On the elliptic curves y(2)=x(3)-c with embedding degree one

Date

2011-06-15

Author

Kirlar, Baris Bulent

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In this paper, we give a family of elliptic curves E in the form y(2) = x(3) - c over the prime field F-p with embedding degree k = 1. This was carried out by computing the explicit formula of the number of points #E(F-p) of the elliptic curve y(2) = x(3) - c. Using this computation, we show that the elliptic curve y(2) = x(3) - 1 over F-p for the primes p of the form 27A(2) + 1 has an embedding degree k = 1. Finally, we give examples of those primes p for which the security level of the pairing-based cryptographic protocols on the curve y(2) = x(3) - 1 over F-p is equivalent to 128-, 192-, or 256-bit AES keys.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/64361

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2010.08.020

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. B. Kirlar, “On the elliptic curves y(2)=x(3)-c with embedding degree one,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 4724–4728, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64361.