A Parallel Algorithm for Dot Product over Word-Size Finite Field Using Floating-Point Arithmetic

2010 ◽  
Author(s):  
Je Jean ◽  
Stef Graillat
Keyword(s):  
Finite Field ◽  
Parallel Algorithm ◽  
Floating Point ◽  
Word Size ◽  
Floating Point Arithmetic ◽  
Dot Product ◽  
Point Arithmetic

Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials

2016 ◽  
Vol 26 (07) ◽  
pp. 1650112 ◽  
Author(s):  
Ali Shakiba ◽  
Mohammad Reza Hooshmandasl ◽  
Mohsen Alambardar Meybodi
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key ◽  
Floating Point ◽  
Real Numbers ◽  
Public Key Cryptosystems ◽  
Floating Point Arithmetic ◽  
Security Models ◽  
Point Arithmetic

In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.

scholarly journals Numerical algorithms for high-performance computational science

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190066 ◽  
Author(s):  
Jack Dongarra ◽  
Laura Grigori ◽  
Nicholas J. Higham
Keyword(s):  
High Performance ◽  
Numerical Algorithms ◽  
Computational Science ◽  
Floating Point ◽  
Important Criterion ◽  
Data Movement ◽  
Floating Point Arithmetic ◽  
High Performance Computers ◽  
Point Arithmetic ◽  
Speed And Accuracy

A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

Fast and robust mesh arrangements using floating-point arithmetic

2020 ◽  
Vol 39 (6) ◽  
pp. 1-16
Author(s):  
Gianmarco Cherchi ◽  
Marco Livesu ◽  
Riccardo Scateni ◽  
Marco Attene
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic

Floating-point arithmetic with 84-bit numbers

1964 ◽  
Vol 7 (1) ◽  
pp. 10-13 ◽  
Author(s):  
Robert T. Gregory ◽  
James L. Raney
Keyword(s):  
Floating Point ◽  
Floating Point Arithmetic ◽  
Point Arithmetic
Sign in / Sign up

Export Citation Format

Share Document