Results 321 to 330 of about 177,129 (337)

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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The State of Elliptic Curve Cryptography

2000
Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffie and Hellman was defined explicitly as the problem of finding logarithms with respect to a ...
Scott A. Vanstone, Alfred Menezes, Neal Koblitz   +2 more
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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 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 on WISPs

2013
In this chapter, the authors explore the feasibility of Elliptic Curve Cryptography (ECC) on Wireless Identification and Sensing Platforms (WISPs). ECC is a public-key based cryptographic primitive that has been widely adopted in embedded systems and Wireless Sensor Networks (WSNs).
Michael Hutter, Erich Wenger, Markus Pelnar, Christian Pendl   +3 more
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Supersingular Elliptic Curves in Cryptography

2007
I will survey the checkered history of supersingular elliptic curves in cryptography, from their first consideration in the seminal papers of Koblitz and Miller, to their rejection after the discovery of the Weil and Tate pairing attacks on the discrete logarithm problem for these curves, and concluding with their resurrection alongside the discovery ...
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An Introduction to Elliptic Curve Cryptography

2012
This chapter presents an introduction to elliptic curve cryptography. Elliptic curves provide an important source of finite abelian groups in which cryptographic schemes relying on the hardness of the discrete logarithm problem (DLP) can be implemented.
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Cryptography based on elliptic curves

2014
A plane curve X over the field F is the set of points ( x, y ) in the plane F 2 that are the zeros of some fixed irreducible bivariate polynomial p(x, y ) over F . If one can define a pairwise operation ( x, y ) + ( x ′, y ′) taking any two points ( x, y ) and ( x ′, y ′) of the curve into a third point of the curve so as to form an ...
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ECC — Elliptic Curves Cryptography [PDF]

, 2010
Wie versprochen, mochte ich nach dem Gruppengesetz elliptischer Kurven nun die hervorstechendste Anwendung elliptischer Kurven in der Praxis vorstellen: Die Verwendung in der Kryptographie. Insbesondere gehe ich dabei auf Schlusselaustausch. asymmetrische Ver- und Entschlusselung sowie Signierung mit Hilfe von elliptischen Kurven ein.
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Overview of elliptic curve cryptography

1998
In this article, we look at the elliptic curve cryptography, which is believed to be one of the most promising candidates for the next generation cryptographic tool. The following issues are addressed here; 1. Discrete Logarithm Problem in finite fields 2. Elliptic Curve Discrete Logs 3.
Kiyomichi Araki, Takakazu Satoh, Shinji Miura   +2 more
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