One-Way Functions Using Algorithmic and Classical Information Theories
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://repositorio.inesctec.pt/handle/123456789/7072 http://dx.doi.org/10.1007/s00224-012-9418-z |
Resumo: | We prove several results relating injective one-way functions, time-bounded conditional Kolmogorov complexity, and time-bounded conditional entropy. First we establish a connection between injective, strong and weak one-way functions and the expected value of the polynomial time-bounded Kolmogorov complexity, denoted here by E(K-t (x vertical bar f (x))). These results are in both directions. More precisely, conditions on E(K-t (x vertical bar f (x))) that imply that f is a weak one-way function, and properties of E(K-t (x vertical bar f (x))) that are implied by the fact that f is a strong one-way function. In particular, we prove a separation result: based on the concept of time-bounded Kolmogorov complexity, we find an interval in which every function f is a necessarily weak but not a strong one-way function. Then we propose an individual approach to injective one-way functions based on Kolmogorov complexity, defining Kolmogorov one-way functions and prove some relationships between the new proposal and the classical definition of one-way functions, showing that a Kolmogorov one-way function is also a deterministic one-way function. A relationship between Kolmogorov one-way functions and the conjecture of polynomial time symmetry of information is also proved. Finally, we relate E(K-t (x vertical bar f (x))) and two forms of time-bounded entropy, the unpredictable entropy H-unp, in which "one-wayness" of a function can be easily expressed, and the Yao(+) entropy, a measure based on compression/decompression schema in which only the decompressor is restricted to be time-bounded. |
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One-Way Functions Using Algorithmic and Classical Information TheoriesWe prove several results relating injective one-way functions, time-bounded conditional Kolmogorov complexity, and time-bounded conditional entropy. First we establish a connection between injective, strong and weak one-way functions and the expected value of the polynomial time-bounded Kolmogorov complexity, denoted here by E(K-t (x vertical bar f (x))). These results are in both directions. More precisely, conditions on E(K-t (x vertical bar f (x))) that imply that f is a weak one-way function, and properties of E(K-t (x vertical bar f (x))) that are implied by the fact that f is a strong one-way function. In particular, we prove a separation result: based on the concept of time-bounded Kolmogorov complexity, we find an interval in which every function f is a necessarily weak but not a strong one-way function. Then we propose an individual approach to injective one-way functions based on Kolmogorov complexity, defining Kolmogorov one-way functions and prove some relationships between the new proposal and the classical definition of one-way functions, showing that a Kolmogorov one-way function is also a deterministic one-way function. A relationship between Kolmogorov one-way functions and the conjecture of polynomial time symmetry of information is also proved. Finally, we relate E(K-t (x vertical bar f (x))) and two forms of time-bounded entropy, the unpredictable entropy H-unp, in which "one-wayness" of a function can be easily expressed, and the Yao(+) entropy, a measure based on compression/decompression schema in which only the decompressor is restricted to be time-bounded.2018-01-19T11:15:37Z2013-01-01T00:00:00Z2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/7072http://dx.doi.org/10.1007/s00224-012-9418-zengLuís Filipe AntunesMatos,AAlexandre Miranda PintoSouto,AAndreia Sofia Teixeirainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-05-15T10:19:44Zoai:repositorio.inesctec.pt:123456789/7072Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:52:09.882741Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
One-Way Functions Using Algorithmic and Classical Information Theories |
title |
One-Way Functions Using Algorithmic and Classical Information Theories |
spellingShingle |
One-Way Functions Using Algorithmic and Classical Information Theories Luís Filipe Antunes |
title_short |
One-Way Functions Using Algorithmic and Classical Information Theories |
title_full |
One-Way Functions Using Algorithmic and Classical Information Theories |
title_fullStr |
One-Way Functions Using Algorithmic and Classical Information Theories |
title_full_unstemmed |
One-Way Functions Using Algorithmic and Classical Information Theories |
title_sort |
One-Way Functions Using Algorithmic and Classical Information Theories |
author |
Luís Filipe Antunes |
author_facet |
Luís Filipe Antunes Matos,A Alexandre Miranda Pinto Souto,A Andreia Sofia Teixeira |
author_role |
author |
author2 |
Matos,A Alexandre Miranda Pinto Souto,A Andreia Sofia Teixeira |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Luís Filipe Antunes Matos,A Alexandre Miranda Pinto Souto,A Andreia Sofia Teixeira |
description |
We prove several results relating injective one-way functions, time-bounded conditional Kolmogorov complexity, and time-bounded conditional entropy. First we establish a connection between injective, strong and weak one-way functions and the expected value of the polynomial time-bounded Kolmogorov complexity, denoted here by E(K-t (x vertical bar f (x))). These results are in both directions. More precisely, conditions on E(K-t (x vertical bar f (x))) that imply that f is a weak one-way function, and properties of E(K-t (x vertical bar f (x))) that are implied by the fact that f is a strong one-way function. In particular, we prove a separation result: based on the concept of time-bounded Kolmogorov complexity, we find an interval in which every function f is a necessarily weak but not a strong one-way function. Then we propose an individual approach to injective one-way functions based on Kolmogorov complexity, defining Kolmogorov one-way functions and prove some relationships between the new proposal and the classical definition of one-way functions, showing that a Kolmogorov one-way function is also a deterministic one-way function. A relationship between Kolmogorov one-way functions and the conjecture of polynomial time symmetry of information is also proved. Finally, we relate E(K-t (x vertical bar f (x))) and two forms of time-bounded entropy, the unpredictable entropy H-unp, in which "one-wayness" of a function can be easily expressed, and the Yao(+) entropy, a measure based on compression/decompression schema in which only the decompressor is restricted to be time-bounded. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-01-01T00:00:00Z 2013 2018-01-19T11:15:37Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.inesctec.pt/handle/123456789/7072 http://dx.doi.org/10.1007/s00224-012-9418-z |
url |
http://repositorio.inesctec.pt/handle/123456789/7072 http://dx.doi.org/10.1007/s00224-012-9418-z |
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eng |
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eng |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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