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arXiv:quant-ph/0603263 · Physical Review A

Quantum-noise randomized ciphers

Ranjith Nair, Horace P. Yuen, Eric Corndorf, Takami Eguchi, Prem Kumar

Published Nov 7, 2006• 61 citations
arXivHTMLPDF

Abstract

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as $\ensuremath{\alpha}\ensuremath{\eta}$ and show that it is equivalent to a random cipher in which the required randomization is affected by coherent-state quantum noise. We describe the currently known security features of $\ensuremath{\alpha}\ensuremath{\eta}$ and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how $\ensuremath{\alpha}\ensuremath{\eta}$ used in conjunction with any standard stream cipher such as the Advanced Encryption Standard provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that $\ensuremath{\alpha}\ensuremath{\eta}$ is equivalent to a nonrandom stream cipher.

DOI
10.1103/physreva.74.052309

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We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as \ensuremathα\ensuremathη\ensuremath{\alpha}\ensuremath{\eta}\ensuremathα\ensuremathη and show that it is equivalent to a random cipher in which the required randomization is affected by coherent-state quantum noise. We describe the currently known security features of \ensuremathα\ensuremathη\ensuremath{\alpha}\ensuremath{\eta}\ensuremathα\ensuremathη and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how \ensuremathα\ensuremathη\ensuremath{\alpha}\ensuremath{\eta}\ensuremathα\ensuremathη used in conjunction with any standard stream cipher such as the Advanced Encryption Standard provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that \ensuremathα\ensuremathη\ensuremath{\alpha}\ensuremath{\eta}\ensuremathα\ensuremathη is equivalent to a nonrandom stream cipher.
This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the quantum no cloning theorem and randomizations based on quantum noise effect. The randomizations for the ciphertext which is the output from the mathematical encryption box is crucial to realize a quantum enigma cipher. Especially, by randomizations, it is necessary to make a substantial difference in accuracy of ciphertext in eavesdropper's observation and legitimate user's observation. The quantum illumination protocol can make a difference in error performance of the legitimate's receiver and the eavesdropper's receiver. This difference is due to differences in ability of the legitimate's receiver with entanglement and the eavesdropper's receiver without entanglement. It is shown in this note that the quantum illumination can be employed as an element of the most simple quantum enigma cipher.
Among physical layer encryption schemes, the quantum noise stream cipher (QNSC) has garnered significant attention due to its compatibility with high-speed commercial fiber-optic communication systems. After careful analysis of the encryption scheme, we reveal that QNSC transmission systems exhibit a security vulnerability in their encoding scheme. This vulnerability limits quantum noise to alerting high-order information bits in plaintext-dependent regions, creating structured ciphertext concealment. Numerical simulation and experimental verification both indicate that an eavesdropper can use quantization-attack to crack this vulnerability. Existing security assessment methods will overestimate the system’s security under quantization-attack. In addition, system security demonstrates a strong linear dependence on the plaintext modulation format, rather than the ciphertext modulation format as is widely presumed. To further enhance system security, the probability distribution is further introduced into the encoding process of ciphertext. The experiment results show that we not only achieved random concealment of ciphertext by quantum noise but also enhanced the eavesdropper’s symbol error rate by ∼86 % and maximally expanded the key space of the QAM-QNSC system by 2 27.2 .
Quantum Noise Stream Cipher (QNSC) has emerged as a physical-layer encryption technique that exploits quantum noise and non-orthogonal coherent-state modulation to secure optical communication. However, the security of QNSC relies exceedingly on the secrecy and freshness of its seed key. Quantum Key Distribution (QKD), on the other hand, provides information-theoretically secure key exchange rooted in the laws of quantum mechanics. The convergence of these two paradigms, i.e., integrated QKD-QNSC architectures, offers a compelling solution to each of their limitations. In such integrated systems, QKD continuously supplies and refreshes the secret seed key that governs QNSC modulation. Thus, governing a unified security framework that couples provably secure key establishment with high-speed quantum-enhanced physical-layer encryption. This work presents a comprehensive review of QNSC systems, examining their operating principles, security models under various attacks, and their integration with QKD systems. We analyze the security interplay between the key generation and encryption layers and survey experimental demonstrations and architectural progress toward practical deployment. Furthermore, we identify the open challenges and future research directions that must be addressed to realize fully integrated, quantum-secured optical communication networks at a practical scale.
This paper is dedicated to the late Professor H.P. Yuen in commemoration to our 50-year friendship. He invented the concept of quantum stream cipher. It is designed based on a completely different concept from conventional ciphers. The purpose of this cipher is to provide information-theoretic security of long data and secret key with short key length. It is based on hiding the ciphertext of mathematical cipher with quantum noise, achieving unprecedented information-theoretic security in any cipher. The protocol corresponds to randomizing the ciphertext by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. In this paper, we introduce some progress on the specific method to develop from the standard type to generalized quantum stream cipher (Quantum Enigma Cipher). There are two methods for generalization. One is the additional randomization method by the product cipher form and the other is the M-th order extended quantum coding method. Here we discuss the former. The results proved that it has sufficient information-theoretic security against known plaintext attack on key in comparison with quantum data locking. The latter method will be reported in Part II.
Quantum-based cryptographic protocols are often said to enjoy security guaranteed by the fundamental laws of physics. However, even carefully designed quantum-based cryptographic schemes may be susceptible to subtle attacks that are outside the original design. As an example, we give attacks against a recently proposed ``secure communication using mesoscopic coherent states'', which employs mesoscopic states, rather than single-photon states. Our attacks can be used either as a known-plaintext attack or in the case where the plaintext has not been randomized. One of our attacks requires beamsplitters and the replacement of a lossy channel by a lossless one. It is successful provided that the original loss in the channel is so big that Eve can obtain 2k2^k2k copies of what Bob receives, where kkk is the length of the seed key pre-shared by Alice and Bob. In addition, substantial improvements over such an exhaustive key search attack can be made, whenever a key is reused. Furthermore, we remark that, under the same assumption of a known or non-random plaintext, Grover's exhaustive key search attack can be applied directly to "secure communication using mesoscopic coherent states", whenever the channel loss is more than 50 percent. Therefore, as far as information-theoretic security is concerned, optically amplified signals necessarily degrade the security of the proposed scheme, when the plaintext is known or non-random. Our attacks apply even if the mesoscopic scheme is used only for key generation with a subsequent use of the key for one-time-pad encryption. Studying those attacks can help us to better define the risk models and parameter spaces in which quantum-based cryptographic schemes can operate securely. Finally, we remark that our attacks do not affect standard protocols such as Bennett-Brassard BB84 protocol or Bennett B92 protocol, which rely on single-photon signals.