# Quantum Stream Cipher Based on Holevo-Yuen Theory
## 2 Current Status of Quantum Communication Security Technology  
### Quantum Cryptography  
As introduced in the above section, there are two quantum cryptography techniques. Let us give their brief introduction below. (1) Quantum Key Distribution  
BB-84 quantum key distribution (QKD) was proposed by [PERSON] and [PERSON] in 1984. It is a protocol to share a secret key sequence by using photon communication, that is guaranteed to be quantum nature. Since the photons used in this protocol are weak light, the transmission speed and distance are limited. In addition, many of the sequence of photons that carry information are lost due to attenuation effects in the transmission line, and the sequence of photons that reaches the receiver is also subject to errors due to noise effects. So, the operation involves discarding the majority of the received bit sequence. Therefore, data itself cannot be sent, only random numbers can be sent. Thus, only the delivery of the secret key for symmetric key cipher is possible. This is why it is called QKD. Recently, many newspapers have reported that several R&D groups can provide the commercial systems of QKD. The transmission speed is the order of 100 Kbit/s, and transmission length is below 100 km. The satellite system is one of the solutions to cope with the distance. However, the transmission speed is so small. In any case, if one tries to increase the transmission speed, then there is a trade-off, and one has to shorten the relay interval. Since the maximum transmission speed is about a megabit, it is difficult to supply keys to the one-time pad cipher for data after key delivery, and it is likely to be limited to supplying initial keys (secret keys) for AES and others. Figure 1: Classification of cryptographic techniques. (2) Quantum Stream Cipher  
Y-00 quantum stream cipher is a protocol for physical symmetric key cipher proposed by [PERSON] of Northwestern University in the DARPA project (2000) [3]. The details are explained in the next section, but a simple concept is presented here. This technique is characterized by the fact that it does not allow the physical signals consisting of the mathematical random generator and information data to be obtained without error. In this scheme, the ciphertext in Y-00 circuit system of the mathematical cipher consisting of the generator and data, which is the target of the eavesdropper, as described by \(y=\alpha_{i}(X,f_{g}(K_{s}),R_{p})\). Then, we design the system such that the ciphertext \(y=\alpha_{i}(X,f_{g}(K_{s}),R_{p})\) is mapped into ensemble of coherent state \(\mid\Psi(X,K_{s},R_{p})>\) with the quantumness based on the Holevo-Yuen theory [4; 5; 6]. This is called Y-00 signal, which corresponds to ciphertext on the Hilbert space. Thus, the ciphertext as the classical signal is protected by the quantumness. Let us describe it shortly. Although ordinary laser light of high power is used as the transmission signal, signals on the communication channel can be made to have very strong quantum properties in the sense of quantum detection theory [7]. This is the Y-00 principle [3]. That is, a large number of physical binary light communication base is prepared to transmit electric binary data, and the binary data is transmitted by using one communication base which is randomly selected from many communication bases by a mathematical cipher. Let \(M\) be the number of the base. The optical signals on the communication channel become ultra-multiple-valued signals (\(2M=4096\) or more values are common) against the eavesdropper without the knowledge of communication base. At this time, strong quantum nature in the signal ensemble appears even if the one signal is in high power light, when it is constructed by such ultra-multiple-valued signal. In other words, this method means that the quantum nature in the sense of quantum detection theory [7] is created artificially by modulation schemes, so that it does not require light with strong physical quantum nature, such as a photon.