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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Error performance of intensity modulation-based quantum stream cipher by Yuen 2000 protocol with nonlinear pseudorandom number generator

Kentaro Kato

Published Jul 21, 2009• 2 citations
Publisher

Abstract

This paper is concerned with the intensity modulation-based quantum stream cipher by Yuen 2000 protocol with a nonlinear pseudorandom number generator. First we show the minimum error probability of the basic model of the intensity modulation-based quantum stream cipher in cases of ciphertext-only attacks and known plaintext attack, by using the quantum signal detection theory. Second we propose the intensity modulation-based quantum stream cipher having a nonlinear pseudorandom number generator that is realized by the basis converter. We compare the error profile of the system having the nonlinear pseudorandom number generator with that of the basic model. As a result we will see that the use of the nonlinear pseudorandom number generator yields an advantage to the legitimate users.

DOI
10.1117/12.825798

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Physical Review A•Mar 27, 2008•25 citations
This paper is concerned with the intensity modulation-based quantum stream cipher by Yuen 2000 protocol with a nonlinear pseudorandom number generator. First we show the minimum error probability of the basic model of the intensity modulation-based quantum stream cipher in cases of ciphertext-only attacks and known plaintext attack, by using the quantum signal detection theory. Second we propose the intensity modulation-based quantum stream cipher having a nonlinear pseudorandom number generator that is realized by the basis converter. We compare the error profile of the system having the nonlinear pseudorandom number generator with that of the basic model. As a result we will see that the use of the nonlinear pseudorandom number generator yields an advantage to the legitimate users.
A quantum stream cipher by Yuen 2000 (Y-00) protocol with a feedback shift register - a linear feedback shift register (LFSR) or a nonlinear feedback shift register - is very attractive in implementing a secure high-speed optical data transmission system for next-generation optical networking. So far, a LFSR has been used in a quantum stream cipher by Y-00 as a running key generator, rather than a nonlinear feedback shift register. But, it is well-known that an appropriately designed nonlinear feedback shift register has larger period and linear complexity than the corresponding quantities of a LFSR driven by a secret key of the same length. Although large linear complexity of a key generator does not immediately guarantee the security of the key generator itself, it forces the eavesdropper at least to collect more measurement data to carry out the attacks. This motivates us to use a nonlinear feedback shift register as a running key generator in a quantum stream cipher by Y-00. The purpose of this study is to make a quantum stream cipher more costly in terms of cryptoanalysis, enhancing the advantages of using a nonlinear feedback shift register. For this purpose, we propose a new randomization technique for a running key generator in this paper. First, we state the basics of a quantum stream cipher by Y-00. Second, we propose the randomization on a running key consisting of two different type of basis converter. To evaluate the effect of the randomization in terms of the amount of information that is extracted by her measurement, numerical simulation is performed in the cases of an optical heterodyne receiver and a quantum optimal receiver under the assumption that the eavesdropper knows plaintext. Finally, we summarize the results.
This paper considers two issues on the quantum stream cipher by Yuen-2000 (Y-00) protocol. In the fist part of this paper we investigate the optimal modulation scheme for the basic model of the quantum stream cipher by Y-00 protocol, and in the remaining part we study the deliberate signal randomization. For the problem on the optimal modulation scheme, several modulation schemes are investigated for the cipher text-only attacks and the known plaintext attack under the error probability criterion and the information criterion to find the preferable modulation scheme. As a result, it will be shown that the phase shift keying signal yields the best performance among the modulation schemes investigated in our consideration by numerical simulations. After that, the roperty of the randomization technique called the deliberate signal randomization is considered for the cipher text-only attacks and the known plaintext attack in the information criterion. From this, it will be shown by numerical simulations that the amount of leakage of information from the legitimate user to the eavesdropper is reduced by the deliberate signal randomization. At the last section we will mention about the implementation issues of the deliberate signal randomization, taking account of the numerical results.
We investigate the Yuen 2000 (so-called Y-00)-protocol, which can realize a randomized stream cipher with high bit rate (Gbit/s) for long distances (several hundreds km). The randomized stream cipher with randomization by quantum noise based on the Y-00 protocol is called a quantum stream cipher in this paper, and it may have security against known plaintext attacks which has no analog with any conventional symmetric key ciphers. We present a simple cryptanalysis based on an attacker's heterodyne measurement and a quantum unambiguous measurement to make clear the strength of the Y-00 protocol in real communication. In addition, we give a design for the implementation of an intensity-modulation scheme and report an experimental demonstration of 1Gbit∕s1\phantom{\rule{0.3em}{0ex}}\mathrm{Gbit}∕\mathrm{s}1Gbit∕s quantum stream cipher through a $20\text{\ensuremath{-}}\mathrm{km}$-long transmission line.
In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen based on quantum communication theory. It is applicable to direct encryption, for example quantum stream cipher based on Yuen protocol(Y-00), with high speeds and for long distance by sophisticated optical devices which can work under the average photon number per signal light pulse:<n>=1000sim10000<n> = 1000 \\sim 10000<n>=1000sim10000. In addition, it may provide information-theoretic security against known/chosen plaintext attack, which has no classical analogue. That is, one can provide secure communication, even the system has H(K)<<H(X)H(K) << H(X)H(K)<<H(X). In this paper, first, we give a brief review on the general logic of Yuen's theory. Then, we show concrete security analysis of quantum stream cipher to quantum individual measurement attacks. Especially by showing the analysis of Lo-Ko known plaintext attack, the feature of Y-00 is clarified. In addition, we give a simple experimental result on the advantage distillation by scheme consisting of intensity modulation/direct detection optical communication.
In 2000, an attractive new quantum cryptography was discovered by H.P.Yuen based on quantum communication theory. It is applicable to direct encryption, for example quantum stream cipher based on Yuen protocol(Y-00), with high speeds and for long distance by sophisticated optical devices which can work under the average photon number per signal light pulse: <n> = 1000 ~ 10000. In addition, it may provide information-theoretic security against known/chosen plaintext attack, which has no classical analogue. That is, one can provide secure communication, even the system has H(K)<<H(X). This is a challenge to overcome Shannon limit in the cryptography theory. In this paper, first, we give a brief review on the general logic of Yuen's theory. Then, we show concrete security analysis of quantum stream cipher to quantum individual measurement attacks. Especially by showing the analysis of Lo-Ko known plaintext attack, the feature of Y-00 is clarified. In addition, we give a simple experimental result on the scheme consisting of intensity modulation/direct detection optical communication.
A quantum stream cipher by Yuen 2000 protocol (so-called Y00 protocol or $\ensuremath{\alpha}\ensuremath{\eta}$ scheme) consisting of linear feedback shift register of short key is very attractive in implementing secure 40 Gbits/s optical data transmission, which is expected as a next-generation network. However, a basic model of the Y00 protocol with a very short key needs a careful design against fast correlation attacks as pointed out by Donnet et al. This Brief Report clarifies an effectiveness of irregular mapping between running key and physical signals in the driver for selection of MMM-ary basis in the transmitter, and gives a design method. Consequently, quantum stream cipher by the Y00 protocol with our mapping has immunity against the proposed fast correlation attacks on a basic model of the Y00 protocol even if the key is very short.