[Paper Review] Repeatable classical one-time-pad crypto-system with quantum mechanics

Fu‐Guo Deng, Gui‐Lu Long|arXiv (Cornell University)|Feb 12, 2019

Quantum Computing Algorithms and Architecture1 references4 citations

TL;DR

This paper proposes a repeatable classical one-time-pad cryptosystem using single-photon quantum states, enabling unconditional security with key reuse through quantum mechanics. By encoding messages via unitary operations on prepared qubits and leveraging quantum non-cloning and measurement collapse, eavesdropping is detectable, allowing the same classical key to be securely reused across multiple transmissions without compromising security.

ABSTRACT

Classical one-time-pad key can only be used once. We show in this Letter that with quantum mechanical information media classical one-time-pad key can be repeatedly used. We propose a specific realization using single photons. The reason why quantum mechanics can make the classical one-time-pad key repeatable is that quantum states can not be cloned and eavesdropping can be detected by the legitimate users. This represents a significant difference between classical cryptography and quantum cryptography and provides a new tool in designing quantum communication protocols and flexibility in practical applications. Note added: This work was submitted to PRL as LU9745 on 29 July 2004, and the decision was returned on 11 November 2004, which advised us to resubmit to some specialized journal, probably, PRA, after revision. We publish it here in memory of Prof. Fu-Guo Deng (1975.11.12-2019.1.18), from Beijing Normal University, who died on Jan 18, 2019 after two years heroic fight with pancreatic cancer. In this work, we designed a protocol to repeatedly use a classical one-time-pad key to transmit ciphertext using single photon states. The essential idea was proposed in November 1982, by Charles H. Bennett, Gilles Brassard, Seth Breidbart, which was rejected by Fifteenth Annual ACM Symposium on Theory of Computing, and remained unpublished until 2014, when they published the article, Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP, Natural Computing (2014) 13:453-458, DOI 10.1007/s11047-014-9453-6. We worked out this idea independently. This work has not been published, and was in cooperated into quant-ph 0706.3791 (Kai Wen, Fu Guo Deng, Gui Lu Long, Secure Reusable Base-String in Quantum Key Distribution), and quant-ph 0711.1632 (Kai Wen, Fu-Guo Deng, Gui Lu Long, Reusable Vernam Cipher with Quantum Media).

Motivation & Objective

• To overcome the fundamental limitation in classical cryptography that one-time-pad keys can only be used once.
• To develop a protocol that allows repeated use of a classical one-time-pad key while maintaining unconditional security.
• To leverage quantum mechanical properties—such as non-cloning and measurement collapse—to detect eavesdropping and enable key reuse.
• To provide a practical and flexible framework for quantum communication protocols that combines classical one-time-pad security with quantum information carriers.

Proposed method

• Using single photons prepared in |0⟩, |1⟩, |+⟩, or |−⟩ states based on a shared classical key of length 2N.
• Encoding secret messages via unitary operations: identity (I) for bit 0 and Pauli-Y (σy) for bit 1 on the prepared photons.
• Transmitting the encoded photons through a quantum channel, where eavesdropping attempts disturb the quantum states and are detectable.
• After transmission, the receiver measures in the correct basis, and both parties publicly announce the basis choices to verify channel security.
• Discarding the basis sequence (MS) after public announcement to prevent key leakage, while reusing the classical key for future transmissions.
• Using error correction and privacy amplification techniques to mitigate noise and reduce information leakage to an eavesdropper.

Experimental results

Research questions

• RQ1 Can a classical one-time-pad key be securely reused in a quantum communication framework?
• RQ2 How can quantum mechanics enable detection of eavesdropping to allow key reuse without compromising security?
• RQ3 What is the maximum information an eavesdropper can obtain about the key in this repeatable system compared to standard BB84 QKD?
• RQ4 Can this protocol be implemented without single-photon sources, using error-correcting codes instead?
• RQ5 What is the relationship between the error rate in the quantum channel and the information leakage to an eavesdropper in this system?

Key findings

• The classical one-time-pad key can be reused multiple times securely when carried by single photons, due to quantum mechanical detection of eavesdropping.
• Eve’s mutual information about the measuring basis (I′AE) is strictly less than in BB84 QKD, with I′AE < 0.41 when the error rate Dm ≤ 0.05.
• The protocol ensures perfect secrecy even if Eve knows the message in advance, as she cannot extract the key without measuring the quantum states in the correct basis.
• The system achieves unconditional security through quantum non-cloning and measurement collapse, enabling key reuse under secure channel conditions.
• The protocol is robust under low-noise conditions and can be implemented with error-correcting codes even without ideal single-photon sources.
• The scheme avoids the need for quantum memory and enables one-way transmission, offering advantages over two-way quantum one-time-pad protocols.