Cryptology ePrint Archive: Report 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.

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)

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