On Cryptographic Application Of Logistic Map

With the great development of computer network and communication technologies,the popularity of social networking technologies, especially by the rapid adoption ofsmart phones based personal digital portable devices, people can be more convenientand quick to get various of information from the Internet, correspondingly，informationsecurity has become more and more important. Especially in recent years, theimage-based multimedia data has an increasing proportion which data transmit over thenetwork, it can be predicted that image will become a major information expression in thefuture. However, the traditional encryption technology can’t effectively to protect thesafety of image information, so, insistently demand the research and development ofmore information security techniques with security, reliability and high efficiency.Since some researchers have found that chaotic system has the sensitivity to initialconditions or control parameters which similar to the nature of the cryptography, a largenumber of chaotic encryption algorithms were put forward, at the same time, it is one ofthe hottest frontier topics on the combination of nonlinear science and informationscience to apply chaos theory into information security.The Logistic map is a well-known one-dimensional chaotic map. Because of itssimple form, and it has a complex dynamic behavior, and Logistic map has been widelyused in designing encryption scheme and pseudo-random bit generator. Compared withtraditional encryption algorithms, the encryption algorithm based on Logistic map isfaster, more efficient and security. This paper analyzes and summarizes the typicalapplication route of Logistic map in cryptographic, and examines negative effect of thismap from the perspective of cryptanalysis. The main contents are as follows:1. The origin and development of Logistic map is introduced detailedly, as well asseveral definitions in the form of Logistic map. Through a lot of experiments, wefocuse on the dynamics property of Logistic map, and put emphasis on thecharacteristics of Logistic map such as sensitivity, randomness and correlationand so on. Through analysis and research, it confirmed the superior sensitivityand good randomness of the Logistic map which can be fully used in the field ofinformation security. In addition, for some defects which exist in the Logisticmap, it gives some improvement methods. 2. Through concluding and summarizing the encryption algorithms based onLogistic map which were published in recently years, it cam be divided intothree categories. And for each type, it provides a very typical example withdetailed description which include detailed description of the encryptionalgorithm and the corresponding conventional cryptanalysis.3. Some specifical security defects of Logistic map are detailly introduced in thisarticle. Simultaneously, analysis and study of these defects may lead to someconsequences, in addition, it gives some examples which breaking the imageencryption algorithms based on Logistic map by using special flaws of Logisticmap. Finally, some suggestions are given when we applied the Logistic map incryptographic system.Finally, the research work of this paper is comprehensively summarized, and thefuture research work is indicated.