Proc. SPIE. 10771, Quantum Communications and Quantum Imaging XVI
KEYWORDS: Signal to noise ratio, Transceivers, Modulation, Sensors, Interference (communication), Signal generators, Signal detection, Binary data, Quantum communications, Computer security
As a security parameter of Y-00 quantum stream cipher, a guessing probability by an eavesdropper for a secret key of legitimate users is discussed. Assuming that Eve employs the direct detection and Gaussian intensity distribution of each intensity level of Y-00 cipher signals are same, an analytic solution of probability of correct guessing of the secret key in a case of the ciphertext-only attack is derived. The solution is applied to experimentally measure the probabilities of our Y-00 quantum stream cipher transceiver. A very low probability of the Y-00 cipher transceiver is experimentally confirmed.
A power distribution of optical signals as the ciphertext of Y-00 quantum stream cipher transceivers should be uniform,
even when the bit sequence of plaintext is a non-uniform sequence. For examining the uniformity, we experimentally
measure powers of optical signals with 4096 intensity levels and calculate the ratio of signal numbers over and under the
average power. The ratios for various kinds of bit sequences are 0.5 with measurement error of 1%, which is an evidence
of the uniformity of the power distribution. In addition, the effectiveness of a randomization technique of overlapping
selection keying for enhancing the security against the known plaintext attack is experimentally observed.
A unified treatment of typical optical modulation formats is given toward a future development of the quantum enigma cipher. In our analysis, the intensity shift keying (ISK), amplitude shift keying (ASK), phase shift keying (PSK), and quadrature amplitude modulation (QAM) coherent state signals are compared in terms of the masking number of potential signals through the numerical calculations of the square-root measurement. Through this comparison, we see that the use of ISK coherent state signal is the best choice for cryptographic purpose among these formats in achieving an appropriate balance between the number of signal photons and the number of quantum state signals.
For protecting physical layer of optical fiber communication systems, quantum stream cipher called Y-00 and Alpha-Eta is promising. So far, we demonstrated secure and high speed optical fiber communication experiments using Y-00 quantum stream cipher. Our theoretical research revealed that the randomization techniques could enhance the security performance. In this work, we fabricated a novel Y-00 transceiver for GbE where the randomization technique was implemented. The transceiver employed the optical intensity modulated Y-00 quantum stream cipher with intensity levels of 4096. An appropriately designed irregular mapping as the randomization technique was experimentally demonstrated. The transceiver was successfully applied to secure optical fiber transmission of GbE signals.
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.
The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.
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.
It has been reported that error-free quantum reading of a classical digital memory is possible when the entangled coherent state |a〉 |a〉– |– a〉|–a〉 is used as the probe state for quantum reading with binary phase shift keying format under the assumption that the channel is noiseless [quant-ph/1108.4163v2]. In this paper, the theoretical performance limits of the minimum error probability and classical capacity of quantum reading with binary phase shift keying entangled coherent state signal are investigated in the presence of channel loss.
Proc. SPIE. 8518, Quantum Communications and Quantum Imaging X
KEYWORDS: Quantum key distribution, Failure analysis, Probability theory, Information security, Quantum communications, Current controlled current source
It is claimed in the many papers that a trace distance: d guarantees the universal composition security in quantum key distribution (QKD) like BB84 protocol. In this introduction paper, at first, it is explicitly explained what is the main misconception in the claim of the unconditional security for QKD theory. In general terms, the cause of the misunderstanding on the security claim is the Lemma in the paper of Renner. It suggests that the generation of the perfect random key is assured by the probability (1-d), and its failure probability is d. Thus, it concludes that the generated key provides the perfect random key sequence when the protocol is success. So the QKD provides perfect secrecy to the one time pad. This is the reason for the composition claim. However, the quantity of the trace distance (or variational distance) is not the probability for such an event. If d is not small enough, always the generated key sequence is not uniform. Now one needs the reconstruction of the evaluation of the trace distance if one wants to use it. One should first go back to the indistinguishability theory in the computational complexity based, and to clarify the meaning of the value of the variational distance. In addition, the same analysis for the information theoretic case is necessary. The recent serial papers by H.P.Yuen have given the answer on such questions.
In this paper, we show more concise description of Yuen's theory, and clarify that the upper bound theories for the trace distance by Tomamichel et al and Hayashi et al are constructed by the wrong reasoning of Renner and it is unsuitable as the security analysis. Finally, we introduce a new macroscopic quantum communication to replace Q-bit QKD.
The quantum noise based direct encryption protocol Y-OO is expected to provide physical complexity based
security, which is thought to be comparable to information theoretic security in mathematical cryptography,
for the. physical layer of fiber-optic communication systems. So far, several randomization techniques for the
quantum stream cipher by Y-OO protocol have been proposed, but most of them were developed under the
assumption that phase shift keying is used as the modulation format. On the other hand, the recent progress
in the experimental study on the intensity modulation based quantum stream cipher by Y-OO protocol raises
expectations for its realization. The purpose of this paper is to present design and implementation methods of a
composite model of the intensity modulation based quantum stream cipher with some randomization techniques.
As a result this paper gives a viewpoint of how the Y-OO cryptosystem is miniaturized.
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.
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.
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.
The quadrature amplitude modulation (QAM) signal of coherent state of light is applied to the quantum stream cipher by Y-00 protocol. We first discuss on the performance of the square-root measurement (SRM) for the QAM signals in comparison with the optimum receiver. It is shown that the quantum stream cipher with the QAM signals is designed by using the SRM, taking account of the ciphertext-only attack and the known/chosen plain attack. Furthermore, the modification of the quantum stream cipher with the QAM signals is considered.
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/Y_{E})=H(K/Y_{E})=H(K), H(K/Y_{E},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.
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)<
Previously the present protocol was referred as Yuen-Kim second version in our papers. In this paper, it is called Yuen protocol (Y-00) and we present an efficient implementation method of physical layer of Y-00 which can support a secure communication and a quantum key distribution (more generally key expansion) by IMDD (intensity modulation/direct detection) or FSK (frequency shift keying) optical fiber communication network. Although the general proof of the security is not yet given, a brief sketch of security analysis is shown, which involve an entanglement attack.
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