scholarly journals Parallel machine arithmetic for recurrent number systems in non-quadratic fields

2020 ◽  
Vol 44 (2) ◽  
pp. 274-281
Author(s):  
V.M. Chernov
Keyword(s):  
Finite Fields ◽  
Computer Arithmetic ◽  
Parallel Machine ◽  
Quadratic Fields ◽  
Recurrent Sequence ◽  
Direct Sum ◽  
Quadratic Extensions ◽  
Number Systems ◽  
Residue Number ◽  
The Difference

The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of modular rings is the parallelization of calculations in non-quadratic extensions of simple finite fields whose elements are represented in number systems generated by sequences of powers of roots of the characteristic polynomial of the recurrent sequence.

scholarly journals Fibonacci, tribonacci, …, hexanacci and parallel “error-free” machine arithmetic

2019 ◽  
Vol 43 (6) ◽  
pp. 1072-1078 ◽  
Author(s):  
V.M. Chernov
Keyword(s):  
Characteristic Polynomial ◽  
Fibonacci Sequence ◽  
Parallel Computations ◽  
New Method ◽  
Direct Sum ◽  
Number Systems ◽  
Residue Number Systems ◽  
Residue Number ◽  
The Difference ◽  
Free Machine

The paper proposes a new method of synthesis of machine arithmetic systems for “error-free” parallel computations. The difference of the proposed approach from calculations in traditional Residue Number Systems (RNS) for the direct sum of rings is the parallelization of calculations in finite reductions of non-quadratic global fields whose elements are represented in number systems generated by sequences of powers of roots of the characteristic polynomial for the n-Fibonacci sequence.

scholarly journals High-Performance RNS Modular Exponentiation by Sum-Residue Reduction

2020 ◽  
Author(s):  
Tao Wu
Keyword(s):  
High Performance ◽  
Computer Arithmetic ◽  
Number System ◽  
Residue Number System ◽  
Modular Exponentiation ◽  
Number Systems ◽  
Diffie Hellman ◽  
Residue Number ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

Abstract Modular exponentiation is fundamental in computer arithmetic and is widely applied in cryptography such as ElGamal cryptography, Diffie-Hellman key exchange protocol, and RSA cryptography. Implementation of modular exponentiation in residue number system leads to high parallelism in computation, and has been applied in many hardware architectures. While most RNS based architectures utilizes RNS Montgomery algorithm with two residue number systems, the recent modular multiplication algorithm with sum-residues performs modular reduction in only one residue number system with about the same parallelism. In this work, it is shown that high-performance modular exponentiation and RSA cryptography can be implemented in RNS. Both the algorithm and architecture are improved to achieve high performance with extra area overheads, where a 1024-bit modular exponentiation can be completed in 0.567 ms in Xilinx XC6VLX195t-3 platform, costing 26,489 slices, 87,357 LUTs, 363 dedicated multipilers of $18\times 18$ bits, and 65 Block RAMs.

scholarly journals Number systems in modular rings and their applications to "error-free" computations

2019 ◽  
Vol 43 (5) ◽  
pp. 901-911 ◽  
Author(s):  
V.M. Chernov
Keyword(s):  
Golden Ratio ◽  
Digital Signal ◽  
Number System ◽  
Parallel Machine ◽  
New Class ◽  
Number Systems ◽  
Residue Number ◽  
Discrete Orthogonal ◽  
Redundant Number System ◽  
Modular Reductions

The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

A fast near optimum VLSI implementation of FFT using residue number systems

Integration ◽  
1984 ◽  
Vol 2 (2) ◽  
pp. 133-147 ◽  
Author(s):  
G. Alia ◽  
F. Barsi ◽  
E. Martinelli
Keyword(s):  
Vlsi Implementation ◽  
Number Systems ◽  
Residue Number Systems ◽  
Residue Number
Sign in / Sign up

Export Citation Format

Share Document