scholarly journals The Study of Monotonic Core Functions and Their Use to Build RNS Number Comparators

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1041
Author(s):  
Mikhail Babenko ◽  
Stanislaw J. Piestrak ◽  
Nikolay Chervyakov ◽  
Maxim Deryabin
Keyword(s):  
Homomorphic Encryption ◽  
Number System ◽  
Residue Number System ◽  
Modular Arithmetic ◽  
The Core ◽  
Number Comparison ◽  
Core Function ◽  
Potential Applications ◽  
A New Technique ◽  
Diagonal Function

A non-positional residue number system (RNS) enjoys particularly efficient implementation of addition and multiplication, but non-modular arithmetic operations in RNS-like number comparison are known to be difficult. In this paper, a new technique for designing comparators of RNS numbers represented in an arbitrary moduli set is presented. It is based on using the core function for which it was shown that it must be monotonic to allow for RNS number comparison. The conditions of the monotonicity of the core function were formulated, which also ensured the minimal range of the core function (essential to obtain the best characteristics of the comparator). The best choice is a core function in which only one coefficient corresponding to the largest modulus is set to 1 whereas all other coefficients are set to 0. It is also shown that the already known diagonal function is nothing else but the special case of the core function with all coefficients set to 1. Performance evaluation suggests that the new comparator uses less hardware and in some cases also introduces smaller delay than its counterparts based on diagonal function. The potential applications of the new comparator include some recently developed homomorphic encryption algorithms implemented using RNS.

scholarly journals RNS Number Comparator Based on a Modified Diagonal Function

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1784
Author(s):  
Mikhail Babenko ◽  
Maxim Deryabin ◽  
Stanislaw J. Piestrak ◽  
Piotr Patronik ◽  
Nikolay Chervyakov ◽  
...  
Keyword(s):  
Number System ◽  
Residue Number System ◽  
Modular Arithmetic ◽  
Delay Reduction ◽  
Number Comparison ◽  
Residue Number ◽  
A New Technique ◽  
Diagonal Function ◽  
Reduced Power Consumption ◽  
Monotonic Properties

Number comparison has long been recognized as one of the most fundamental non-modular arithmetic operations to be executed in a non-positional Residue Number System (RNS). In this paper, a new technique for designing comparators of RNS numbers represented in an arbitrary moduli set is presented. It is based on a newly introduced modified diagonal function, whose strictly monotonic properties make it possible to replace the cumbersome operations of finding the remainder of the division by a large and awkward number with significantly simpler computations involving only a power of 2 modulus. Comparators of numbers represented in sample RNSs composed of varying numbers of moduli and offering different dynamic ranges, designed using various methods, were synthesized for the 65 nm technology. The experimental results suggest that the new circuits enjoy a delay reduction ranging from over 11% to over 75% compared to the fastest circuits designed using existing methods. Moreover, it is achieved using less hardware, the reduction of which reaches over 41%, and is accompanied by significantly reduced power-consumption, which in several cases exceeds 100%. Therefore, it seems that the presented method leads to the design of the most efficient current hardware comparators of numbers represented using a general RNS moduli set.

scholarly journals Improved Modular Division Implementation with the Akushsky Core Function

Computation ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Mikhail Babenko ◽  
Andrei Tchernykh ◽  
Viktor Kuchukov
Keyword(s):  
Approximate Method ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Incorrect Result ◽  
Core Function ◽  
Residue Number ◽  
Division Operation

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

scholarly journals A Proposed Method to Enhance the Quality of Data Communication in WSN using Modular Arithmetic

2020 ◽  
Vol 9 (8) ◽  
pp. 879-881
Keyword(s):  
Data Transmission ◽  
Spread Spectrum ◽  
Fault Tolerant ◽  
High Reliability ◽  
Data Communication ◽  
Number System ◽  
Residue Number System ◽  
Modular Arithmetic ◽  
Signal Spectrum ◽  
Quality Of Data

Wireless sensor networks (WSN) are the current direction to monitor the resources and processes by developing fault tolerant distributed auto configure systems. High reliability is required to use WSN in safety systems, real time monitoring systems, guard systems and industrial control for all levels of the OSI model. To eliminate the noise and to process the information parallel by extending the signal spectrum using FHSS and Residue number system (RNS) based transformation. These approaches increase the reliability of data transmission in a WSN physical layer only. It is essential to have reliable data transmission in the network layer. When network topology is modified, packet loss is caused by overload and emergency or inaccessibility of units. Delay time increases because of packet retransmission. These considerations have led us to propose to work on “Performance studies on RNS based spread spectrum techniques for few communication channels”

scholarly journals Neural network method for base extension in residue number system

2020 ◽  
Author(s):  
M. Babenko ◽  
E. Shiriaev ◽  
A. Tchernykh ◽  
E. Golimblevskaia
Keyword(s):  
Neural Network ◽  
Elliptic Curve ◽  
Chinese Remainder Theorem ◽  
Homomorphic Encryption ◽  
Computational Cost ◽  
Number System ◽  
Residue Number System ◽  
Pseudorandom Sequence ◽  
Base Extension ◽  
Residue Number

Confidential data security is associated with the cryptographic primitives, asymmetric encryption, elliptic curve cryptography, homomorphic encryption, cryptographic pseudorandom sequence generators based on an elliptic curve, etc. For their efficient implementation is often used Residue Number System that allows executing additions and multiplications on parallel computing channels without bit carrying between channels. A critical operation in Residue Number System implementations of asymmetric cryptosystems is base extension. It refers to the computing a residue in the extended moduli without the application of the traditional Chinese Remainder Theorem algorithm. In this work, we propose a new way to perform base extensions using a Neural Network of a final ring. We show that it reduces 11.7% of the computational cost, compared with state-of-the-art approaches.

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