A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866914828346458112 |
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| author | Battarbee, Christopher Kahrobaei, Delaram Perret, Ludovic Shahandashti, Siamak F. |
| author_facet | Battarbee, Christopher Kahrobaei, Delaram Perret, Ludovic Shahandashti, Siamak F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02814 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem Battarbee, Christopher Kahrobaei, Delaram Perret, Ludovic Shahandashti, Siamak F. Cryptography and Security Group Theory Quantum Physics 94A60, 81P94, 20M30 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. |
| title | A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem |
| topic | Cryptography and Security Group Theory Quantum Physics 94A60, 81P94, 20M30 |
| url | https://arxiv.org/abs/2209.02814 |