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dc.contributor.authorKnapp, Edward
dc.date.accessioned2009-01-21 20:33:13 (GMT)
dc.date.available2009-01-21 20:33:13 (GMT)
dc.date.issued2009-01-21T20:33:13Z
dc.date.submitted2008
dc.identifier.urihttp://hdl.handle.net/10012/4208
dc.description.abstractIn 2001, Boneh, Lynn, and Shacham presented a pairing-based signature scheme known as the BLS signature scheme. In 2003, Boneh, Gentry, Lynn, and Shacham presented the first aggregate signature scheme called the BGLS aggregate signature scheme. The BGLS scheme allows for N users with N signatures to combine their signatures into a single signature. The size of the resulting signature is independent of N. The BGLS signature scheme enjoys roughly the same level of security as the BLS scheme. In 2005, Waters presented a pairing-based signature scheme which does not assume the existence of random oracles. In 2007, Lu, Ostrovsky, Sahai, Shacham, and Waters presented the LOSSW aggregate signature scheme which does not assume the existence of random oracles. The BLS, BGLS, Waters, and LOSSW authors each chose to work with a restricted class of pairings. In each scheme, it is clear that the scheme extend to arbitrary pairings. We present the schemes in their full generality, explore variations of the schemes, and discuss optimizations that can be made when using specific pairings. Each of the schemes we discuss is secure assuming that the computational Diffie-Hellman (CDH) assumption holds. We improve on the security reduction for a variation of the BGLS signature scheme which allows for some restrictions of the BGLS signature scheme can be dropped and provides a stronger guarantee of security. We show that the BGLS scheme can be modified to reduce public-key size in presence of a certifying authority, when a certain type of pairing is used. We show that patient-free bit-compression can be applied to each of the scheme with a few modifications.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectmathematicsen
dc.subjectcryptographyen
dc.subjectsignature schemesen
dc.subjectprovable securityen
dc.subjectelliptic curvesen
dc.subjectpublic-key cryptographyen
dc.titleOn Pairing-Based Signature and Aggregate Signature Schemesen
dc.typeMaster Thesisen
dc.comment.hiddenSecond submission. Removed latex from abstract. Added page numbers to reference section.en
dc.pendingfalseen
dc.subject.programCombinatorics and Optimizationen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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