相关密钥安全性若干关键问题研究

With the continuous development of the techniques of modern cryptanalysis, the classical definitions of cryptographic schemes, such as chosen plaintext attack security, chosen ciphertext attack security etc., is not sufficient to depict the attacks appeared in practical scenarios, including related-key attack (RKA). The related-key security, corresponding to RKA, has been drawn attentions for its novelty and practicability, and studied by many cryptographers. Many results about it have also been obtained. However, there still exist a lot of basic but important issues being not resolved. In our project, we will sduty the following problems about the RKA security as well as related ones..(1). Study the RKA security for some new cryptographic primitives..(2). Construct public-key encryption schemes with the RKA-KDM security and prove them..(3). In the case of RKA, if it is possible to imply multiple bits public-key encryption scheme from single bit one..It is very necessary to study about those problems from the view of both theory and applications. For theory, it can further enrich the system of modern cryptography. Then for application, it can enhance confidence of people using the cryptographic schemes and enlarge the number of tools when constructing complicated protocols.

随着现代密码分析技术的不断发展，密码方案的标准安全性定义，如选择明文攻击安全性、选择密文攻击安全性等，已经无法刻画实际应用场景中的攻击，如相关密钥攻击 (Related-Key Attack, RKA) 。与 RKA 相对应的相关密钥安全性因其新颖性和实用性，引起了很多密码学家的关注和研究，也取得了许多研究成果。但是在该领域还有许多基本而重要的问题未被解决。本项目拟从以下几个方面对 RKA 安全性及相关问题进行研究：.(1). 对一些新的密码学原语进行 RKA 安全性研究。.(2). 构造并证明具有 RKA-KDM 安全性的公钥加密方案。.(3). RKA 情形下单比特公钥加密方案是否可以蕴含多比特公钥加密方案。.对于这些问题的研究无论从理论还是应用角度来说都是非常必要的：理论上，可以更加丰富现代密码学理论体系；应用上，增强人们使用密码方案的信心、丰富人们构造复杂安全协议时的工具。

相关密钥攻击(Related-Key Attack)是近年来出现的一类物理侧信道攻击。它刻画了敌手通过一定的“错误注入技术”来改变密码设备的内部状态从而达到破坏数据的隐私性或完整性等目标。本项目以RKA为研究主体，对与之密切相关的若干关键问题进行了研究。具体来说，.1）对一些重要密码原语，如：基于身份签名，基于身份同态签名以及随机谕言机模型和标准模型下网络编码签名方案的RKA安全性进行了研究。.2）对若干重要的公钥密码体制，如：REACT，DHIES，基于身份加密体制等，研究了其密钥相关消息(Key-Dependent Message, KDM)安全性。由于RKA与KDM在某些性质上非常相似，所以对这些公钥密码方案KDM安全性的研究有助于人们更进一步认识RKA。.3）在单比特情形下，探讨了基于LWE(Learning with Errors)假设的全同态密码方案的构造以及明文空间为0，1矩阵的全同态方案实现。.4）对已构造实现的RKA安全密码原语进行了广泛的应用。如：应用于云数据完整性验证，同态消息认证码以及外包计算等。.对于这些关键问题的研究进一步丰富了RKA研究的理论框架，同时，对于RKA安全密码方案在其它领域的应用有着极为重要的推动作用。