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Abstract: . In this article we survey recent developments concerning the discrete logarithm problem. Both theoretical and practical results are discussed. We emphasize the case of finite fields, and in particular, recent modifications of the index calculus method, including the number field sieve and the function field sieve. We also provide a sketch of the some of the cryptographic schemes whose security depends on the intractibility of the discrete logarithm problem. 1 Introduction Let G be a cyclic... (Update)
Context of citations to this paper: More
...about them. Even in the area of complexity of the discrete log problem there have been several general surveys [Lebedev, McCurley, Odlyzko1, Odlyzko2, SchirokauerWD], as well as several more recent papers on specialized subfields. Therefore in this paper I will only give...
...time algorithm. A detailed theoretical survey of both methods and on the current status concerning the gap can be found in [22]. 4.2 Experimental Results Perhaps the most remarkable result of the DL variant of the NFS has probably been the success in solving...
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BibTeX entry: (Update)
O. Schirokauer, D. Weber, and T. Denny, Discrete logarithms: The effectiveness of the index calculus method, pp. 337--362 in Algorithmic Number Theory: Second Intern. Symp., ANTS-II, H. Cohen, ed., Lecture Notes in Math. #1122, Springer, 1996. http://citeseer.ist.psu.edu/article/schirokauer96discrete.html More
@inproceedings{ schirokauer96discrete,
author = "Oliver Schirokauer and Damian Weber and Thomas F. Denny",
title = "Discrete Logarithms: The Effectiveness of the Index Calculus Method",
booktitle = "{ANTS}",
pages = "337-361",
year = "1996",
url = "citeseer.ist.psu.edu/article/schirokauer96discrete.html" }
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