Generic Hardness of the Multiple Discrete Logarithm Problem

  • Aaram YunEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9057)


We study generic hardness of the multiple discrete logarithm problem, where the solver has to solve \(n\) instances of the discrete logarithm problem simultaneously. There are known generic algorithms which perform \(O(\sqrt{np})\) group operations, where \(p\) is the group order, but no generic lower bound was known other than the trivial bound. In this paper we prove the tight generic lower bound, showing that the previously known algorithms are asymptotically optimal. We establish the lower bound by studying hardness of a related computational problem which we call the search-by-hyperplane-queries problem, which may be of independent interest.


Multiple discrete logarithm Search-by-hyperplane-queries Generic group model 


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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.Ulsan National Institute of Science and Technology (UNIST)UlsanRepublic of Korea

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