Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening

Abstract

The existence of encryption and commitment schemes secure under selective opening attack (SOA) has remained open despite considerable interest and attention. We provide the first public key encryption schemes secure against sender corruptions in this setting. The underlying tool is lossy encryption. We then show that no non-interactive or perfectly binding commitment schemes can be proven secure with black-box reductions to standard computational assumptions, but any statistically hiding commitment scheme is secure. Our work thus shows that the situation for encryption schemes is very different from the one for commitment schemes.