**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.

**Category / Keywords: **public-key cryptography / Elliptic Curve Cryptography(ECC), Elliptic Curve Discrete Logarithm Problem(ECDLP), Quadratic Twist, Trace of an Elliptic Curve

**Date: **received 1 Jan 2020, last revised 1 Jan 2020

**Contact author: **manoj gyawali at ncit edu np,danieleditullio@hotmail it

**Available format(s): **PDF | BibTeX Citation

**Version: **20200102:230253 (All versions of this report)

**Short URL: **ia.cr/2020/001

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