Smooth NIZK Arguments with Applications to Asymmetric UC-PAKE and Threshold-IBE

We introduce a novel notion of smooth (-verifier) noninteractive zero-knowledge proofs (NIZK) which parallels the familiar notion of smooth projective hash functions (SPHF). We also show that the recent single group element quasi-adaptive NIZK (QA-NIZK) of Jutla and Roy (CRYPTO 2014) for linear subspaces can be easily extended to be computationally smooth. One important distinction of the new notion from SPHFs is that in a smooth NIZK the public evaluation of the hash on a language member using the projection key does not require the witness of the language member, but instead just requires its NIZK proof. This has the remarkable consequence that in the Gennaro-Lindell paradigm of designing universally-composable password-authenticated keyexchange (UC-PAKE) protocols, if one replaces the traditionally employed SPHFs with the novel smooth QA-NIZK, one gets highly efficient UC-PAKE protocols that are secure even under dynamic corruption. This simpler and modular design methodology allows us to give the first single-round asymmetric UC-PAKE protocol, which is also secure under dynamic corruption in the erasure model. We also define a related concept of smooth signatures, which we show is black-box equivalent to identity-based encryption (IBE). The novel abstraction allows us to give the first threshold (private-key generation) fully-secure IBE in the standard model.