Paper 2022/1165

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Christopher Battarbee, University of York
Delaram Kahrobaei, Queens College, CUNY
Ludovic Perret, Sorbonne University
Siamak F. Shahandashti, University of York

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its relationship to more well-known hardness problems, particularly with respect to its security against quantum adversaries, has not been well understood and was a significant open problem for researchers in this area. In this paper we give the first dedicated security analysis of SDLP. In particular, we provide a connection between SDLP and group actions, a context in which quantum subexponential algorithms are known to apply. We are therefore able to construct a subexponential quantum algorithm for solving SDLP, thereby classifying the complexity of SDLP and its relation to known computational problems.

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Cryptographic protocols
Publication info
Published elsewhere. arXiv
key exchange hidden shift problem semidirect product group action
Contact author(s)
cb2036 @ york ac uk
DKahrobaei @ gc cuny edu
ludovic perret @ lip6 fr
siamak shahandashti @ york ac uk
2022-11-02: revised
2022-09-06: received
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      author = {Christopher Battarbee and Delaram Kahrobaei and Ludovic Perret and Siamak F. Shahandashti},
      title = {A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1165},
      year = {2022},
      note = {\url{}},
      url = {}
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