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The Research Progress of Elliptic Curves Cryptosystem

Xiao Zhang

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Abstract

In this paper, the research progress of elliptic curves cryptosystem are summarized. The development and mathematics foundation of elliptic curves cryptosystem are simply described. Introduction is given to some cryptographic algorithms supported by elliptic curves and their actual application and related standards. Finally we analyze the attack present condition, point out the research direction of this kind of cryptosystem.

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What this paper is about

In this paper, the research progress of elliptic curves cryptosystem are summarized. The development and mathematics foundation of elliptic curves cryptosystem are simply described. Introduction is given to some cryptographic algorithms supported by elliptic curves and their actual application and related standards. Finally we analyze the attack present condition, point out the research direction of this kind of cryptosystem.

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Available abstract

In this paper, the research progress of elliptic curves cryptosystem are summarized. The development and mathematics foundation of elliptic curves cryptosystem are simply described. Introduction is given to some cryptographic algorithms supported by elliptic curves and their actual application and related standards. Finally we analyze the attack present condition, point out the research direction of this kind of cryptosystem.

Key concepts: Cryptosystem, Elliptic curve, Elliptic curve cryptography, Elliptic curve point multiplication, Curve25519, Computer science, Point (geometry), Hybrid cryptosystem

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