Two Cubic Polynomials Selection for the Number Field Sieve 


Vol. 36,  No. 10, pp. 614-620, Oct.  2011


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  Abstract

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

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  Cite this article

[IEEE Style]

G. H. Jo, N. Koo, S. Kwon, "Two Cubic Polynomials Selection for the Number Field Sieve," The Journal of Korean Institute of Communications and Information Sciences, vol. 36, no. 10, pp. 614-620, 2011. DOI: .

[ACM Style]

Gooc Hwa Jo, Namhun Koo, and Soonhak Kwon. 2011. Two Cubic Polynomials Selection for the Number Field Sieve. The Journal of Korean Institute of Communications and Information Sciences, 36, 10, (2011), 614-620. DOI: .

[KICS Style]

Gooc Hwa Jo, Namhun Koo, Soonhak Kwon, "Two Cubic Polynomials Selection for the Number Field Sieve," The Journal of Korean Institute of Communications and Information Sciences, vol. 36, no. 10, pp. 614-620, 10. 2011.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880