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Elliptic Curve Cryptography Implementation and Security Analysis

Author: ZhaoYunHui
Tutor: JiangWaiWenï¼›YinShuangYun
School: Central South University
Course: Software Engineering
Keywords: Elliptic Curve Elliptic curve discrete logarithm ECC Algorithm Security
CLC: TN918.1
Type: Master's thesis
Year: 2005
Downloads: 358
Quote: 3
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Abstract


Elliptic Curve Cryptography its special advantages and password information security has attracted academic attention , from the safety and efficacy of view, this cryptosystem has broad prospects , generally agreed that it would replace the current general RSA cryptosystem and a new generic public key cryptography . Elliptic Curve Cryptography has become the mainstream of public key cryptography research , has now become public key cryptography in the research and development of hot spots. And as elliptic curve cryptosystem is based on a finite field defined by the points on the elliptic curve additive Abelian group consisting of a collection , which can be defined as the discrete logarithm, ie the elliptic curve discrete logarithm. This paper systematically discusses the theory of Elliptic Curve Cryptography Research , describes the basic algorithms on elliptic curves and elliptic curve cryptography fundamental nature , focused on the determination of finite fields ; secure elliptic curve and base point selection algorithm selection algorithm ; ECC fast algorithm design and implementation ; elliptic curve cryptosystem security. Compared with the classic ECC public key cryptography system between the merits ; secure elliptic curve structure and basis of selection is achieved elliptic curve cryptography key . Scalar multiplication is the impact ECC to achieve a critical step in accelerating the scalar multiplication implementation of ECC to improve the speed , is the ECC to achieve an important research topic. On the elliptic curve discrete logarithm problem algorithm, attacks can challenge elliptic curve case , secure elliptic curve selection, comparison with other public-key cryptography gives a detailed exposition reflects the latest achievements in the field , and the future of ECC possible direction of development and research content made ??observations . Description ECC public key cryptosystem than other encryption strength can provide better , faster and smaller key length, so a smaller overhead and delay can achieve high security.

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