Study On KDM Security Of Encryption Scheme

Nowadays, proven security has been the main method of analyzing the security of cryptographic schemes, with the premise of security definitions. The classical definitions, such as IND-CPA, IND-CCA and IND-CCA2 etc, are based on the assumption that plaintexts and secrete keys are independent. In practice, however, the adversary may get the encryption of the information related to the secrete key. To analyze and solve the security problem of this special case, a definition of KDM security is proposed in this paper.KDM(Key-dependent message)security is introduced to address the case where message is a function of the secret key of encryption scheme. In recent years, KDM security has become an active research area in the field of international cryptography. People are trying to construct better encryption schemes of KDM security based on several different assumptions. Firstly, this paper gives an introduction of the application background of KDM security scheme, showing the necessity and importance of the KDM security, and summarizes the current main technical means of constructing encryption scheme of KDM security. Secondly, by Universal Hash Function, a stateless symmetric encryption scheme is presented that is information-theoretically KDM secure based on an extended version of Left-over Hash Lemma in the standard model. The scheme is secure under a bound of near exponent number of encryptions for which the messages depend on an arbitrary way of the secret key. Thirdly, through choosing parameters properly and making comparisons of existing schemes, the security and efficiency of the proposed scheme in our paper are proved to be improved. Finally, by combining the Universal Hash Function with the Ideal Cipher Model, the KDM problem is converted to a common symmetric encryption issue, and a symmetric encryption scheme of KDM security is proposed that can resist the active attacks. Moreover, the scheme is proved to be secure against the attacker with unbounded ability under the Ideal Cipher Model.