2026-09-20T17:21:23Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/42280 2023-07-11 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

Blahut, Richard E. Sisneros, Severiano 2013-02-03T19:30:10Z 2013-02-03T19:30:10Z 2012-12 2013-02-03T19:30:10Z 2012-12 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-09-06T20:05:17Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 sisneros_severiano.pdf: 847055 bytes, checksum: dd480283918f2888e71407b7f27e840f (MD5) Made available in DSpace on 2013-02-03T19:30:10Z (GMT). No. of bitstreams: 2 Severiano_Sisneros.pdf: 847055 bytes, checksum: dd480283918f2888e71407b7f27e840f (MD5) license.txt: 4068 bytes, checksum: 217088c4b3b1af87ce336c6b0548e35b (MD5) http://hdl.handle.net/2142/42280 en Copyright 2012 Severiano Sisneros Cryptography Bilinear Pairings Composite Order Groups On the implementation of composite-order bilinear groups in cryptographic protocols text Electrical & Computer Eng 1933 Electrical & Computer Engr 1200 University of Illinois at Urbana-Champaign Thesis M.S. MS:Electr & Computer Eng-UIUC 10KS1200MS