Logic encryption is a powerful hardware protection technique that uses extra key inputs to lock a circuit from piracy or unauthorized use. The recent discovery of the SAT-based attack with Distinguishing Input Pattern (DIP) generation has rendered all traditional logic encryptions vulnerable, and thus the creation of new encryption methods. However, a critical question for any new encryption method is whether security against the DIP-generation attack means security against all other attacks. In this paper, a new high-level SAT-based attack called SigAttack has been discovered and thoroughly investigated. It is based on extracting a key-revealing signature in the encryption. A majority of all known SAT-resilient encryptions are shown to be vulnerable to SigAttack. By formulating the condition under which SigAttack is effective, the paper also provides guidance for the future logic encryption design.