Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz [3] and Victor Miller [5]. 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. 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 factoring problem, there is no subexponential-timealgorithm known for the ECDLP. Consequently, significantly smaller parameters can be selected for elliptic curve schemes than for ordinary discrete loga-rithm schemes or for RSA, and achieve the same level of security. Smaller parameters can poten-tially result in significant...
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Hankerson, D., Menezes, A. (2005). Elliptic Curve Cryptography. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_131
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