One-Way Functions and Polynomial Isomorphisms

本研究旨在更好地了解 单向函数的存在性和 使用多项式思想的复杂性类的完备集 创造力 特别是，目标是探索一个合理的 单向函数的条件，意味着非同构。 早期 解决这个问题的方法，假设某些强大的 存在单向函数，要么证明简单，要么需要 单向函数的定义取决于特定的 全套。 该项目的方法使用了最近的结果， 多项式创造性的方法。

This research aims to better understand the relationships between the existence of one-way functions and the polynomial isomorphisms of complete sets for complexity classes using the idea of polynomial creativity. In particular, the goal is to explore a reasonable condition on one-way functions that implies non-isomorphisms. Early approaches to this problem, under the assumption that certain strong one-way functions exist, either turn out a trivial proof or require that the definition of one-way functions be dependent on a particular complete set. The approach in this project uses recent results and methods of polynomial creativity.