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

信息论视角下的信息安全与随机数生成研究

基本信息

批准号：
13650415
负责人：
OOHAMA Yasutada
金额：
$ 1.15万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650415/
关键词：
Chaotic Binary Sequence Relay Channels Confidential Massages Identification General Noisy Channels Multiple Access Channels Broadcast Channels Information Security 同定誤り確率

项目摘要

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.

我们的研究结果总结在以下1。一维图产生的混乱二元海上的统计特性：有几种尝试通过使用一维图来产生混乱的二进制序列。从工程应用的角度来看，有必要评估有限长度样本序列的统计特性。使用大型偏差理论的动力学系统框架，我们将此问题提出了计算速率函数的问题。此外，对于由二元映射和阈值函数产生的混乱二进制序列，我们获得了某些阈值函数的速率函数的明确形式。2。使用继电器通道的机密消息的传输问题：在继电器通道中继电器有助于将消息从一个发件人传输到一个接收器。继电器也被视为可以获得有关传输消息的一些知识的电线。从上面的角度来看，我们已经讨论了中继渠道的安全性，并得出了一些明确的结果3。通过嘈杂通道的识别：我们已经研究了通过一般噪声通道识别的相反编码定理。我们估计了标识能力以外的率的两种类型的误差概率，从而得出了一些函数，这些功能是两个识别识别概率的总和的下限。特别是，在固定离散无内存通道的情况下，我们已经证明了两个误差概率的总和呈指数趋向于一个，并得出了该指数函数的显式下限。此外，我们在两种多用户渠道的情况下扩展了论点。一个是多个访问渠道，另一个是广播频道。对于这两个多用户通道，我们为识别能力区域的外界获得了结果。