Finite field is the most popular for Elliptic Curve primes modulo integer domain (see modular arithmetic), or the characteristics of the Galois field GF (2m). Which is calculated on specialized hardware implementations more effective, while the former often are more effective in a general-purpose processor. The patent issue is also relevant. Some other primes Galois field size and capacity have been proposed, but the password experts think there is a little problem. Given an elliptic curve E, ​ ​ and a domain, we consider having a form rationals point Abelian group, where x and y are in and define the group operation on this curve "+" (operation "+" in the article elliptic curve described). We then define a second operator "*" | Z ×: if P is a point on, then we define. Note that given the integers j and k. Elliptic curve discrete logarithm problem (ECDLP) is a given point P and Q, determine the integer k so.- Is generally believed that the discrete logarithm problem (DLP)

ECC\ecc.c
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ECC

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