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arXiv:quant-ph/0407067 · Physics Letters A

Security of Y-00 and similar quantum cryptographic protocols

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

Published Jul 8, 2004• 6 citations
arXivHTMLPDF

Abstract

It is claimed in Phys. Lett. A by T. Nishioka et. al. 327 (2004) 28-32, that the security of Y-00 is equivalent to that of a classical stream cipher. In this paper it is shown that the claim is false in either the use of Y-00 for direct encryption or key generation, in all the parameter ranges it is supposed to operate including those of the experiments reported thus far. The security of Y-00 type protocols is clarified.

DOI
10.48550/arxiv.quant-ph/0407067

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In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen, which can realize secure communication with high speeds and at long distance by conventional optical devices. Recently, a criticism of the Yuen protocol, so called Y-00, was made by Nishioka, and Imai group(Mitsubishi and University of Tokyo), and they claimed Y-00 is essentially a classical stream cipher. This paper shows that the claim is incorrect. In particular, it is shown that the relation $l_i=r_i\oplus \tilde{k}_i$, which is their basis for attack, has no essential role for any security analysis. In addition, we give a brief introduction of the general logic for the security of Y-00 as direct encryption and also for key generation. Several industries have started to make a test-bed of Y-00 for digital optical fiber highway, following Kumar's leading work. We hope that this discussion encourages experimental works which realize a secure communication against quantum computer and quantum attacks based on physical principle.

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Barbosaet al.Reply:

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Yuan and Shields claim that our data-encryption protocol is entirely equivalent to a classical stream cipher utilizing no quantum phenomena. Their claim is, indeed, false. Yuan and Shields also claim that schemes similar to the one presented in Phys. Rev. Lett. 90, 227901 are not suitable for key generation. This claim is also refuted. In any event, we welcome the opportunity to clarify the situation for a wider audience.

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It is claimed in Phys. Lett. A by T. Nishioka et. al. 327 (2004) 28-32, that the security of Y-00 is equivalent to that of a classical stream cipher. In this paper it is shown that the claim is false in either the use of Y-00 for direct encryption or key generation, in all the parameter ranges it is supposed to operate including those of the experiments reported thus far. The security of Y-00 type protocols is clarified.
In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen, which can realize secure communication with high speeds and at long distance by conventional optical devices. Recently, a criticism of the Yuen protocol, so called Y-00, was made by Nishioka, and Imai group(Mitsubishi and University of Tokyo), and they claimed Y-00 is essentially a classical stream cipher. This paper shows that the claim is incorrect. In particular, it is shown that the relation li=ri⊕k~il_i=r_i\oplus \tilde{k}_ili​=ri​⊕k~i​, which is their basis for attack, has no essential role for any security analysis. In addition, we give a brief introduction of the general logic for the security of Y-00 as direct encryption and also for key generation. Several industries have started to make a test-bed of Y-00 for digital optical fiber highway, following Kumar's leading work. We hope that this discussion encourages experimental works which realize a secure communication against quantum computer and quantum attacks based on physical principle.
What obstructs the realization of useful quantum cryptography is single photon scheme or entanglement which is not applicable to the current infrastructure of optical communication network. We are concerned with the following question: Can we realize the information theoretically secure symmetric key cipher under "the finite secret key" based on quantum-optical communications? A role of quantum information theory is to give an answer for such a question. As an answer for the question a new quantum cryptography was proposed by H. P. Yuen which can realize a secure symmetric key cipher with high speeds(Gbps) and for long distance(1000 Km). Although some researchers claim that Yuen protocol(Y-OO) is equivalent to the classical cryptography they arc all mistaken. Indeed it has no classical analogue and also provides a generalization even in the conventional cryptography. At present it is proved that a basic model of Y-OO has at least the security such as H(X/YE)=H(K/YE)=H(K), H(K/YE,X)~0 under the average photon number per signal light pulse:<n>~10000. Towards our final goal in this paper we clarify a role of classical randomness(secret key) and quantum randomness in Y-OO and give a rigorous quantum mechanical interpretation of the security showing an analysis of quantum collective attack.
There exists a great gap between one-time pad with perfect secrecy and conventional mathematical encryption. The Yuen 2000 (Y00) protocol or $\ensuremath{\alpha}\ensuremath{\eta}$ scheme may provide a protocol which covers from the conventional security to the ultimate one, depending on implementations. This paper presents the complexity-theoretic security analysis on some models of the Y00 protocol with nonlinear pseudo-random-number-generator and quantum noise diffusion mapping (QDM). Algebraic attacks and fast correlation attacks are applied with a model of the Y00 protocol with nonlinear filtering like the Toyocrypt stream cipher as the running key generator, and it is shown that these attacks in principle do not work on such models even when the mapping between running key and quantum state signal is fixed. In addition, a security property of the Y00 protocol with QDM is clarified. Consequently, we show that the Y00 protocol has a potential which cannot be realized by conventional cryptography and that it goes beyond mathematical encryption with physical encryption.
Various types of randomizations for the quantum stream cipher by Y00 protocol have been developed so far. In particular, it must be noted that the analysis of immunity against correlation attacks with a new type of randomization by Hirota and Kurosawa prompted a new look at the quantum stream cipher by Y00 protocol (Quant. Inform. Process. 6(2) 2007). From the preceding study on the quantum stream cipher, we recognized that the quantum stream cipher by Y00 protocol would be able to be generalized to a new type of physical cipher that has potential to exceed the Shannon limit by installing additional randomization mechanisms, in accordance with the law of quantum mechanics. We call this new type of physical random cipher the quantum enigma cipher. In this article, we introduce the recent developments for the quantum stream cipher by Y00 protocol and future plans toward the quantum enigma cipher.
In a series of articles concerned with quantum stream cipher by Y-00 protocol on this conference, we have claimed that the quantum stream cipher has a pretty good security against several concrete attacks. On the other hand, it has been pointed out that one can improve the security level by using various additional randomization techniques. In this paper, we will show some concrete randomization techniques for quantum stream cipher. First we will sketch the framework of the deliberate signal randomization (DSR) that is realized by randomizing the signals deliberately with true-random numbers or with pseud-random numbers generated by a secret key. Secondly, we will consider about the deliberate error randomization (DER) by using concrete models. It will be shown that these randomization techniques enhance the security level of the quantum stream cipher.