对依赖密钥的明文进行安全加密的性质研究

In modern cryptography, one of important tasks is to explore the security definitions that are used in real world. Recently, a new kind of security definition called Key-Dependent Message (KDM) security has been proposed. It essentially requires that, in an encryption scheme, it is infeasible for an adversary to obtain information of a message from its ciphertext even if the adversary has access to other encryptions of messages that can been seen as functions of the secret keys (the functions are chosen from some ensembles). Many cryptographers focus on the research about it for its novelty and practical applications, and obtain many interesting results. However, there are still many important open problems left to be resolved. Our aims here are to make a systematic and an intensive study on KDM securities from a whole including the size of function ensemble, the efficiency of the schemes, the rank of security as well as the assumptions security based on in the schemes. We will seek the schemes achieving KDM security with respect to larger ensembles as well as those with stronger KDM security which is based on weaker assumptions. For applications, we try to establish even richer relationships between the KDM security and other cryptographic primaries and tools so as to apply our new results to practice.

在现代密码学中，如何使用适当安全的加密是最重要、最基本的任务之一。近年来出现的新的安全性定义--对于依赖于密钥的明文(Key-Dependent Message，KDM)加密的安全性要求:即使敌手得到了私钥的某些函数(来自于某一函数族)值的密文，也不能获得新的密文所对应明文的任何信息。这一安全性因其新颖性和实用性，引起很多密码学家关注和研究, 取得了许多研究成果。但是，还有很多重要的公开问题未被解决。本项目将从函数族的大小、方案的效率、安全性的强弱以及所依赖的假设等方面对KDM安全性进行系统而充分的研究和探讨。期望能够构造出对更广的函数族满足KDM安全的方案来。并期望能在尽可能弱的假设基础上，构建满足更强的KDM安全方案。在应用方面，我们试图建立KDM安全性与其他的密码理论或工具之间更多的联系拓展其应用范围；同时, 将最新的研究成果转化到实际应用中。

近年来出现了一种对于依赖密钥的明文(Key-Dependent Message，KDM)加密的新的安全性要求:即使敌手得到了私钥的某些函数值的密文，也不能获得新的密文所对应明文的任何信息。在过去十几年的实践中人们发现，明文消息往往确实依赖于私钥本身，故研究KDM安全性具有重要的理论和实际意义。.本项目对于各种密码方案的KDM安全性进行了系统的研究与探讨，通过对函数加密和全同态加密进行研究，得到了更大函数族上的KDM安全的加密方案；从一些经典的CCA安全的加密方案着手，构造出了满足KDM-CCA安全性且实用的加密方案；研究了与KDM安全性相关的其他安全性，针对不同的密码学原语，构造了满足相应安全性的密码方案；从不同的安全性假设入手，构造了基于不同假设且具备不同功能的密码方案；研究了与KDM安全性相关的其它密码学原语，如同态消息认证码、可验证计算、可搜索加密等，提出了多个高效实用的方案；此外，还对实际应用过程中所涉及到的程序漏洞检测技术进行了相关研究。