Inspired by the idiom, “Mitigation (prevention) is better than cure!”, this work presents a random yet cognitive side-channel mitigation technique that is independent of underlying architecture and/or operating system. Unlike malware and other cyber-attacks, side-channel attacks (SCAs) exploit the architectural and design vulnerabilities and obtain sensitive information through the side channels. In contrast to the existing randomization-based side-channel defenses, we introduce a cognitive perturbation-based defense, Covert-Enigma, where the introduced perturbations look legit, but lead to an incorrect observation when interpreted by the attacker. To achieve this, the perturbations are injected at appropriate time instances to introduce additional operations, thereby misleading the attacker making the extracted data futile. To further make the attack more intricate for the attacker, proposed Covert-Enigma offers two modes of operation, chosen by the user, to determine the kind of induced cognitive perturbations— arbitrary and cyclic modes. Arbitrary mode selects a group of key bits and flips them during every execution of the victim. Cyclic mode exhibits similar behavior, except it selects a new set of bits to flip after “ $N$ ” cycles as chosen by the user. The cognitive perturbations are introduced in the form of a wrapper application to the victim, thus imposing no requirements on architectural level modifications nor soft updates/edits to the operating system. We report rigorous evaluation of the proposed Covert-Enigma protecting RSA cryptosystem attacked by Flush+Reload crypto SCA along with the bit(s) recovered after observing RSA under attack. Compared to traditional randomization-based defenses, proposed cognitive Covert-Enigma leads to 50% less overhead.