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A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography

Wilcox, Nicholas
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473

Abstract Details

2018, BA, Oberlin College, Mathematics.
At its core, cryptography relies on problems that are simple to construct but difficult to solve unless certain information (the “key”) is known. Many of these problems come from number theory and group theory. One method of obtaining groups from which to build cryptosystems is to define algebraic curves over finite fields and then derive a group structure from the set of points on those curves. This thesis serves as an exposition of Elliptic Curve Cryptography (ECC), preceded by a discussion of some basic cryptographic concepts and followed by a glance into one generalization of ECC: cryptosystems based on hyperelliptic curves.
Benjamin Linowitz (Advisor)
22 p.
Computer Science; Mathematics
algebraic geometry; computational complexity; cryptography; discrete logarithm problem; elliptic curve cryptography; finite fields; group theory; hyperelliptic curve cryptography

Recommended Citations

Citations

  • Wilcox, N. (2018). A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography [Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473

    APA Style (7th edition)

  • Wilcox, Nicholas. A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography. 2018. Oberlin College, Undergraduate thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473.

    MLA Style (8th edition)

  • Wilcox, Nicholas. "A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography." Undergraduate thesis, Oberlin College, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473

    Chicago Manual of Style (17th edition)

oberlin1528649455201473
625
© 2018, some rights reserved.Creative Commons License A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography by Nicholas Wilcox is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.