Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behaviour of an algorithm on typical (almost all) inputs and ignores the rest of inputs. Many classical undecidable or hard algorithmic problems become feasible in the generic case. But there are gener-ically hard problems. In this paper, we consider generic complexity of the classical discrete logarithm problem. We fit this problem in the frameworks of generic complexity and prove that its natural subproblem is generically hard provided that the discrete logarithm problem is hard in the worst case.
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- Title On generic complexity of the discrete logarithm problem
- Headline On generic complexity of the discrete logarithm problem
- Publesher
Tomsk State University
- Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 3(33)
- Date:
- DOI 10.17223/20710410/33/8
Keywords
генерическая сложность, проблема дискретного логарифма, вероятностный алгоритм, generic complexity, discrete logarithm problem, probabilistic algorithmAuthors
References
Kapovich I., Miasnikov A, Schupp P., and Shpilrain V. Generic-case complexity, decision problems in group theory and random walks //J. Algebra. 2003. V. 264. No. 2. P. 665-694.
Kapovich I., Miasnikov A., Schupp P., and Shpilrain V. Average-case complexity for the word and membership problems in group theory // Adv. Math. 2005. V. 190. P. 343-359.
Hamkins J. D. and Miasnikov A. G. The halting problem is decidable on a set of asymptotic probability one // Notre Dame J. Formal Logic. 2006. V. 47. No. 4. P. 515-524.
GilmanR., Miasnikov A. G., Myasnikov A. D., and Ushakov A. Report on generic case complexity // Herald of Omsk University. 2007. Special Issue. P. 103-110.
Мао В. Современная криптография: теория и практика. М.: Вильямс, 2005. 768с.
Impagliazzo R. and Wigderson A. P = BPP unless E has subexponential circuits: Derandomizing the XOR Lemma // Proc. 29th STOC. El Paso: ACM, 1997. P. 220-229.
Myasnikov A. and Rybalov A. Generic complexity of undecidable problems //J. Symbolic Logic. 2008. V. 73. No. 2. P. 656-673.
Rybalov A. Generic complexity of presburger arithmetic // Theory Comput. Systems. 2010. V. 46. No. 1. P. 2-8.

On generic complexity of the discrete logarithm problem | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2016. № 3(33). DOI: 10.17223/20710410/33/8
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