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Entropy 2014, 16(9), 5144-5158;

Nonlinearities in Elliptic Curve Authentication

Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah Campus, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Informatics, University of Craiova, Street A.I Cuza 13, 200585 Craiova, Romania
Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Author to whom correspondence should be addressed.
Received: 2 September 2014 / Accepted: 19 September 2014 / Published: 25 September 2014
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
Full-Text   |   PDF [233 KB, uploaded 24 February 2015]


In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these solutions. Optimization in this area means finding the majority of points on the elliptic curve and minimizing the time to compute the solution in contrast with the necessary time to compute the inverse solution. We can compute the positive solution of PDE (partial differential equation) like oscillations of f(s)/s around the principal eigenvalue λ1 of -Δ in H 0 1 (Ω).Translating mathematics into cryptographic applications will be relevant in everyday life, where in there are situations in which two parts that communicate need a third part to confirm this process. For example, if two persons want to agree on something they need an impartial person to confirm this agreement, like a notary. This third part does not influence in anyway the communication process. It is just a witness to the agreement. We present a system where the communicating parties do not authenticate one another. Each party authenticates itself to a third part who also sends the keys for the encryption/decryption process. Another advantage of such a system is that if someone (sender) wants to transmit messages to more than one person (receivers), he needs only one authentication, unlike the classic systems where he would need to authenticate himself to each receiver. We propose an authentication method based on zero-knowledge and elliptic curves. View Full-Text
Keywords: partial differential equation; elliptic curve; zero knowledge; authentication partial differential equation; elliptic curve; zero knowledge; authentication
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Alsaedi, R.; Constantinescu, N.; Rādulescu, V. Nonlinearities in Elliptic Curve Authentication. Entropy 2014, 16, 5144-5158.

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