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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Analysis on a generalized algorithm for the strong discrete logarithm problem with auxiliary inputs


Authors: Minkyu Kim, Jung Hee Cheon and In-Sok Lee
Journal: Math. Comp. 83 (2014), 1993-2004
MSC (2010): Primary 68Q25; Secondary 11Y16
Published electronically: February 11, 2014
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Abstract: We investigate a recently proposed algorithm solving the strong discrete logarithm problem with auxiliary inputs, and show that this algorithm in general is not more efficient than ordinary discrete-logarithm-solving algorithms such as Pollard's rho method, by analyzing a lower bound on the sum of digits of integers.


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Additional Information

Minkyu Kim
Affiliation: The Attached Institute of ETRI, P.O. Box 1, Yuseong, Daejeon, 305-600, Korea
Email: mkkim@ensec.re.kr

Jung Hee Cheon
Affiliation: ISaC and Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: jhcheon@snu.ac.kr

In-Sok Lee
Affiliation: ISaC and Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: isll@snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02813-5
PII: S 0025-5718(2014)02813-5
Keywords: Discrete logarithm problem, (strong) Diffie-Hellman problem, sum of digits
Received by editor(s): February 14, 2012
Received by editor(s) in revised form: November 1, 2012
Published electronically: February 11, 2014
Additional Notes: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2012-0001243)
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.