Elliptic Curves in Cryptography

Megan Ly

Elliptic Curves in Cryptography

Megan Ly

Research output: Thesis › Honors Thesis

Abstract

Elliptic curves have a rich algebraic structure which can, in fact, be used in applications to cryptography. In this paper we give the necessary background to understand a few such applications. We define the group formed by rational points on an elliptic curve and then, working with curves over finite fields, show how divisors can be used to define the Weil Pairing. Two applications to cryptography are explained: Lenstra's Elliptic Curve Method, inspired by Pollard's p - 1 algorithm, and Joux's three party key exchange, extending the idea of a two-party key exchange such as Diffie-Hellman.

Original language	English
Awarding Institution	Loyola Marymount University
Supervisors/Advisors	Khadjavi, Lily, Advisor
State	Published - May 4 2012
Externally published	Yes

Access to Document

http://digitalcommons.lmu.edu/honors-thesis/50

Cite this

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title = "Elliptic Curves in Cryptography",

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N2 - Elliptic curves have a rich algebraic structure which can, in fact, be used in applications to cryptography. In this paper we give the necessary background to understand a few such applications. We define the group formed by rational points on an elliptic curve and then, working with curves over finite fields, show how divisors can be used to define the Weil Pairing. Two applications to cryptography are explained: Lenstra's Elliptic Curve Method, inspired by Pollard's p - 1 algorithm, and Joux's three party key exchange, extending the idea of a two-party key exchange such as Diffie-Hellman.

AB - Elliptic curves have a rich algebraic structure which can, in fact, be used in applications to cryptography. In this paper we give the necessary background to understand a few such applications. We define the group formed by rational points on an elliptic curve and then, working with curves over finite fields, show how divisors can be used to define the Weil Pairing. Two applications to cryptography are explained: Lenstra's Elliptic Curve Method, inspired by Pollard's p - 1 algorithm, and Joux's three party key exchange, extending the idea of a two-party key exchange such as Diffie-Hellman.

M3 - Honors Thesis

ER -