【作者】 余小龙；

【导师】 林迎珍；

【作者基本信息】 哈尔滨工业大学 ， 计算数学， 2010， 硕士

【摘要】 本文把香农密码学的完全保密概念与混沌密码学联系起来,设计了一类理论上是完全保密的加密方案。在该保密方案中,采用了新的一类复合映射,证明了该类映射在Devaney定义下是混沌的,并讨论了该映射的不变分布和密码学特性。证明了该映射在有限分割生成的符号序列是独立均匀分布的,从而设计了一种加密结构使得加密方案理论上是完全保密方案。在实际应用中,由于有限精度计算,该类方案不可能真正达到完全保密。为了对抗有限精度效应,引入一类简单位操作使得加密方案在实际应用中也具有较强的抗破译能力。该类实际加密方案至少能有效对抗唯密文攻击、选择明文攻击。在对算法分析方面,至少能对抗符号动力学攻击、差分攻击。该算法具有一定的实用价值。本文还探讨了有限精度方面的问题,建立了有限精度下的该类方案的实现模型,对有限精度下的Lyapunov指数也做了简单讨论。最后,选取这类算法的一个具体算法应用于图像加密领域。基于图像的实验和性能分析指出该加密算法有较高的安全性。更多还原

【Abstract】 This paper introduces the concept of the Shonnon’s perfect security into chaoticcryptography and designs a class of chaotic encryption systems who is perfectsecurity in theory. In these systems, we use a class of new compound chaoticmappings, which is chaotic by Deva ney chaotic theory. Then we discuss the invariantdistribution and the good cipher quality of these mappings. It’s proven that symbolicsequences generated using finite partition by these mappings have uniformdistribution and are independent of each other. The paper designs an encryptionarchitecture, which links with symbolic sequences are proven is perfect security intheory. In actual applica tion, to the limited precision computation, perfect security ofthe scheme is inaccessible . To fight the limited precision of computer, the paper addssome bit-ma nipulations in encryption algorithm process, this option can possessstrong anti-translated capability in actual applica tion. The actual encryption schemecan resist cipher text-only attack and known-pla intext attack effectively at least. Inalgorithm analysis , the scheme can resist symbolic dynamic analysis and differentialanalysis at least. Therefore, this class of the chaotic cryptographies have thepractica lly applied value . Besides, the article studies some theories about the limitedprecision of computer, establishes the limited precision model based on the schemeand discusses Lyapunov exponent in limited precision computer. At last, we apply anexample of a class of chaotic encryption systems to ima ge encryption . The statistica ltests and related analysis prove that the actual encryption scheme has high security.更多还原