You are here
discrete logarithm problem in nonabelian groups
 Date Issued:
 2010
 Summary:
 This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in nonabelian 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 nonabelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the TillichZemor 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.
Title:  The discrete logarithm problem in nonabelian groups. 
137 views
46 downloads 

Name(s): 
Iliâc, Ivana. Charles E. Schmidt College of Science Department of Mathematical Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2010  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  vii, 94 p. : ill. (some col.)  
Language(s):  English  
Summary:  This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in nonabelian 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 nonabelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the TillichZemor 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.  
Identifier:  702127124 (oclc), 3356783 (digitool), FADT3356783 (IID), fau:3978 (fedora)  
Note(s): 
by Ivana Iliâc. Thesis (Ph.D.)Florida Atlantic University, 2010. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web. FboU 

Subject(s): 
Data encryption (Computer science) Computer security Cryptography Combinatorial group theory  Data processing Mapping (Mathematics) 

Persistent Link to This Record:  http://purl.flvc.org/FAU/3356783  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 