منابع مشابه
Algebraic curves and cryptography
Algebraic curves over finite fields are being extensively used in the design of public-key cryptographic schemes. This paper surveys some topics in algebraic curve cryptography, with an emphasis on recent developments in algorithms for the elliptic and hyperelliptic curve discrete logarithm problems, and computational problems in pairing-based cryptography.
متن کاملElliptic Curves and Cryptography
results in more than 30.000 hits, ranging from articles in mathematics and computer science to books and implementations and applications of the algorithms. There are a lot of different algorithms and also different ways to attack them, many of them involving a huge amount of theory. Moreover, the fact that still there is not an accepted standard on elliptic curve cryptography benefits the exis...
متن کاملElliptic Curves and Cryptography
Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demo...
متن کاملElliptic Curves and Cryptography
This paper begins by discussing the foundations of the study of elliptic curves and how a the points on an elliptic curve form an additive group. We then explore some of the interesting features of elliptic curves, including the fact that elliptic curves are complex tori. At the end we briefly discuss how elliptic curves can be used in cryptography.
متن کاملHyperelliptic Curves and Cryptography
In 1989, Koblitz proposed using the jacobian of a hyperelliptic curve defined over a finite field to implement discrete logarithm cryptographic protocols. This paper provides an overview of algorithms for performing the group law (which are necessary for the efficient implementation of the protocols), and algorithms for solving the hyperelliptic curve discrete logarithm problem (whose intractab...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2005
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2005.05.001