Comparison of security mechanisms of Mathematical cipher, Wyner scheme, QKD, and Quantum stream cipher

TL;DR

Comparative explanations of the security principles underlying these various cryptographic technologies are likely to promote mutual understanding among researchers across different fields to promote mutual understanding among researchers across different fields.

Abstract

A new generation of global communications technology has been emerging. These systems, which utilize established device technologies and quantum effect devices, require ultra-high speeds, low cost, and strong security. In recent years, global communication systems have faced various practical security challenges depending on their configurations, and research efforts are underway to address these issues. In particular, the issue of the security of physical layer security from microwave wireless systems to quantum optical communication systems is urgent problem. However, concepts of cryptographic schemes have also been diversifying. Typical examples are mathematical ciphers, the Wyner scheme and QKD. Then, the Y-00 protocol has recently emerged as a third pillar cryptographic technology in the optical quantum domain. These security principles differ significantly from one another. This makes it difficult for different fields to understand each other. At this stage, comparative explanations of the security principles underlying these various cryptographic technologies are likely to promote mutual understanding among researchers across different fields. As the first trial, this lecture note explains the security mechanism of the third pillar (Y-00), comparing it with the principles of other mechanisms.

Figures (14)

• Figure 1: Summary of comparison of security mechanisms of early and current QKD, and quantum stream cipher (Y-00). $\chi_H$ is the Holevo capacity, $\chi_H(\Xi)$ is the Holevo capacity as function of randomization by modulation ;$\Xi$. The purpose of this note is to provide an explanation of this diagram. A detailed comparison is discussed in the appendix.
• Figure 2: Scheme of encryption and decryption of standard quantum stream cipher. The optical modulator system selects one basis from a set of $M$ communication bases according to a running key. It is done by phase controller. Then it performs binary PSK for plaintext (data) by using selected basis.
• Figure 3: Quantum noise effect to Bob and Eve on plaintext. Upper part shows the phase signals on phase plain of light wave which correspond to the physical ciphertext. The phase reference frame of Bob's receiver is adaptively rotated by the running key sequence. So Bob's decision becomes always $+\alpha$ or $-\alpha$. Because she does not know the secret key, Eve has to adopt a receiver for $2M$ value, and she has to identify adjacent signals hidden by quantum noise. In order for Eve to obtain the key information, she needs to identify the exact value of the phase signals that correspond to the running key.
• Figure 4: Comparison of the quantum measurement and quantum decision described by POVM. A shows the simple quantum measurement for Born effect. B shows the application of classical communication theory for decision. C shows the quantum decision by decision operator derived from quantum communication theory. The asymmetry of channels of Bob with key and Eve without key come from the decision in the cases of B and C.
• Figure 5: This shows a channel model of attack against data. Data sequences obtained by an eavesdropper in quantum stream cipher is encrypted at measurement by quantum error. The quantum error can be controlled by Alice's randomization based on modulation scheme. In the case of conventional cipher, received sequence is ciphertext enrypted by PRNG.