Abstract
We study characterizations of one-way functions in terms of time-bounded Kolmogorov complexity. As the main contribution, we propose definitions for strong and weak Kolmogorov one-way functions and show that these are equivalent to classical strong and weak one-way functions, respectively. The new definitions were motivated by the fact that the expected value approach is not able to characterize strong one-way functions as we prove in the paper.
Highlights
One-way functions are polynomially computable functions that are hard to invert, meaning that, given a set of images, there should not exist an efficient algorithm to compute its pre-image.One-way functions are not known to exist
A function f is a deterministic one-way function if all polynomial-time deterministic algorithms fail to invert at least a polynomial fraction of the inputs; f is a weak one-way function if at least a polynomial fraction of the inputs are resilient to polynomial time probabilistic algorithms; and, f is a strong one-way function if any polynomial-time probabilistic algorithm can only invert a negligible fraction of the inputs
We introduced alternative characterizations of one-way functions based on time-bounded Kolmogorov complexity
Summary
One-way functions are polynomially computable functions that are hard to invert, meaning that, given a set of images, there should not exist an efficient algorithm to compute its pre-image.One-way functions are not known to exist. One-way functions are polynomially computable functions that are hard to invert, meaning that, given a set of images, there should not exist an efficient algorithm to compute its pre-image. It is possible to find three definitions of one-way functions that essentially differ on the power of the polynomial-time algorithm that is used to invert the function and on its probability of success: deterministic, weak and strong (by increasing order of strength). Despite the distinctly different hardness assumptions, it is known that weak one-way functions exist if and only if strong one-way functions exist (see [1] for details)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
