IJPAM: Volume 77, No. 3 (2012)

ID-BASED SIGNATURE SCHEME USING
THE CONIC CURVE OVER $Z_{n}$
ON TWO HARD PROBLEMS

Nedal Tahat$^1$, E.S. Ismail$^2$, Feras Bani-Ahmad$^3$
$^{1,3}$ Department of Mathematics
Faculty of Sciences
The Hashemite University
Zarqa 13133, JORDAN
$^2$School of Mathematical
Faculty of Science and Technology
National University of Malaysia
43600, UKM, Bangi, Selangor, MALAYSIA


Abstract. This paper proposes a new identity signature scheme on the conic curve over $Z_{n}$. The scheme security is based on the factoring and discrete logarithms simultaneously. The paper gives the representation of the order and base point on $C_{n}(a,b)$, and introduces the representation of operation by parameters to simplify its calculation. The major advantage of our scheme is that it is very unlikely that the two assumptions can be efficiently solved simultaneously, and therefore offers a longer/higher security than that scheme based on a single cryptographic assumption. Furthermore,the numeric simulation for our scheme is presented. Some possible attacks will be considered, and our security analysis will show that none of them can successfully break any proposed schemes. In addition, our scheme protects the signer from chosen-message attack and also identifies a forged signature.

Received: March 31, 2012

AMS Subject Classification:

Key Words and Phrases: digital signature scheme, identification scheme, conic curve over $Z_{n}$, factoring problems, chosen message attack

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 3