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arXiv:1404.4675

Masking Property of Quantum Random Cipher with Phase Mask Encryption -Towards Quantum Enigma Cipher-

Masaki Sohma, Osamu Hirota

Published Apr 18, 2014• 0 citations
arXivHTMLPDF

Abstract

The security analysis of physical encryption protocol based on coherent pulse position modulation(CPPM) originated by Yuen is one of the most interesting topics in the study of cryptosystem with a security level beyond the Shannon limit. Although the implementation of CPPM scheme has certain difficulty, several methods have been proposed recently. This paper deals with the CPPM encryption in terms of symplectic transformation, which includes a phase mask encryption as a special example, and formulates a unified security analysis for such encryption schemes. Specifically, we give a lower bound of Eve's symbol error probability using reliability function theory to ensure that our proposed system exceeds the Shannon limit. Then we assume the secret key is given to Eve after her heterodyne measurement. Since this assumption means that Eve has a great advantage in the sense of the conventional cryptography, the lower bound of her error indeed ensures the security level beyond the Shannon limit. In addition, we show some numerical examples of the security performance.

DOI
10.48550/arxiv.1404.4675

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The security analysis of physical encryption protocol based on coherent pulse position modulation(CPPM) originated by Yuen is one of the most interesting topics in the study of cryptosystem with a security level beyond the Shannon limit. Although the implementation of CPPM scheme has certain difficulty, several methods have been proposed recently. This paper deals with the CPPM encryption in terms of symplectic transformation, which includes a phase mask encryption as a special example, and formulates a unified security analysis for such encryption schemes. Specifically, we give a lower bound of Eve's symbol error probability using reliability function theory to ensure that our proposed system exceeds the Shannon limit. Then we assume the secret key is given to Eve after her heterodyne measurement. Since this assumption means that Eve has a great advantage in the sense of the conventional cryptography, the lower bound of her error indeed ensures the security level beyond the Shannon limit. In addition, we show some numerical examples of the security performance.
A quantum cipher supported by a secret key so called keyed communication in quantum noise (KCQ) is very attractive in implementing high speed key generation and secure data transmission. However, Yuen-2000 as a basic model of KCQ has a difficulty to ensure the quantitative security evaluation because all physical parameter for the cipher system is finite. Recently, an outline of a generalized scheme so called coherent pulse position modulation(CPPM) to show the rigorous security analysis is given, where the parameters are allowed to be asymptotical. This may open a new way for the quantum key distribution with coherent states of considerable energy and high speed. In this paper, we clarify a generation method of CPPM quantum signal by using a theory of unitary operator and symplectic transformation, and show an asymptotic property of security and its numerical examples.
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm for cryptanalysis and ability of computers. This kind of cipher cannot exceed the Shannon limit of cryptography, and it can be decrypted with proba- bility one in principle by trying all the possible keys against the data length equal to the secret key length. A cipher with quantum effect in physical layer may exceed the Shannon limit of cryptography. The quantum stream cipher by α/η or Yuen-2000 protocol (Y-00) which operates at Gbit/sec is a typical example of such a cipher. That is, ciphertext of mathematical cipher with a secret key is masked by quantum noise of laser light when an eavesdropper observes optical signals as a ciphertext of the mathematical cipher, while the legitimate receiver does not suffer the quantum noise effect. As a result, the inherent difference of accuracy of ciphertext between eavesdropper and legitimate receiver arises. This is a necessary condition to exceed the Shannon limit of cryptography. In this note, we present a new method to generate an inherent difference of accuracy of the ciphertext, taking into account a fundamental properties of quantum detection schemes.
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm for cryptanalysis and ability of computers. This kind of cipher cannot exceed the Shannon limit of cryptography,and it can be decrypted with probability one in principle by trying all the possible keys against the data length equal to the secret key length. A cipher with quantum effect in physical layer may exceed the Shannon limit of cryptography. The quantum stream cipher by α/ηα/ηα/η or Yuen-2000 protocol (Y-00) which operates at Gbit/sec is a typical example of such a cipher. That is, ciphertext of mathematical cipher with a secret key is masked by quantum noise of laser light when an eavesdropper observes optical signals as a ciphertext of the mathematical cipher, while the legitimate receiver does not suffer the quantum noise effect. As a result, the inherent difference of accuracy of ciphertext between eavesdropper and legitimate receiver arises. This is a necessary condition to exceed the Shannon limit of cryptography. In this note, we present a new method to generate an inherent difference of accuracy of the ciphertext, taking into account a fundamental properties of quantum detection schemes.
In any communication system, all data including encrypted data by the mathematical cipher are transmitted under the strict rule of the interface frame. Attacker can easily acquire the whole data the same as the data of legitimate users including the address, routing information and so on from the transmission line by tapping. This is very risky, especially for the secret sharing data center operations. So to hide the whole data in the transmission line is very attractive to ensure the high security level. This can be realized by Y-00 type random cipher that the ciphertext of simple mathematical cipher by PRNG is randomized by quantum noise and it gives a masking effect against the attacker's security analysis. This paper clarifies quantitative properties on the masking effect in the random cipher by Y-00 protocol, and shows the fact that a scheme by the intensity modulation may provide the greatest masking effect, even if the attacker employs the universal heterodyne receiver.
This paper surveys a new way for research of quantum cryptography. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm for the cryptanalysis and ability of computers. This kind of cipher cannot exceed the Shannon limit of cryptography, and it can be decrypted with probability one in principle by trying all the possible keys against the data length equal to the secret key length. A cipher based on quantum effect so called physical cipher may exceed the Shannon limit of the cryptography. The quantum stream cipher by �/� or Yuen-2000 protocol (Y- 00) which operates at Gbit/sec is a typical example of such a cipher, and may exceed the Shannon limit. In this paper, we show an existence of cipher which exceeds the Shannon limit, and discuss practical realization methods for them. First, the conditions to exceed the Shannon limit are summarized. Then we discuss the generalized secret capacity of the wiretap channel model supported by a secret key to discuss an existence of cipher exceeding the Shannon limit. The generalized secret capacities for space communication and fiber communication are given. In gen- eral, one needs quantum optimum receiver to realize such capacity. But when bandwidth limitation of users is deleted or the eavesdropper has a device limit, a cipher scheme exceeding the Shannon limit may be realized merely by the conventional optical communication devices which are affected by quantum noise at optical signal measurement.