A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation
N.I. Chervyakov,Pavel A. Lyakhov,Mikhail Babenko,Anton Nazarov,Maxim Deryabin,I.N. Lavrinenko,Anton V. Lavrinenko +6 more
Reads0
Chats0
TLDR
A new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed, which has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers.Abstract:
In this paper, a new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed. It requires less computational resources than the CRT with integers and mixed radix number systems (MRNS). The main idea of the algorithm is (a) to transform the residual representation of the dividend and divisor into a weighted fixed-point code and (b) to find the higher power of 2 in the divisor written in a residue number system (RNS). This information is acquired using the CRT with fractions: higher power is defined by the number of zeros standing before the first significant digit. All intermediate calculations of the algorithm involve the operations of right shift and subtraction, which explains its good performance. Due to the abovementioned techniques, the algorithm has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers than the algorithms described earlier. The new algorithm suggested in this paper has O (log2 Q) iterations, where Q is the quotient. For multidigit numbers, its modular division complexity is Q(N), where N denotes the number of bits in a certain fraction required to restore the number by remainders. Since the number N is written in a weighed system, the subtraction-based comparison runs very fast. Hence, this algorithm might be the best currently available.read more
Citations
More filters
Journal ArticleDOI
Using Floating-Point Intervals for Non-Modular Computations in Residue Number System
TL;DR: This work proposes to compute the interval evaluation of the fractional representation of an RNS number in floating-point arithmetic of limited precision and proposes new algorithms for magnitude comparison and general division in RNS and implements them for GPUs using the CUDA platform.
Journal ArticleDOI
Fast division in the residue number system {2n + 1,2n, 2n-1} based on shortcut mixed radix conversion
TL;DR: This work designed a faster-than-RDF RNS divider for the popular moduli set 2n + 1, 2n,2n − 1 via mixed radix representation of the operands and two parallel 2n-bit dividers, and obtains the accurate quotient via additional hardware.
Journal ArticleDOI
FPGA-Based Hardware Matrix Inversion Architecture Using Hybrid Piecewise Polynomial Approximation Systolic Cells
Javier Vazquez-Castillo,Alejandro Castillo-Atoche,Roberto Carrasco-Alvarez,O. Longoria-Gandara,Jaime Ortegón-Aguilar +4 more
TL;DR: This paper introduces an Field-Programmable Gate Array (FPGA)-based full matrix inversion architecture using hybrid piecewise polynomial approximation systolic cells and shows a well-balanced improvement in the design achieving high throughput and, hence, less resource utilization in comparison to state-of-the-art FPGA-based architectures.
Proceedings ArticleDOI
Improvement of Information Protection and Data Transmission Methods in the Power Industry Using Neural Networks and a System of Residual Classes
TL;DR: In this article, the issue of secure systems development in power industry has been discussed and it was suggested to use systems of residual classes in order to raise stability index of cyphering algorithms as well as mathematical calculation such as for example neural network training.
Journal ArticleDOI
A Division Algorithm in a Redundant Residue Number System Using Fractions
Nikolay I. Chervyakov,Pavel A. Lyakhov,Mikhail Babenko,I.N. Lavrinenko,Maxim Deryabin,Anton V. Lavrinenko,Anton Nazarov,Maria V. Valueva,Alexander Voznesensky,Dmitry Kaplun +9 more
TL;DR: 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, is proposed.
References
More filters
Journal ArticleDOI
A novel division algorithm for the residue number system
Mi Lu,Jen-Shiun Chiang +1 more
TL;DR: A novel general algorithm for signed number division in the residue number system (RNS) is presented that is simple, efficient, and practical for implementation on a real RNS divider.
Proceedings ArticleDOI
HORNS: A homomorphic encryption scheme for Cloud Computing using Residue Number System
TL;DR: A homomorphic encryption scheme using Residue Number System (RNS), in this scheme, a secret is split into multiple shares on which computations can be performed independently.
Journal ArticleDOI
Parallel DNA arithmetic operation based on n-moduli set
Xuedong Zheng,Jin Xu,Wu Li +2 more
TL;DR: An improved DNA representation of an integer is presented and applied in DNA arithmetic operation based on a special n-moduli set and the degree of parallelism in residue arithmetic operation is n.
Journal ArticleDOI
A New RNS based DA Approach for Inner Product Computation
TL;DR: A novel method to perform inner product computation based on the distributed arithmetic principles using the thermometer code encoded residues provides a simple means to perform the modular inner products computation due to the absence of the 2 modulo operation encountered in conventional binary code encoded system.