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Elliptic Curves in Cryptography

1999
In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As digital signatures become more and more important in the commercial world the use of elliptic curve-
Blake, I F, Seroussi, G, Smart, N P
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Arithmatic of Elliptic Curves and Use in Cryptography

2006 IEEE 14th Signal Processing and Communications Applications, 2006
In this study, first of all, we categorized encryption algorithms and exposed the structure and specifications of the symmetric and asymmetric algorithms. We explained that asymmetric encryption algorithms are based on hard problems (NP) and explained what these problems are. In addition, we showed how addition and doubling are realized on the elliptic
Yerlikaya, Tarik   +2 more
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Elliptic Curve Cryptography

2010
Elliptic curve cryptography, in essence, entails using the group of points on an elliptic curve as the underlying number system for public key cryptography. There are two main reasons for using elliptic curves as a basis for public key cryptosystems.
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Elliptic curve cryptography

Proceedings of the 1st annual conference on Information security curriculum development, 2004
The use of Java in developing commercial Internet applications is growing very rapidly. A major requirement for e-commerce applications is the provision of security. In this work we consider Elliptic Curve Cryptography (ECC) because of the high level of security it provides with small key sizes.
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Applications of elliptic curve cryptography

Proceedings of the 12th Annual Conference on Cyber and Information Security Research, 2017
Elliptic curve cryptography (ECC) is a relatively newer form of public key cryptography that provides more security per bit than other forms of cryptography still being used today. We explore the mathematical structure and operations of elliptic curves and how those properties make curves suitable tools for cryptography.
R. Harkanson, Y. Kim
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Elliptic Curve Cryptography

International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2022
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Elliptic curve cryptography in Java

2015 IEEE International Conference on Intelligence and Security Informatics (ISI), 2015
The strength of public key cryptography utilizing Elliptic Curves relies on the difficulty of computing discrete logarithms in a finite field. Other public key cryptographic algorithms, such as RSA, rely on the difficulty of integer factorization.
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Elliptic Curves and Cryptography

2003
In the earlier cryptography articles, we have seen classical cryptosystems, various public-key cryptosystems and many primality tests. In this article we shall see how elliptic curves are used in cryptography. When public-key cryptography was introduced to the research community by Diffe and Hellman in 1976 [4], it represented an exciting innovation in
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Elliptic Curve Cryptography

2018
Just the same as DLP, ECDLP (Elliptic Curve Discrete Logarithm Problem) is also hard to solve, so it is natural to think about designing cryptographic system based on ECDLP. In this chapter we shall first discuss the Elliptic Curve Discrete Logarithm Problem (ECDLP) and the classical solutions to ECDLP, then we shall present some popular and useful ...
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Elliptic Curve Cryptography

2006
Darrel Hankerson, Alfred Menezes
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