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dc.contributor.authorKim, Kyung-Mien
dc.date.accessioned2006-08-22 14:27:09 (GMT)
dc.date.available2006-08-22 14:27:09 (GMT)
dc.date.issued2003en
dc.date.submitted2003en
dc.identifier.urihttp://hdl.handle.net/10012/1118
dc.description.abstractLet <b>A</b> and <b>B</b> be finite sets with |<b>A</b>|=<i>n</i> and |<b>B</b>|=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)-<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> such that for any <b>X</b> &#8838; <b>A</b> with |<b>X</b>|=<i>w</i>, there exists at least one ? &#8712; <i>F</i> such that ? is one-to-one when restricted to <b>X</b>. Perfect hash families are basic combinatorial structures and they have played important roles in Computer Science in areas such as database management, operating systems, and compiler constructions. Such hash families are used for memory efficient storage and fast retrieval of items such as reserved words in programming languages, command names in interactive systems, or commonly used words in natural languages. More recently, perfect hash families have found numerous applications to cryptography, for example, to broadcast encryption schemes, secret sharing, key distribution patterns, visual cryptography, cover-free families and secure frameproof codes. In this thesis, we survey constructions and applications of perfect hash families. For constructions, we divided the results into three parts, depending on underlying structure and properties of the constructions: combinatorial structures, linear functionals, and algebraic structures. For applications, we focus on those related to cryptography.en
dc.formatapplication/pdfen
dc.format.extent755109 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.rightsCopyright: 2003, Kim, Kyung-Mi. All rights reserved.en
dc.subjectMathematicsen
dc.subjectPerfect Hash Familiesen
dc.subjectCombinatorial Structuresen
dc.subjectCryptographyen
dc.subjectProbability Methodsen
dc.titlePerfect Hash Families: Constructions and Applicationsen
dc.typeMaster Thesisen
dc.pendingfalseen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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