One-Way Functions Using Algorithmic and Classical Information Theories

• Type: Article in International Scientific Journal
• Date: 2013

Authors

antunes, l (Author) FCUP; matos, a (Author) Other; pinto, a (Author) Other; souto, a (Author) Other; teixeira, a (Author) FCUP

Journal

Title: Theory of Computing Systems

Vol. 52

Pages: 162-178

ISSN: 1432-4350

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 7 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17