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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.

我们的研究成果总结如下.一维映射产生的混沌二进制序列的统计特性：有几种尝试通过使用一维映射来产生混沌二进制序列。从工程应用的角度来看，有必要对有限长样本序列的统计性质进行评估。利用动力系统大偏差理论的框架，我们将这个问题归结为一个计算速率函数的问题。此外，对于由并元映射和阈值函数产生的混沌二进制序列，我们得到了一类阈值函数的速率函数的显式形式.使用中继信道的机密消息传输问题：在中继信道中，中继帮助将消息从一个发送者传输到一个接收者。中继器也被看作是一个窃听器，可以获得有关传输信息的一些知识。从上述观点出发，我们讨论了中继信道的安全性，并得到了一些明确的结果.通过噪声信道的识别：我们已经研究了通过一般的噪声信道的识别的匡威编码定理。我们估计了两种类型的错误识别率以外的识别能力，导出了一些函数，作为一个下界的两个错误识别概率之和。特别是，在固定的离散无记忆通道的情况下，我们已经证明了两个错误概率的总和趋于一个指数，并推导出这个指数函数的显式下界。此外，我们已经扩展了我们的论点在两种情况下的多用户信道。一个是多址信道，另一个是广播信道。对于这两个多用户信道，我们得到的结果的识别能力区域的外边界。