Elliptic Curves of Nearly Prime Order

Daniele Di Tullio; Manoj Gyawali

doi:10.1007/978-3-030-80129-8_61

Elliptic Curves of Nearly Prime Order

Daniele Di Tullio^*
, Manoj Gyawali^*

^*Corresponding author for this work

Roma Tre University

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

1 Citation (Scopus)

Abstract

Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. Precisely, this algorithm produces an elliptic curve of cofactor 2. Presently, the most known working algorithms for generating elliptic curves of prime order are based on complex multiplication. The advantages of proposed algorithm are: it is relatively simple, easy to implement and produces an elliptic curve of a remarkably simple expression.

Original language	English
Title of host publication	Intelligent Computing - Proceedings of the 2021 Computing Conference
Editors	Kohei Arai
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	923-932
Number of pages	10
ISBN (Print)	9783030801281
DOIs	https://doi.org/10.1007/978-3-030-80129-8_61
Publication status	Published - 2021
Event	Computing Conference, 2021 - Virtual, Online Duration: 15 Jul 2021 → 16 Jul 2021

Publication series

Name	Lecture Notes in Networks and Systems
Volume	285
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	Computing Conference, 2021
City	Virtual, Online
Period	15/07/21 → 16/07/21

Keywords

Elliptic Curve Cryptography (ECC)
Elliptic Curve Discrete Logarithm Problem (ECDLP)
Miller-Rabin primality test
Trace of an elliptic curve

Access to Document

10.1007/978-3-030-80129-8_61

Cite this

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title = "Elliptic Curves of Nearly Prime Order",

abstract = "Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. Precisely, this algorithm produces an elliptic curve of cofactor 2. Presently, the most known working algorithms for generating elliptic curves of prime order are based on complex multiplication. The advantages of proposed algorithm are: it is relatively simple, easy to implement and produces an elliptic curve of a remarkably simple expression.",

keywords = "Elliptic Curve Cryptography (ECC), Elliptic Curve Discrete Logarithm Problem (ECDLP), Miller-Rabin primality test, Trace of an elliptic curve",

author = "\{Di Tullio\}, Daniele and Manoj Gyawali",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.; Computing Conference, 2021 ; Conference date: 15-07-2021 Through 16-07-2021",

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language = "English",

isbn = "9783030801281",

series = "Lecture Notes in Networks and Systems",

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}

Di Tullio, D & Gyawali, M 2021, Elliptic Curves of Nearly Prime Order. in K Arai (ed.), Intelligent Computing - Proceedings of the 2021 Computing Conference. Lecture Notes in Networks and Systems, vol. 285, Springer Science and Business Media Deutschland GmbH, pp. 923-932, Computing Conference, 2021, Virtual, Online, 15/07/21. https://doi.org/10.1007/978-3-030-80129-8_61

Elliptic Curves of Nearly Prime Order. / Di Tullio, Daniele; Gyawali, Manoj.
Intelligent Computing - Proceedings of the 2021 Computing Conference. ed. / Kohei Arai. Springer Science and Business Media Deutschland GmbH, 2021. p. 923-932 (Lecture Notes in Networks and Systems; Vol. 285).

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

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AU - Gyawali, Manoj

PY - 2021

Y1 - 2021

N2 - Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. Precisely, this algorithm produces an elliptic curve of cofactor 2. Presently, the most known working algorithms for generating elliptic curves of prime order are based on complex multiplication. The advantages of proposed algorithm are: it is relatively simple, easy to implement and produces an elliptic curve of a remarkably simple expression.

AB - Constructing an elliptic curve of prime order has a significant role in elliptic curve cryptography. In this paper, we propose an efficient technique to generate an elliptic curve of nearly prime order. Precisely, this algorithm produces an elliptic curve of cofactor 2. Presently, the most known working algorithms for generating elliptic curves of prime order are based on complex multiplication. The advantages of proposed algorithm are: it is relatively simple, easy to implement and produces an elliptic curve of a remarkably simple expression.

KW - Elliptic Curve Cryptography (ECC)

KW - Elliptic Curve Discrete Logarithm Problem (ECDLP)

KW - Miller-Rabin primality test

KW - Trace of an elliptic curve

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DO - 10.1007/978-3-030-80129-8_61

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PB - Springer Science and Business Media Deutschland GmbH

T2 - Computing Conference, 2021

Y2 - 15 July 2021 through 16 July 2021

ER -

Elliptic Curves of Nearly Prime Order

Abstract

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Keywords

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