Solution of Welch-Berlekamp key equation by Euclidean algorithm

1993 ◽  
Vol 29 (11) ◽  
pp. 1031-1031 ◽  
Author(s):  
W.G. Chambers
Keyword(s):  
Euclidean Algorithm ◽  
Key Equation

scholarly journals The Symmetric Key Equation for Reed–Solomon Codes and a New Perspective on the Berlekamp–Massey Algorithm

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1357
Author(s):  
Maria Bras-Amorós ◽  
Michael E. O’Sullivan
Keyword(s):  
Euclidean Algorithm ◽  
Reed Solomon Codes ◽  
Degree Bounds ◽  
Key Equation ◽  
Symmetric Key ◽  
New Perspective

This paper presents a new way to view the key equation for decoding Reed–Solomon codes that unites the two algorithms used in solving it—the Berlekamp–Massey algorithm and the Euclidean algorithm. A new key equation for Reed–Solomon codes is derived for simultaneous errors and erasures decoding using the symmetry between polynomials and their reciprocals as well as the symmetries between dual and primal codes. The new key equation is simpler since it involves only degree bounds rather than modular computations. We show how to solve it using the Euclidean algorithm. We then show that by reorganizing the Euclidean algorithm applied to the new key equation we obtain the Berlekamp–Massey algorithm.

scholarly journals Public-key cryptosystem based on invariants of diagonalizable groups

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
František Marko ◽  
Alexandr N. Zubkov ◽  
Martin Juráš
Keyword(s):  
Linear Algebra ◽  
Finite Fields ◽  
Number Fields ◽  
Euclidean Algorithm ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Finite Rings

AbstractWe develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).

Current situation and development direction of sports industry in colleges and universities based on euclidean algorithm

2021 ◽  
pp. 1-7
Author(s):  
Shunjiang Ma ◽  
Gaicheng Liu ◽  
Zhiwu Huang
Keyword(s):  
Computer Technology ◽  
Colleges And Universities ◽  
Status Quo ◽  
Euclidean Algorithm ◽  
Test Results ◽  
Sports Industry ◽  
Development Direction ◽  
The Status ◽  
Traditional Sports ◽  
And Function

With the development of sports in colleges and universities, the research on innovation reform of sports industry has been deepened. Therefore, based on the above situation, a study of the status quo and development direction of sports industry in colleges and universities based on the Euclid algorithm is proposed. In the research here, according to the traditional sports industry concept to sum up, and then according to the advantages of computer technology to deal with the relevant data. In order to realize good overlap between data, an application of Euclidean algorithm is proposed. In the test of Euclidean algorithm, the efficiency and function of the algorithm are tested comprehensively, and the test results show that the research is feasible.

scholarly journals Acceleration of Euclidean Algorithm and Rational Number Reconstruction

2003 ◽  
Vol 32 (2) ◽  
pp. 548-556 ◽  
Author(s):  
Xinmao Wang ◽  
Victor Y. Pan
Keyword(s):  
Rational Number ◽  
Euclidean Algorithm

74.6 The Euclidean Algorithm and Fibonacci

1990 ◽  
Vol 74 (467) ◽  
pp. 47 ◽  
Author(s):  
Ian Cook
Keyword(s):  
Euclidean Algorithm
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