Cryptography based on operator theory (I): quantum no-key protocols

TL;DR

This paper introduces a new framework for quantum no-key cryptography based on operator theory, defining security measures and proposing two types of protocols utilizing unitary transformations and commutative sets.

Contribution

It presents a novel operator-theoretic framework for quantum no-key protocols, including security definitions and two distinct protocol constructions.

Findings

Framework expressed via trace-preserving operators and natural presentations

Defined information-theoretical security for QNK protocols

Proposed two types of QNK protocols based on different mathematical structures

Abstract

We study cryptography based on operator theory, and propose quantum no-key (QNK) protocols from the perspective of operator theory, then present a framework of QNK protocols. The framework is expressed in two forms: trace-preserving quantum operators and natural presentations. Then we defined the information-theoretical security of QNK protocols and the security of identification keys. Two kinds of QNK protocols are also proposed. The first scheme is constructed based on unitary transformation, and the other is constructed based on two multiplicative commutative sets.