This article is cited in 2 scientific papers (total in 2 papers)
Good and bad uses of elliptic curves in cryptography
N. I. Koblitz
University of Washington
In the first part of this article I describe the construction of cryptosystems using elliptic curves, discuss the Elliptic Curve Discrete Logarithm Problem (upon which the security of all elliptic curve cryptosystems rests), and survey the different types of elliptic curves that can be chosen for cryptographic applications. In the second part I describe three unsuccessful approaches to breaking various cryptosystems by means of liftings to global elliptic curves. I explain how the failure of these attacks is caused by fundamental properties of the global curves.
Key words and phrases:
Public key cryptography, elliptic curve cryptography, discrete logarithm, digital signature, global elliptic curve, index calculus, canonical height, torsion group, uniform boundedness.
MSC: Primary 14G50, 11G05, 94A60; Secondary 11T71, 14H52
Received: February 22, 2002
N. I. Koblitz, “Good and bad uses of elliptic curves in cryptography”, Mosc. Math. J., 2:4 (2002), 693–715
Citation in format AMSBIB
\paper Good and bad uses of elliptic curves in cryptography
\jour Mosc. Math.~J.
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