Article

Variation on variation on Euclid's algorithm

France Telecom Res. & Dev., Cesson-Sevigne, France
IEEE Signal Processing Letters (impact factor: 1.39). 06/2004; DOI:10.1109/LSP.2004.824053 pp.457 - 458
Source: IEEE Xplore

ABSTRACT In a paper entitled "Variation on Euclid's Algorithm for Plynomials", Calvez et al. has shown that the extended Euclid's algorithm can be partially obtained by the nonextended one; in fact, it can obtain only two of the three unknowns of the Bezout's theorem. This letter goes further and shows that all polynomials given by the extended Euclid's algorithm and all the intermediate values can be obtained directly by the nonextended Euclid's algorithm. Consequently, only remainder computations are used. Avoiding multiplications and divisions of polynomials decreases the computational complexity. This variation of Calvez et al. justifies the title of the present letter.

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    Article: Computing the Modular Inverse of a Polynomial Function over GF(2^P) Using Bit Wise Operation
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    [show abstract] [hide abstract]
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Keywords

Avoiding multiplications
 
Bezout's theorem
 
computational complexity
 
divisions
 
Euclid's Algorithm
 
extended Euclid's algorithm
 
intermediate values
 
nonextended
 
nonextended Euclid's algorithm
 
Plynomials"
 
polynomials
 
polynomials decreases
 
present letter
 
three unknowns