Current Search: Combinatorial group theory -- Data processing (x)
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Title
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The discrete logarithm problem in non-abelian groups.
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Creator
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Iliâc, Ivana., Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are...
Show moreThis dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are not good candidates for cryptographic applications which rely on the hardness of the GDLP. Results are presented on generalizing existing cryptographic primitives and protocols based on the hardness of the GDLP in non-abelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the Tillich-Zemor hash function, has been cryptanalyzed. In particular, an algorithm for constructing collisions of short length for any input parameter is presented. A series of mathematical results are developed to support the algorithm and to prove existence of short collisions.
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Date Issued
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2010
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PURL
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http://purl.flvc.org/FAU/3356783
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Subject Headings
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Data encryption (Computer science), Computer security, Cryptography, Combinatorial group theory, Data processing, Mapping (Mathematics)
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Format
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Document (PDF)
