Square and Cube Root Algorithms in Finite Field and Their Applications

- Journal title : The Journal of Korean Institute of Communications and Information Sciences
- Volume 37A, Issue 12, 2012, pp.1031-1037
- Publisher : The Korean Institute of Communications and Information Sciences
- DOI : 10.7840/kics.2012.37A.12.1031

Title & Authors

Square and Cube Root Algorithms in Finite Field and Their Applications

Cho, Gook Hwa; Ha, Eunhye; Koo, Namhun; Kwon, Soonhak;

Cho, Gook Hwa; Ha, Eunhye; Koo, Namhun; Kwon, Soonhak;

Abstract

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

Keywords

NFS;Tonelli-Shanks algorithm;CRT;Finite Field;

Language

Korean

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