Elliptic Curves of Nearly Prime Order

Manoj Gyawali; Daniele Di Tullio

Paper 2020/001

Elliptic Curves of Nearly Prime Order

Manoj Gyawali and Daniele Di Tullio

Abstract

Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. For security purposes, we need an elliptic curve of almost prime order. In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. In practice, this algorithm produces an elliptic curve of order 2 times a prime number. Therefore, these elliptic curves are appropriate for practical uses. Presently, the most known working algorithms for generating elliptic curves of prime order are based on complex multiplication. The advantages of the proposed technique are: it does not require a deep mathe- matical theory, it is easy to implement in any programming language and produces an elliptic curve with a remarkably simple expression.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Elliptic Curve Cryptography(ECC)Quadratic Twist Trace of an Elliptic Curve
Contact author(s): manoj gyawali @ ncit edu np
danieleditullio @ hotmail it
History: 2020-01-02: received
Short URL: https://ia.cr/2020/001
License: CC BY

BibTeX

@misc{cryptoeprint:2020/001,
      author = {Manoj Gyawali and Daniele Di Tullio},
      title = {Elliptic Curves of Nearly Prime Order},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/001},
      year = {2020},
      url = {https://eprint.iacr.org/2020/001}
}