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Definition
Elliptic curve cryptography (ECC) encompasses the design and analysis of public-key cryptographic schemes that can be implemented using elliptic curves.
Background
Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz [5] and Victor Miller [6]. They are the elliptic curve analogues of schemes based on the discrete logarithm problem, where the underlying group is the group of points on an elliptic curve defined over a finite field [1, 3]. See [4] for a historical account of the development and commercial acceptance of ECC.
Theory
The security of all elliptic curve signature schemes, elliptic curve key agreement schemes and elliptic curve public-key encryption schemes is based on the apparent intractability of the elliptic curve discrete logarithm problem (ECDLP). Unlike the case of the ordinary discrete logarithm problem in the multiplicative group of a finite field, or with the integer...
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Recommended Reading
Blake I, Seroussi G, Smart N (1999) Elliptic curves in cryptography, Cambridge University Press Cambridge
Cohen H, Frey G, Avanzi R, Doche C, Lange T, Nguyen K, Vercauteren F (2005) Handbook of elliptic and hyperelliptic curve cryptography, Chapman & Hall/CRC Boca Raton, FL
Hankerson D, Menezes A, Vanstone S (2003) Guide to elliptic curve cryptography, Springer, New York
Hibner Koblitz A, Koblitz N, Menezes A (in press), Elliptic curve cryptography: the serpentine course of a paradigm shift. J Numb Theory
Koblitz N (1987) Elliptic curve cryptosystems. Math Comput 48:203–209
Miller V (1986) Use of elliptic curves in cryptography. Advances in Cryptology—CRYPTO ’85, Lecture Notes in Computer Science, vol 218. Springer, pp 417–426
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Hankerson, D., Menezes, A. (2011). Elliptic Curve Cryptography. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_245
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