A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
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 re...
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| creator | Battarbee, Christopher Kahrobaei, Delaram Perret, Ludovic Shahandashti, Siamak F |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2209.02814 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2209.02814</identifier><language>eng</language><subject>Computer Science - Cryptography and Security ; Mathematics - Group Theory ; Physics - Quantum Physics</subject><creationdate>2022-09</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2209.02814$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2209.02814$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Battarbee, Christopher</creatorcontrib><creatorcontrib>Kahrobaei, Delaram</creatorcontrib><creatorcontrib>Perret, Ludovic</creatorcontrib><creatorcontrib>Shahandashti, Siamak F</creatorcontrib><title>A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem</title><description>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.</description><subject>Computer Science - Cryptography and Security</subject><subject>Mathematics - Group Theory</subject><subject>Physics - Quantum Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz0tqwzAUhWFNOihpF9BRtQG7sl62hiZ9gqEpydxcS9eJwLKCIpd096VJR2fyc-Aj5KFipWyUYk-Qzv675JyZkvGmkrdk09LtMuD5GGecs4eJfi0w5yXQdtrH5PMh0DEmmg9Itxi88wltps_-ZBNmpF3cw7XapDhMGO7IzQjTCe__d0V2ry-79XvRfb59rNuuAF3LQuMwagDZCI1MYcXrhg1Ya2OlFTUDJ7hEMIYbJyWHUTPFlHOyYlqgsFKsyOP19kLqj8kHSD_9H62_0MQvY3BJag</recordid><startdate>20220906</startdate><enddate>20220906</enddate><creator>Battarbee, Christopher</creator><creator>Kahrobaei, Delaram</creator><creator>Perret, Ludovic</creator><creator>Shahandashti, Siamak F</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220906</creationdate><title>A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem</title><author>Battarbee, Christopher ; Kahrobaei, Delaram ; Perret, Ludovic ; Shahandashti, Siamak F</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-6ebf6aa4836e05e12780be769c4c370ad324ea9929d442af60505dd41063e3c43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Cryptography and Security</topic><topic>Mathematics - Group Theory</topic><topic>Physics - Quantum Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Battarbee, Christopher</creatorcontrib><creatorcontrib>Kahrobaei, Delaram</creatorcontrib><creatorcontrib>Perret, Ludovic</creatorcontrib><creatorcontrib>Shahandashti, Siamak F</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Battarbee, Christopher</au><au>Kahrobaei, Delaram</au><au>Perret, Ludovic</au><au>Shahandashti, Siamak F</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem</atitle><date>2022-09-06</date><risdate>2022</risdate><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.</abstract><doi>10.48550/arxiv.2209.02814</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Cryptography and Security Mathematics - Group Theory Physics - Quantum Physics |
| title | A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem |
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