On Search Complexity of Discrete Logarithm
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438467" target="_blank" >RIV/00216208:11320/21:10438467 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.60" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.60</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.60" target="_blank" >10.4230/LIPIcs.MFCS.2021.60</a>
Alternative languages
Result language
angličtina
Original language name
On Search Complexity of Discrete Logarithm
Original language description
In this work, we study the discrete logarithm problem in the context of TFNP - the complexity class of search problems with a syntactically guaranteed existence of solutions for all instances. Our main results establish that suitable variants of the discrete logarithm problem are complete for the complexity class PPP, respectively PWPP, i.e., the subclasses of TFNP capturing total search problems with a solution guaranteed by the pigeonhole principle, respectively the weak pigeonhole principle. Besides answering an open problem from the recent work of Sotiraki, Zampetakis, and Zirdelis (FOCS'18), our completeness results for PPP and PWPP have implications for the recent line of work proving conditional lower bounds for problems in TFNP under cryptographic assumptions. In particular, they highlight that any attempt at basing average-case hardness in subclasses of TFNP (other than PWPP and PPP) on the average-case hardness of the discrete logarithm problem must exploit its structural properties beyond what is necessary for constructions of collision-resistant hash functions. Additionally, our reductions provide new structural insights into the class PWPP by establishing two new PWPP-complete problems. First, the problem Dove, a relaxation of the PPP-complete problem Pigeon. Dove is the first PWPP-complete problem not defined in terms of an explicitly shrinking function. Second, the problem Claw, a total search problem capturing the computational complexity of breaking claw-free permutations. In the context of TFNP, the PWPP-completeness of Claw matches the known intrinsic relationship between collision-resistant hash functions and claw-free permutations established in the cryptographic literature.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, August 23-27, 2021, Tallinn, Estonia
ISBN
978-3-95977-201-3
ISSN
1868-8969
e-ISSN
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Number of pages
16
Pages from-to
1-16
Publisher name
Schloss Dagstuhl - Leibniz-Zentrum fur Informatik
Place of publication
Dagstuhl
Event location
Tallin
Event date
Aug 23, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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