Calculation of extended gcd by normalization
Marc Wolf, Fran\c{c}ois Wolf, Corentin Le Coz
TL;DR
This paper introduces a new elementary arithmetic-based algorithm for calculating the extended gcd, which finds solutions that minimize one coordinate, improving efficiency in certain computational contexts.
Contribution
The paper presents a novel algorithm for extended gcd calculation that minimizes one coordinate, based on elementary arithmetic properties, offering a potentially more efficient solution.
Findings
Algorithm successfully computes extended gcd with minimized coordinate
Uses elementary arithmetic properties for simplicity and efficiency
Potential applications in computational number theory and cryptography
Abstract
We propose a new algorithm solving the extended gcd problem, which provides a solution minimizing one of the two coordinates. The algorithm relies on elementary arithmetic properties.
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Taxonomy
TopicsAlgorithms and Data Compression · Numerical Methods and Algorithms · Cryptography and Residue Arithmetic