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Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem

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dc.contributor.authorYoshida, Kayo
dc.date.accessioned2009-01-22T16:15:47Z
dc.date.available2009-01-22T16:15:47Z
dc.date.issued2009-01-22T16:15:47Z
dc.date.submitted2009
dc.description.abstractThe Boneh-Boyen signature scheme is a short signature scheme which is provably secure in the standard model under the q-Strong Diffie-Hellman (SDH) assumption. The primary objective of this thesis is to examine the relationship between the Boneh-Boyen signature scheme and SDH. The secondary objective is to survey surrounding topics such as the generic group model, related signature schemes, intractability assumptions, and the relationship to identity-based encryption (IBE) schemes. Along these lines, we analyze the plausibility of the SDH assumption using the generic bilinear group model. We present the security proofs for the Boneh-Boyen signature scheme, with the addition of a small improvement in one of the probability bounds. Our main contribution is to give the reduction in the reverse direction; that is, to show that if the SDH problem can be solved then the Boneh-Boyen signature scheme can be forged. This contribution represents the first known proof of equivalence between the SDH problem and Boneh-Boyen signatures. We also discuss the algorithm of Cheon for solving the SDH problem. We analyze the implications of Cheon's algorithm for the security of the Boneh-Boyen signature scheme, accompanied by a brief discussion on how to counter the attack.en
dc.identifier.urihttp://hdl.handle.net/10012/4219
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectcryptographyen
dc.subjectdigital signaturesen
dc.subjectsignature schemeen
dc.subjectDiffie-Hellmanen
dc.subjectStrong Diffie-Hellmanen
dc.subjectSDHen
dc.subjectBoneh-Boyen signaturesen
dc.subjectPollard rhoen
dc.subjectPollard lambdaen
dc.subjectbaby-step giant-stepen
dc.subjectassumptionsen
dc.subjectshort signaturesen
dc.subjectrandom oracleen
dc.subjectgeneric groupen
dc.subjectBLSen
dc.subjectWatersen
dc.subjectOkamotoen
dc.subjectidentity-based encryptionen
dc.subjectIBEen
dc.subjectCheon's algorithmen
dc.subjectpartial fractionen
dc.subjectsecurityen
dc.subjectexistential forgeryen
dc.subject.programCombinatorics and Optimizationen
dc.titleBoneh-Boyen Signatures and the Strong Diffie-Hellman Problemen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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Combinatorics and Optimization