Guide to Elliptic Curve Cryptography

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Guide to Elliptic Curve Cryptography (2004)

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by Aleksandar Jurisic , Alfred J. Menezes

Citations:

609 - 18 self

BibTeX

@ARTICLE{Jurisic04guideto,
    author = {Aleksandar Jurisic and Alfred J. Menezes},
    title = {Guide to Elliptic Curve Cryptography},
    journal = {},
    year = {2004},
    volume = {19},
    pages = {173--193}
}

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Abstract

Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demonstrate why these systems provide relatively small block sizes, high-speed software and hardware implementations, and offer the highest strength-per-key-bit of any known public-key scheme.

Keyphrases

elliptic curve elliptic curve cryptography known public-key scheme public-key cryptography andrew wile algebraic geometry recent proof small block size number theory mathematician serge lang high-speed software elliptic curve cryptosystems primality proving hardware implementation last theorem enormous amount aesthetic reason

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