A quantum stream cipher by Yuen 2000 protocol with nonlinear random number generator

Abstract

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. First, we state the basics of a quantum stream cipher by Y-00. Second, we propose the randomization on a running key consisting of two different type of basis converter. To evaluate the effect of the randomization in terms of the amount of information that is extracted by her measurement, numerical simulation is performed in the cases of an optical heterodyne receiver and a quantum optimal receiver under the assumption that the eavesdropper knows plaintext. Finally, we summarize the results.