Group Signature Implies PKE with Non-interactive Opening and Threshold PKE

Abstract

In this paper, we show that both Public Key Encryption (PKE) with non-interactive opening and threshold PKE can be constructed from an arbitrary group signature scheme which is secure in the dynamic group setting. This result implies that group signature (in dynamic groups) is a significantly strong cryptographic primitive, since the above PKEs with additional functionalities are already much stronger primitives than the standard chosen-ciphertext secure PKE, which is itself recognized as a very powerful cryptographic tool. We can interpret our result as meaning that designing secure group signatures is significantly harder than many other ordinary cryptographic primitives.