 Hello, my name is Zheng Anhuang. This is a job work with Zheng Zuo Lai, Shui Han, Lin Lv and Jian Wang. The topic is anonymous public key encryption under corruptions. Firstly, let me introduce some background information. For public key encryption under corruptions, both the secret keys and messages could be leaked. As far as we know, the first notion of anonymity for PKE under corruptions is proposed by Behemouda et al. in 2020. In their work, anonymous CRR Secure and ISO Secure PKE is employed to build an evolving committee proactive secret sharing scheme. Unfortunately, there are still some problems left. No known PKE achieves their anonymous CRR security. The adversary is not allowed to obtain any secret key before seeing several text, and each public key is used to encrypt a single message. Moreover, both confidentiality and anonymity under corruptions are needed for constructing an ECPSS scheme. But we notice that for ISO security, the adversary is able to open a specified subset of the training to several texts, and for anonymous CRR security, the adversary does not have this ability. So these two security notions are formalized under different types of corruptions. Focusing on these problems, we define anonymous ISOK and C security for PKE, which is anonymity under receiver's lack of opening a text in the k-training setting and adaptive user corruptions. And then we define a confidentiality notion under the same types of corruptions. Now we turn to the definition of anonymous ISOK and C security. In the real game, there are totally n public keys. The adversary specifies the public key distribution and k-t-training messages. In other words, the adversary knows all the encrypted messages, but he does not know which public keys are used for encryption exactly. The adversary can make two kinds of auto-call queries. User corruption queries and selective opening queries. For the user corruption queries, the adversary submits i and receives s-k-i. For the selective opening queries, the adversary queries on j and receives s-k-i-j, which means that he asks to open the j self-text. Finally, he returns output. The ideal game is similar, except that there are no public keys and no encryptions. So we use the indices of public keys to replace the public keys. Know that the simulator will not receive any self-text, so she does not have any information about the indices of the public keys corresponding to the unopened and uncorrupted users. This is how we formalize the notion of anonymous ISOK and C security. The confidentiality notion under the same type of corruption is similarly defined. The main difference is that the distribution of public keys is replaced with a distribution of messages, and all the other details are similarly modified. And then, we show that anonymous ISOK and C CPA security implies anonymous COR security, and the corresponding confidentiality implies the standard ISOK security. For constructions, we show a framework of constructing PKE achieving both anonymous ISOK and C CCA security and confidentiality under the same types of corruptions. Specifically, we propose a primitive code key and message in non-committee encryption, KMNCE, and use it to show a PKE scheme achieving both of the two new security requirements. And then, we use a new primitive code key openable hash proof system to construct KMNCE. The obtained MDDH-based PKE scheme has compact server text and tight security reduction, and is the first PKE scheme achieving anonymous COR security. Well, this is the brief introduction of our work. Thanks for your attention.