Square and Cube Root Algorithms in Finite Field and Their Applications 


Vol. 37,  No. 12, pp. 1031-1037, Dec.  2012


PDF
  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.

  Statistics
Cumulative Counts from November, 2022
Multiple requests among the same browser session are counted as one view. If you mouse over a chart, the values of data points will be shown.


  Cite this article

[IEEE Style]

G. H. Cho, E. Ha, N. Koo, S. Kwon, "Square and Cube Root Algorithms in Finite Field and Their Applications," The Journal of Korean Institute of Communications and Information Sciences, vol. 37, no. 12, pp. 1031-1037, 2012. DOI: .

[ACM Style]

Gook Hwa Cho, Eunhye Ha, Namhun Koo, and Soonhak Kwon. 2012. Square and Cube Root Algorithms in Finite Field and Their Applications. The Journal of Korean Institute of Communications and Information Sciences, 37, 12, (2012), 1031-1037. DOI: .

[KICS Style]

Gook Hwa Cho, Eunhye Ha, Namhun Koo, Soonhak Kwon, "Square and Cube Root Algorithms in Finite Field and Their Applications," The Journal of Korean Institute of Communications and Information Sciences, vol. 37, no. 12, pp. 1031-1037, 12. 2012.

Search
(IN TITLE, AUTHOR, ABSTRACT,KEYWORDS)

Advanced Search ▼

POPULAR KEYWORDS
(TOP 10 KEYWORDS)

Recent Publications
(LAST 3 YEARS)






pISSN : 1226 - 4717
eISSN : 2287 - 3880