solutions for a given scenario, but mechanisms to adapt the current solution to changes in the environment. In this article, we present a multicloud storage architecture called WA-MRC-RRNS that combines the weighted access scheme, threshold secret sharing, and redundant residue number system with multiple failure detection/recovery mechanisms and homomorphic ciphers. We provide a theoretical analysis of the probability of information loss, data redundancy, speed of encoding/decoding, and show how to dynamically configure parameters to cope with different objective preferences, workloads, and cloud properties. We propose a multiobjective optimization mechanism to adjust redundancy, encryption–decryption speed, and data loss probability. Comprehensive experimental analysis with real data shows that our approach provides a secure way to mitigate the uncertainty of the use of untrusted and not reliable IoT infrastructure.

Protecting scratchpad memory addresses against soft errors

Scratchpad memories (SPMs) are intensively utilized in modern embedded processors where a demand on improving reliability without compromising performance-predictability and area/power efficiency is on rise. Our observations imply that one target for this reliability improvement is to combat ever increasing threats of multiple bit upsets (MBUs) occurring in the SPM addresses as well as multiple event transients (METs) happening in the SPM address decoders (SADs). This paper proposes two masking techniques that protect SPM addresses in their lifespan across multiple on-chip structures prone to MBU/MET errors. The strategy behind both techniques is to replicate narrow-width SPM addresses at compile time, and to mask errors at the SAD stage. The first technique is triplication of SPM addresses (TSA), and using a triplicated SAD. For the processors having limited memory address widths, the second technique uses the concept of redundant residue number system to provide a residual replication of SPM addresses (RRSA), and a residually replicated SAD. Simulation results showed that interleaving the retained bits between replicas/residues extends error masking coverage of TSA and RRSA from 86% and 78% to 91% and 97% with no performance loss, while imposing only 0.23% and 0.11% power and 0.02% and 0.01% area to the processor.

An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System

The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.

A Division Algorithm in a Redundant Residue Number System Using Fractions

The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach.

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

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.

Perspective and Opportunities of Modulo 2n−1 Multipliers in Residue Number System: A Review

Modulo multiplier has been attracting considerable attention as one of the essential components of residue number system (RNS)-based computational circuits. This paper contributes a comprehensive review in the design of modulo [Formula: see text] multipliers for the first time. The modulo multipliers can be implemented using ROM (look-up-table) as well as VLSI components (memoryless); however, the former is preferable for lower word-length and later for larger word-length. The modular and parallelism properties of RNS are used to improve the performance of memoryless multipliers. Moreover, a Booth-encoding algorithm is used to speed-up the multipliers. Also, an advanced modulo [Formula: see text] multiplier based on redundant RNS (RRNS) could be further chosen for very high dynamic range. These perspectives of modulo [Formula: see text] multipliers have been extensively studied for recent state-of-the-art and analyzed using Synopsis design compiler tool.

Steganography over Redundant Residue Number System Codes

In this paper we define steganography over Redundant Residue Number System (RRNS) Codes. We describe distortion-less RRNS based steganographic schemes, analyse their corresponding embedding capacities, discuss their linearity and compare them with well known steganographic protocols. Specifically, we take advantage of the redundancy and correction capacity of these codes to hide secret information in such way that the number of the altered residues does not exceed half the redundancy of the code.