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

Quantum stream cipher: Part V. On the optimal modulation scheme and the implementation of deliberate signal randomization

Kentaro Kato, Osamu Hirota

Published Sep 11, 2007• 4 citations
Publisher

Abstract

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.

DOI
10.1117/12.733296

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 5, 2008•3 citations
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 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.
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.
The notion of the deliberate error randomization (DER) for the Y-00 quantum stream cipher was introduced by Yuen [arXiv:quant-ph/0311061v6], and concrete schemes of DER were proposed by the author for the phase shift keying Y-00 quantum stream cipher (PSK-Y00) [Proc. SPIE 6305, 630508 (2006)]. In this paper, it is shown that one of our DER schemes, which was referred to as Model B in the literature, is applicable to the intensity shift keying Y-00 quantum stream cipher (ISK-Y00) and the brute-force search complexity Q in the case of ISK-Y00 is enhanced by installing DER as well as in the case of PSK-Y00.
This paper presents the security analysis on the quantum stream cipher so called Yuen-2000 protocol (or αηαηαη scheme) against the fast correlation attack, the typical attack on stream ciphers. Although a very simple experimental model of the quantum stream cipher without a random mapper may be decrypted in the information theoretic sense by the fast correlation algorithm, it is not a basic feature of Yuen 2000 protocol. In fact, we clarify that there exists a randomization scheme which attains the perfect correlation immunity against such attacks under an approximation. And in this scheme, the running key correlation from the second randomization that determines the mapping patterns is dismissed also by quantum noise. In such a case, any fast correlation attack does not work on the quantum stream cipher.
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.