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An increasing number of recent experimental works have demonstrated that the supposedly secure channels in the Internet are prone to privacy breaking under many respects, due to packet traffic features leaking information on the user activity and traffic content. We aim at understanding if and how complex it is to obfuscate the information leaked by packet traffic features, namely packet lengths, directions, and times: we call this technique traffic masking. We define a security model that points out what the ideal target of masking is, and then define the optimized traffic masking algorithm that removes any leaking (full masking). Further, we investigate the tradeoff between traffic privacy protection and masking cost, namely required amount of overhead and realization complexity/feasibility. Numerical results are based on measured Internet traffic traces. Major findings are that: 1) optimized full masking achieves similar overhead values with padding only and in case fragmentation is allowed, and 2) if practical realizability is accounted for, optimized statistical masking attains only moderately better overhead than simple fixed pattern masking does, while still leaking correlation information that can be exploited by the adversary.