A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Christopher Battarbee (1) , Delaram Kahrobaei (2) , Ludovic Perret (3) , Siamak F. Shahandashti (1)

1 CS-YORK - Department of Computer Science [York]
2 Brooklyn College [CUNY]
3 PolSys - Polynomial Systems

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.

Domaines: Informatique [cs]

Christopher Battarbee, Delaram Kahrobaei, Ludovic Perret, Siamak F. Shahandashti. A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem. NIST Fourth PQC Standardization Conference, Nov 2022, On-line conference, United States. ⟨hal-03920653⟩