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The advancing of reverse engineering techniques has complicated the efforts in intellectual property protection. Proactive methods have been developed recently, among which layout-level integrated circuit camouflaging is the leading example. However, existing camouflaging methods are rarely supported by provably secure criteria, which further leads to an over-estimation of the security level when countering latest de-camouflaging attacks, e.g., the SAT-based attack. In this paper, a quantitative security criterion is proposed for de-camouflaging complexity measurements and formally analyzed through the demonstration of the equivalence between the existing de-camouflaging strategy and the active learning scheme. Supported by the new security criterion, two camouflaging techniques are proposed, including the low-overhead camouflaging cell generation strategy and the AND-tree camouflaging strategy, to help achieve exponentially increasing security levels at the cost of linearly increasing performance overhead on the circuit under protection. A provably secure camouflaging framework is then developed combining these two techniques. The experimental results using the security criterion show that camouflaged circuits with the proposed framework are of high resilience against different attack schemes with only negligible performance overhead.