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The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography, 2000This paper surveys the elliptic curve cryptography that is based on the discrete logarithm problem. Compared to their counterparts in groups of integers, elliptic curves usually provide smaller keys and lower computational complexities. The paper gives a brief overview of elliptic curves, discusses the elliptic curve discrete logarithm problem and ...
Scott A. Vanstone +2 more
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2021
In this chapter, we briefly motivate the use of asymmetric cryptography based on ECC systems for applications in resource-constrained devices like flash memory controllers. We review applications and fundamentals of elliptic curve cryptography, the corresponding one-way function, i.e. the so-called PM, as well as associated group laws.
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In this chapter, we briefly motivate the use of asymmetric cryptography based on ECC systems for applications in resource-constrained devices like flash memory controllers. We review applications and fundamentals of elliptic curve cryptography, the corresponding one-way function, i.e. the so-called PM, as well as associated group laws.
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1999 Information Theory and Networking Workshop (Cat. No.99EX371), 2003
Elliptic curve (EC) public key cryptosystems were proposed independently in 1985 by Victor Miller and Neal Koblitz and are gaining favor as an efficient and attractive alternative to the more conventional public key cryptosystems (e.g., RSA) in some applications.
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Elliptic curve (EC) public key cryptosystems were proposed independently in 1985 by Victor Miller and Neal Koblitz and are gaining favor as an efficient and attractive alternative to the more conventional public key cryptosystems (e.g., RSA) in some applications.
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Elliptic Curves and Cryptography
2014The subject of elliptic curves encompasses a vast amount of mathematics. Our aim in this section is to summarize just enough of the basic theory for cryptographic applications. For additional reading, there are a number of survey articles and books devoted to elliptic curve cryptography [14, 68, 81, 135], and many others that describe the number ...
Joseph H. Silverman +2 more
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Investigation into the elliptic curve cryptography
2017 3rd International Conference on Information Management (ICIM), 2017Elliptic curve cryptography (ECC) in TLS, PGP and SSH, which are just three of the main technologies on which the modern web and IT world are based. However, Compared with RSA public key algorithm, ECC is mysterious and not understandable to most. Few literatures introduce how to partition the plaintext into blocks for ECC and how to map the digital ...
Xianjin Fang, Yanting Wu
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Research on elliptic curve cryptography
8th International Conference on Computer Supported Cooperative Work in Design, 2004There are many drawbacks in current encryption algorithms in respect of security, real-time performance and so on, and researchers are presenting various algorithms. Among them, the elliptic curve cryptography (ECC) is evolving as an important cryptography, and shows a promise to be an alternative of RSA.
Qianxing Xiong, Qizhi Qiu
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Elliptic curve cryptography in Java
2015 IEEE International Conference on Intelligence and Security Informatics (ISI), 2015The 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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Advances in Elliptic Curve Cryptography [PDF]
, 2005 Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great ...
Blake, Ian +2 more
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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, 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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Arithmatic of Elliptic Curves and Use in Cryptography
2006 IEEE 14th Signal Processing and Communications Applications, 2006In 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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