Generic case complexity and One-Way functions

TL;DR

This paper introduces generic case complexity to cryptography, providing a new perspective on analyzing algorithm behavior on most inputs, and demonstrates its equivalence to classical definitions of one-way functions.

Contribution

It presents an alternative definition of one-way functions using generic case complexity and shows its practical advantages and equivalence to standard definitions.

Findings

Generic case complexity offers a simple, intuitive analysis method.

The new definition of one-way functions is equivalent to the classical one.

Extending adversaries to larger classes does not weaken security assumptions.

Abstract

The goal of this paper is to introduce ideas and methodology of the generic case complexity to cryptography community. This relatively new approach allows one to analyze the behavior of an algorithm on ''most'' inputs in a simple and intuitive fashion which has some practical advantages over classical methods based on averaging. We present an alternative definition of one-way function using the concepts of generic case complexity and show its equivalence to the standard definition. In addition we demonstrate the convenience of the new approach by giving a short proof that extending adversaries to a larger class of partial algorithms with errors does not change the strength of the security assumption.