{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/42280"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/42280","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the implementation of composite-order bilinear groups in cryptographic protocols","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.","abstract_html":"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. 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