On the implementation of composite-order bilinear groups in cryptographic protocols
Sisneros, Severiano
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https://hdl.handle.net/2142/42280
Description
Title
On the implementation of composite-order bilinear groups in cryptographic protocols
Author(s)
Sisneros, Severiano
Issue Date
2013-02-03T19:30:10Z
Director of Research (if dissertation) or Advisor (if thesis)
Blahut, Richard E.
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Cryptography
Bilinear Pairings
Composite Order Groups
Abstract
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.
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