 Hi, I'm Liu. I'm going to talk about the summary of our work, Functional Encryption with Secure Key Leasing. This is a joint work with Fuyuki Kitagawa. Our question is whether we can copy, protect or delete data. It is easy to copy classical digital information as much as you want. Moreover, it is hard to prove that we delete classical information. However, if we consider quantum information, the situation is completely different. In general, it is impossible to copy quantum state by the no-croning theorem. In addition, we could prove that quantum information is deleted by the uncertainty principle. There are many uncornable cryptographic primitives or cryptographic primitives with certified deletion by using those quantum properties. In this work, we focus on functional encryption. In functional encryption, we can generate a functional decryption key where a function F is hardwired. When we receive a ciphertext of plaintext X, we can compute F of X by the functional decryption key. The question in this work is whether we can copy, protect or delete functional decryption keys by making those keys quantum states. We propose the notion of functional encryption with secure key leasing. In this primitive, a functional decryption key is quantum state. And we also generate a verification key for each decryption key. We can delete a functional decryption key and generate a certificate for deletion. If the certificate is valid, then we can guarantee that the functional decryption key was deleted. After the deletion, we can no longer decrypt ciphertext. We also propose a stronger notion, single decryptor functional encryption. In this primitive, functional decryption key is quantum state as FE with secure key leasing. The difference is that we do not have a deletion process and the copying key is prevented. Even if we try to generate two entangled quantum states from a functional decryption key, one of them does not have the decryption capability. In this work, we present a bounded collusion resistant secret key FE with secure key leasing scheme based on one way functions. We also present a collusion resistant public key single detector FE scheme based on indistinguishability of the session and the one way functions. Please attend my talk or read our paper for detail. Thank you for watching this video.