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Elliptic curve cryptography (ECC) is an approach to publickey cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz^{[1]} and Victor S. Miller^{[2]} in 1985.
Elliptic curves are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization.
Contents
Introduction
Publickey cryptography is based on the intractability of certain mathematical problems. Early publickey systems, such as the RSA algorithm, are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors. For ellipticcurvebased protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publiclyknown base point is infeasible. The size of the elliptic curve determines the difficulty of the problem. It is believed that the same level of security afforded by an RSAbased system with a large modulus can be achieved with a much smaller elliptic curve group. Using a small group reduces storage and transmission requirements.
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