Logic locking is an intellectual property (IP) protection technique that prevents IP piracy, reverse engineering and overbuilding attacks by the untrusted foundry or end-users. Existing logic locking techniques are all based on locking the functionality; the design/chip is nonfunctional unless the secret key has been loaded. Existing techniques are vulnerable to various attacks, such as sensitization, key-pruning, and signal skew analysis enabled removal attacks. In this paper, we propose a tenacious and traceless logic locking technique, TTlock, that locks functionality and provably withstands all known attacks, such as SAT-based, sensitization, removal, etc. TTLock protects a secret input pattern; the output of a logic cone is ipped for that pattern, where this ip is restored only when the correct key is applied. Experimental results confirm our theoretical expectations that the computational complexity of attacks launched on TTLock grows exponentially with increasing key-size, while the area, power, and delay overhead increases only linearly. In this paper, we also coin "parametric locking," where the design/chip behaves as per its specifications (performance, power, reliability, etc.) only with the secret key in place, and an incorrect key downgrades its parametric characteristics. We discuss objectives and challenges in parametric locking.