Abstract
The existence of one-way functions seems to depend, intuitively, on certain irregular properties of polynomial-time computable functions. Therefore, for functions with continuity properties, it suggests that all such functions are not one-way. It is shown here that in the formal complexity theory of real functions, this nonexistence of continuous one-way functions can be proved for one-to-one one-dimensional real functions, but fails for one-to-one two-dimensional real functions, if certain strong discrete one-way functions exist. Furthermore, for k-to-one functions, we can prove the existence of four-to-one one-dimensional one-way functions under the same assumption of the existence of strong discrete one-way functions. (A function f is k-to-one if for any y there exist at most k distinct values x such that f(x)=y.)
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.
