We consider the transfer of digital data over a loud communication channel, which releases significant side-channel emissions, and we try to protect against attacks based on accurate physical measures from these emissions. The method pairs each secret key k with a camouflage value v, and simultaneously transmit both k and v over the channel. This releases an emission measured by e(k; v). The mimic value v is selected to make e(k; v) as undistinguishable as possible from any other e(k′; v′). M¨ullerian mimicry is a related natural phenomenon where two different poisonous species k and k′ evolve to confuse their predators by adopting each other’s warning signals e(k; v) and e(k′; v′). We model the problem and show that optimal mimicry values can be effectively derived from a finite amount of a-priori measures over emission traces (just as the attacker will do), with little other technological assumption. Consequently, the model is applicable across a wide range of readily available technologies. We propose a statistical analysis of mimicry protection, in one, two and more dimensions. We discuss algorithms for constructing the best mimicry from actual emission traces. We propose efficient ones in low dimensions (say up to 4), and heuristic ones beyond. We detail some experimental results obtained on the proposed defensive leakage mimicry against side-channel attacks: for some memories, buses and IO emissions from otherwise tamper-proof black-boxes.