Nikolay I. Chervyakov

Digital filtering of images in a residue number system using finite-field wavelets

A new approach for processing images based on joint application of the residue number system and finite-field wavelets is proposed in this work. It is shown that the residue number system with simple modules can be used for implementation of the digital processing of signals using finite-field wavelets. The principle of organization of computations in the wavelet transform of images in the residue number system is proposed. There are given examples showing how this method can be used for compression of images and protection of confidential information.

An efficient method of error correction in fault-tolerant modular neurocomputers

In this paper, we propose the architecture of a fault-tolerant unit in a modular neurocomputer that is based on decoding with computation of errors syndromes on redundant moduli and implemented using FPGA and a finite ring neural network. The computational complexity of the proposed architecture is about 80% less in comparison with that of the architecture based on number projections in the mixed radix number system.

Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem

ABSTRACT The residue number system (RNS) is an unconventional number system which can lead to parallel and fault-tolerant arithmetic operations. However, the complexity of residue-to-binary conversion for large number of moduli reduces the overall RNS performance, and makes it inefficient for nowadays high-performance computation systems. In this paper, we present an improved approximate Chinese remainder theorem (CRT) with the aim of performing efficient residue-to-binary conversion for general RNS moduli sets. To achieve this aim, the required number of fraction bits for accurate residue-to-binary conversion is derived. Besides, a method is proposed to substitute fractional calculations by similar computations based on integer numbers to have a hardware amenable algorithm. The proposed approach results in high-speed and low-area residue-to-binary converters for general RNS moduli sets. Therefore, with this conversion method, high dynamic range residue number systems suitable for cryptography and digital signal processing can be designed.

AR-RRNS: Configurable reliable distributed data storage systems for Internet of Things to ensure security

Abstract Benefits of Internet of Things and cloud–fog-edge computing are associated with the risks of confidentiality, integrity, and availability related with the loss of information, denial of access for a long time, information leakage, conspiracy and technical failures. In this article, we propose a configurable, reliable, and confidential distributed data storage scheme with the ability to process encrypted data and control results of computations. Our system utilizes Redundant Residue Number System (RRNS) with new method of error correction codes and secret sharing schemes. We introduce the concept of an approximate value of a rank of a number (AR), which allows us to reduce the computational complexity of the decoding from RNS to binary representation, and size of the coefficients. Based on the properties of the approximate value and arithmetic properties of RNS, we introduce AR-RRNS method for error detection, correction, and controlling computational results. We provide a theoretical basis to configure probability of information loss, data redundancy, speed of encoding and decoding to cope with different objective preferences, workloads, and storage properties. Theoretical analysis shows that by appropriate selection of RRNS parameters, the proposed scheme allows not only increasing safety, reliability, and reducing an overhead of data storage, but also processing of encrypted data.

The EC Sequences on Points of an Elliptic Curve Realization Using Neural Networks

This paper shows that pseudorandom number generator based on EC-sequence doesn’t satisfy the condition of Knuth k-distribution. A modified pseudorandom number generator on elliptic curve points built in neural network basis is proposed. The proposed generator allows to improve statistical properties of the sequence based on elliptic curve points so that it satisfies the condition of k-distribution i.e. the sequence is pseudorandom. Application of Neural network over a finite ring to arithmetic operations over finite field allows to increase the speed of pseudorandom number generator on elliptic curve points EC-256 by 1,73 times due to parallel structure.

The Effective Neural Network Implementation of the Secret Sharing Scheme with the Use of Matrix Projections on FPGA

In this paper neural network implementation of the modified secret sharing scheme based on a matrix projection is offered. Transition from a finite simple Galois field to a complex field allows to reduce by 16 times memory size, necessary for storage of the precalculated constants. Implementation of the modified secret sharing scheme based on a matrix projection with use of the neural network of a finite ring for execution of modular arithmetical addition and multiplication operations in a finite field allows to save on average 30% of the device area and increases the speed of scheme’s work on average by 17%.

The architecture of a fault-tolerant modular neurocomputer based on modular number projections

Abstract This paper suggests a rather efficient architecture for an error correction unit of a residue number system (RNS) that is based on a redundant RNS (RRNS) and applied in parallel data processing structures owing to its capability to improve information stability in calculations. However, the high efficiency of error correction is still not achieved due to the need in the expensive and complex operators that require substantial computational resources and considerable execution time. The suggested error correction method employs the Chinese remainder theorem (CRT) and artificial neural networks (ANN) that appreciably simplify the process of error detection, localization and correction. The key components of the error correction procedure are optimized using (a) the mixed radix conversion (MRC), i.e., the parallel conversion of the numbers from an RNS into the mixed radix number system (MRNS), and (b) the adaptation of neural networks to different sets of RNS moduli (bases) and also to the modular arithmetic during the computation of modular number projections and the restoration of the correct residue on a faulty module. Therefore, the expensive topological structures of neural networks are replaced with the reconfiguration using the weight coefficients switching. In comparison with the existing CRT-based method of projection calculation, the suggested method yields a 20%–30% reduction in power consumption, yet requiring by 10%–20% less FPGA resources for implementation.

Efficient implementation of modular multiplication by constants applied to RNS reverse converters

This paper presents a procedure to optimize modular multiplication by constants. Such operations have been demonstrated to be crucial to design efficient reverse converters, which are the bottleneck of RNS. The focus of this work is the use of Residue Number System (RNS) moduli sets without limitation of the number of channels, which are useful for Digital Signal Processing (DSP) applications. Moreover, an improved hardware architecture for a reverse converter algorithm by using balanced generic moduli sets is presented too. The experimental results show that the optimization of modular multiplication by constant on reverse converters provides a speedup of 1.40 times and average area reduction of 27% for maximum dynamic ranges presented in the state of the art.

Towards reliable low cost distributed storage in multi-clouds

We address the construction of a distributed cloud-based storage based on residual number system with modules of a special kind {2ⁿ − 3, 2ⁿ − 1, 2ⁿ + 1, 2ⁿ + 3} to provide reliability and safety of stored data. We show that the proposed scheme allows obtaining an improvement of the coding and decoding rates, and the speed of data loading and data access comparing with the fastest cloud service. The costs associated with data encoding and decoding are minimal.

Towards Mitigating Uncertainty of Data Security Breaches and Collusion in Cloud Computing

Cloud computing has become a part of peoples lives. However, there are many unresolved problems with security of this technology. According to the assessment of international experts in the field of security, there are risks in the appearance of cloud collusion in uncertain conditions. To mitigate this type of uncertainty, and minimize data redundancy of encryption together with harms caused by cloud collusion, modified threshold Asmuth-Bloom and weighted Mignotte secret sharing schemes are used. We show that if the villains do know the secret parts, and/or do not know the secret key, they cannot recuperate the secret. If the attackers do not know the required number of secret parts but know the secret key, the probability that they obtain the secret depends the size of the machine word in bits that is less than 1/2 ((l-1)). We demonstrate that the proposed scheme ensures security under several types of attacks. We propose four approaches to select weights for secret sharing schemes to optimize the system behavior based on data access speed: pessimistic, balanced, and optimistic, and on speed per price ratio. We use the approximate method to improve the detection, localization and error correction accuracy under cloud parameters uncertainty.