Beyond the Shannon limit by quantum stream cipher Y-00 and Holevo-Sohma-Hirota theorem -- General proof

Osamu Hirota

Osamu Hirota, Masaki Sohma

This paper discusses the foundation of security theory for the Quantum stream cipher based on the Holevo-Yuen theory, which allows the use of "optical amplifiers". This type of cipher is a technology that provides information-theoretic security (ITS) to optical data transmission by randomizing ultrafast optical communication signals with quantum noise. In general, the quantitative security of ITS is evaluated in terms of the unicity distance in Shannon theory. However, the quantum version requires modeling beyond the Shannon model of a random cipher to utilize the characteristics of the physical layer. Therefore, as the first step, one has to develop a generalized unicity distance theory and apply it to the evaluation of security. Although a complete theoretical formulation has not yet been established, this paper explains a primitive structure of a generalization of the Shannon random cipher and shows that the realization of this is the generalized quantum stream cipher. In addition, we present several implementation methods of generalized quantum stream ciphers and their security.

Ching–Yi Lai, Kai-Min Chung

Kentaro Kato

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.

Osamu Hirota, Takehisa Iwakoshi, Masaki Sohma +1 more

The security in the next generation optical network which realizes "Cloud Computing System Service with data center" is one of the most important problems. In such a network, the encryption in physical layer which provide super security and small delay is a preferable. It has to be applicable, however, to very high speed data because the basic link is operated at 2.5 Gbit/sec ~ 10 Gbit/sec. The quantum stream cipher by Yuen-2000 protocol (Y00) is a completely new type of random cipher, which can exceed the Shannon limit of the symmetric key cipher. This paper extends some theoretical results on the security for quantum stream cipher such as Y00 protocol and generalized Y00. First, the conditions to exceed the Shannon limit are summarized. We formulate a generalized secret capacity in the sense of wire tap channel supported by secret key to clarify a cipher exceeding the Shannon limit. The generalized secret capacities for space communication and fiber communication based on the generalized Y00 are given. When the relaxation of physical constraint or device limit of the eavesdropper is allowed, we point out that a cipher scheme exceeding the Shannon limit can be realized only by the conventional optical system.

Mario Berta, Matthias Christandl, Renato Renner