Maxim Anatolievich Deryabin

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.

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.

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.

A new model to optimize the architecture of a fault-tolerant modular neurocomputer

Abstract In this paper, we present some results on error detection and correction in a modular neurocomputer that are based on redundant residue number systems. The error correction method developed below involves the modified Chinese Remainder Theorem with fractions and uses a Hopfield neural network to correct the errors. The suggested approach eliminates the need for extending the bases of a residue number system, a costly operation required in case of syndrome decoding with error syndromes calculation on the control bases of the system. Also the approach does not utilize the projection method, another costly operation intended to localize errors (i.e., to detect the moduli associated with faulty digits). The well-known procedures mentioned above seem inefficient in terms of practical implementation, as they employ a mixed radix number system: transition to such a system is iterative and may affect the performance of a whole neurocomputer. Owing to the exclusion of these costly operations, the suggested approach significantly simplifies error correction procedures for integer numbers.

AC-RRNS: Anti-collusion secured data sharing scheme for cloud storage

Abstract Cloud security issues are important factors for data storage and processing. Apart from the existing security and reliability problems of traditional distributed computing, there are new security and reliability problems. They include attacks on a virtual machine, attacks on the synchronization keys, and so on. According to the assessment of international experts in the field of cloud security, there are risks of cloud collusion under uncertain conditions. To mitigate this type of uncertainty and reduce harms it can cause, we propose AC-RRNS algorithm based on modified threshold Asmuth–Bloom and Mignotte secret sharing schemes. We prove that the algorithm satisfies the formal definition of computational security. If the adversary coalition knows the secret shares, but does not know the secret key, the probability to obtain the secret is less than 1 / ( 2 l ⋅ ( k − 1 ) ( 2 l − k − 1 ) ) . The probability is less than 1 / 2 ( l − 1 ) with unknown secret shares and known secret key, and 1 / 2 l ⋅ k with unknown secret key. Its complexity is equal to brute-force method. We demonstrate that the proposed scheme ensures security under several types of attacks. We propose approaches for selection of parameters for AC-RRNS secret sharing scheme to optimize the system behavior and data redundancy of encryption.

Fast modular multiplication execution in residue number system

In the paper, we propose a new method of modular multiplication computation, based on Residue Number System. We use an approximate method to find the approximate method a residue from division of a multiplication on the given module. We substitute expensive modular operations, by fast bit right shift operations and taking low bits. The carried-out simulation on Kintex7 XC7K70T board showed that the offered method allows to win in time on average for 75%, and in the area - on average for 80% relatively to modified method from work [1] that makes it more applicable for the hardware implementation of the cryptography primitives constructed over a simple finite field.