Problems of Existing Unconditional Security Proofs in Quantum Key Distribution

TL;DR

This paper critiques the reliance on a trace criterion $d$ for unconditional security in quantum key distribution, revealing its insufficiency and clarifying core issues in security proofs and protocol analysis.

Contribution

It exposes limitations of the trace criterion $d$ in guaranteeing security and clarifies fundamental problems in existing unconditional security proofs in quantum cryptography.

Findings

Trace criterion $d$ does not ensure security against known-plaintext attacks.

Current security proofs overlook key aspects like privacy amplification and key rate.

The paper highlights the need for more rigorous mathematical approaches.

Abstract

It is repeatedly and persistently claimed in the literature that a specific trace criterion $d$ would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in quantum key distribution. In this paper, it is shown that just security against known-plaintext attacks when the generated key is used in direct encryption is not provided by $d$. The problem is directly connected with several general problems in the existing unconditional security proofs in quantum key distribution. A number of issues will be clarified concerning the nature of true security, privacy amplification, key generation rate and the mathematical approach needed for their determination in concrete protocols.