On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems

The group of the elliptic curve points forms an abelian group, which is considered as a suitable choice for constructing a problem similar to the Discrete Logarithm Problem. This creates and opens a new door for treatments of the special group and new operations. In 2005, Al-Saffar (2005) proposed...

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Main Authors: Al-Saffar, Najlae F. Hameed, Md. Said, Mohamad Rushdan
Format: Article
Language:English
Published: Malaysian Society for Cryptology Research 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30393/
http://psasir.upm.edu.my/id/eprint/30393/1/On%20the%20mathematical%20complexity%20and%20the%20time%20implementation%20of%20proposed%20variants%20of%20elliptic%20curves%20cryptosystems.pdf
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author Al-Saffar, Najlae F. Hameed
Md. Said, Mohamad Rushdan
author_facet Al-Saffar, Najlae F. Hameed
Md. Said, Mohamad Rushdan
author_sort Al-Saffar, Najlae F. Hameed
building UPM Institutional Repository
collection Online Access
description The group of the elliptic curve points forms an abelian group, which is considered as a suitable choice for constructing a problem similar to the Discrete Logarithm Problem. This creates and opens a new door for treatments of the special group and new operations. In 2005, Al-Saffar (2005) proposed two new methods for elliptic curve cryptosystems using the keys from the algorithm of Diffie–Hellman Key Exchange. In addition, she introduced a variant of the ElGamal scheme. Also, three propositions were introduced to develop the Menezes-Vanstone Elliptic Curves Cryptosystem (MVECC). In this paper, we will discuss all of these propositions and will compare them with the original schemes (ElGamal and MVECC) according to the complexity and the time which they took to implement each scheme.
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spelling upm-303932015-09-17T07:18:52Z http://psasir.upm.edu.my/id/eprint/30393/ On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems Al-Saffar, Najlae F. Hameed Md. Said, Mohamad Rushdan The group of the elliptic curve points forms an abelian group, which is considered as a suitable choice for constructing a problem similar to the Discrete Logarithm Problem. This creates and opens a new door for treatments of the special group and new operations. In 2005, Al-Saffar (2005) proposed two new methods for elliptic curve cryptosystems using the keys from the algorithm of Diffie–Hellman Key Exchange. In addition, she introduced a variant of the ElGamal scheme. Also, three propositions were introduced to develop the Menezes-Vanstone Elliptic Curves Cryptosystem (MVECC). In this paper, we will discuss all of these propositions and will compare them with the original schemes (ElGamal and MVECC) according to the complexity and the time which they took to implement each scheme. Malaysian Society for Cryptology Research 2013 Article NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30393/1/On%20the%20mathematical%20complexity%20and%20the%20time%20implementation%20of%20proposed%20variants%20of%20elliptic%20curves%20cryptosystems.pdf Al-Saffar, Najlae F. Hameed and Md. Said, Mohamad Rushdan (2013) On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems. International Journal of Cryptology Research, 4 (1). pp. 42-54. ISSN 1985-5753 http://www.mscr.org.my/ijcr_volumes%204(1).htm
spellingShingle Al-Saffar, Najlae F. Hameed
Md. Said, Mohamad Rushdan
On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title_full On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title_fullStr On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title_full_unstemmed On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title_short On the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
title_sort on the mathematical complexity and the time implementation of proposed variants of elliptic curves cryptosystems
url http://psasir.upm.edu.my/id/eprint/30393/
http://psasir.upm.edu.my/id/eprint/30393/
http://psasir.upm.edu.my/id/eprint/30393/1/On%20the%20mathematical%20complexity%20and%20the%20time%20implementation%20of%20proposed%20variants%20of%20elliptic%20curves%20cryptosystems.pdf