On the implementation of composite-order bilinear groups in cryptographic protocols

In this thesis we present the latest developments in composite-order pairing based cryptography. We first develop the necessary mathematical background. We describe elliptic curves over finite fields, as well as rational functions and divisors on such curves. Bilinear pairings on elliptic curves are explained. We then introduce bilinear groups of composite order and how they are used to create pairing-based cryptosystems. We present two cryptosystems using composite-order groups. We conclude with a discussion of current research.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Sisneros, Severiano

Contributors dc:contributor

• Blahut, Richard E.

• Cryptography
• Bilinear Pairings
• Composite Order Groups

Statement dc:rights

• Copyright 2012 Severiano Sisneros

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/42280

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/42280