One-way functions and circuit complexity

One- Way Functions and Circuit Complexity

A finite function f is a mapping of {1 , 2 ,. .. , m } into {1 , 2 ,. .. , m } ∪ { # } where # is a symbol to be thought of as ''undefined.'' This paper defines a measure M(f) of the difficulty of inverting a finite function f, which is given by M(f) = MIN    log 2 C(f) log 2 C(g) _ _________ : g an inverse of f    where C(f) is a circuit complexity measure of the difficulty of computing ...

Generic case complexity and One-Way functions

Generic case complexity has originated about a decade ago in combinatorial group theory [10, 2]. This area has long computational traditions with many fundamental problems being algorithmic in nature. It has been shown that most computational problems in infinite group theory are recursively undecidable. However, it was also observed that decision algorithms, sometimes very naive ones, exist fo...

Creating Strong, Total, Commutative, Associative One-Way Functions from Any One-Way Function in Complexity Theory

Rabi and Sherman presented novel digital signature and unauthenticated secret-key agreement protocols, developed by themselves and by Rivest and Sherman. These protocols use strong, total, commutative (in the case of multiparty secret-key agreement), associative one-way functions as their key building blocks. Although Rabi and Sherman did prove that associative oneway functions exist if P{NP, t...

One-Way Communication Complexity of Symmetric Boolean Functions

We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are established and applied to the one-way two-party communication complexity of symmetric Boolean functions. It is shown that the number of required communication bits does not depend on the communication direction, provided that neither direction...

An Observation on Associative One-Way Functions in Complexity Theory