A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Christopher Battarbee; Delaram Kahrobaei; Ludovic Perret; Siamak F. Shahandashti

Paper 2022/1165

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Christopher Battarbee

, University of York, Sorbonne University

Delaram Kahrobaei

, Queens College, CUNY

Ludovic Perret, Sorbonne University

Siamak F. Shahandashti

, University of York

Abstract

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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Minor revision. PQCrypto 2024
Keywords: 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
History: 2024-06-07: last of 3 revisions; 2022-09-06: received; See all versions
Short URL: https://ia.cr/2022/1165
License: CC BY

BibTeX

@misc{cryptoeprint:2022/1165,
      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},
      url = {https://eprint.iacr.org/2022/1165}
}