Generalized one-way function and its application

TL;DR

This paper introduces a generalized quantum one-way function derived from provable quantum one-way functions, enabling a secure classical key distribution protocol that remains secure against unlimited computational adversaries.

Contribution

It extends the concept of quantum one-way functions to a generalized form and applies it to develop an unconditionally secure classical key distribution protocol.

Findings

Successfully constructed a generalized quantum one-way function.

Developed a secure key distribution protocol based on classical data processing.

Demonstrated security against adversaries with unlimited computational resources.

Abstract

One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its one-wayness even with unlimited computational resources. Here, we extend the mathematical definition of functions to construct a generalized one-way function by virtually measuring the qubit of provable quantum one-way function and randomly assigning the corresponding measurement outcomes with identical probability. Remarkably, using this generalized one-way function, we have developed an unconditionally secure key distribution protocol based solely on classical data processing, which can then utilized for secure encryption and signature. Our work highlights the importance of information in characterizing quantum systems and the physical significance of the density matrix. We demonstrate that probability theory and randomness are effective tools for countering adversaries with unlimited computational capabilities.