Enhanced Security of Public Key Encryption with Certified Deletion

In classical cryptography, certified deletion is simply impossible. Since classical information can be copied any number of times easily. In quantum cryptography, certified deletion is possible because of theorems of quantum mechanics such as the quantum no-clone theorem, quantum superposition etc. In this paper, we show the PKE-CD (Public Key Encryption with Certified Deletion) scheme constructed in by Bartusek and Khurana in CRYPTO 2023 lack an important security property, which is important in practical applications. Then we show how to enhance this property, and construct a concrete scheme with this property. And we also discuss the relations between PKE-CD and other quantum cryptographic schemes such as quantum seal, quantum bit commitment etc.