Study on Information Security and Random Number Generation from Information Theoretical Viewpoints

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Our research results are summarized in the followings.1. Statistical Properties of Chaotic Binary Seauences Generated by One-dimensional Maps :There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. Using the framework of large deviation theory for dynamical systems, we formulated this problem as a problem of computing the rate function. Furthermore, for the chaotic binary sequence generated by the dyadic map and threshold function, we obtained an explicit form of the rate function for some class of threshold functions.2. Transmission Problem of Confidential Messages Using Relay Channels :In the relay channel a relay helps the transmission of messages from one sender to one receiver. The relay is also regarded as a wire-tapper who can obtain some knowledge about the transmitted messages. From the above viewpoints we have discussed the security of the relay channel and have derived some explicit result.3. Identification via Noisy Channels :We have studied the converse coding theorem for the identification via general noisy channels. We have estimated two types of error probabilities of identification for rates outside the identification capacity, deriving some function which serves as a lower bound of the sum of two error probabilities of identification. In particular, in the case of stationary discrete memoryless channels, we have proved that the sum of two error probabilities tends to one exponentially and derive an explicit lower bound of this exponent function. Furthermore, we have extended our arguments in two cases of multi-user channels. One is the multiple access channels and the other is the broadcast channels. For those two multi-user channels we have obtained results for outer bounds of the identification capacity regions.