One-Way Functions Using Algorithmic and Classical Information Theories

• Tipo: Artigo em Revista Científica Internacional
• Data: 2013

Autores

antunes, l (Autor) FCUP; matos, a (Autor) Outra; pinto, a (Autor) Outra; souto, a (Autor) Outra; teixeira, a (Autor) FCUP

Revista

Título: Theory of Computing Systems

Vol. 52

Páginas: 162-178

ISSN: 1432-4350

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 6 Citações

Scopus - 7 Citações

Outras Informações

ID Authenticus: P-005-3RZ

DOI: 10.1007/s00224-012-9418-z

Abstract (EN): 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17