Logic locking is a technique that is proposed to protect outsourced IC designs from piracy and counterfeiting by untrusted foundries. A locked IC preserves the correct functionality only when a correct key is provided. Recently, the security of logic locking is threatened by a new attack called SAT attack, which can decipher the correct key of most logic locking techniques within a few hours even for a reasonably large key-size. This attack iteratively solves SAT formulas which progressively eliminate the incorrect keys till the circuit is unlocked. In this paper, we present a circuit block (referred to as Anti-SAT block) to enhance the security of existing logic locking techniques against the SAT attack. We show using a mathematical proof that the number of SAT attack iterations to reveal the correct key in a circuit comprising an Anti-SAT block is an exponential function of the key-size thereby making the SAT attack computationally infeasible. Besides, we address the vulnerability of the Anti-SAT block to various removal attacks and investigate obfuscation techniques to prevent these removal attacks. More importantly, we provide a proof showing that these obfuscation techniques for making Anti-SAT un-removable would not weaken the Anti-SAT block's resistance to SAT attack. Through our experiments, we illustrate the effectiveness of our approach to securing modern chips fabricated in untrusted foundries.