From the Two-Capacitor Paradox to Electromagnetic Side-Channel Mitigation in Digital Circuits

The classical two-capacitor paradox of the lost energy is revisited from an electronic circuit security stand-point. The paradox has been solved previously by various researchers, and the energy lost during the charging of capacitors has been primarily attributed to the heat and radiation. We analytically prove this for various standard resistor-capacitor (RC) and resistor-inductor-capacitor (RLC) circuit models. From the perspective of electronic system security, electromagnetic (EM) side-channel analysis (SCA) has recently gained significant prominence with the growth of resource-constrained, internet connected devices. This article connects the energy lost due to capacitor charging to the EM SCA leakage in electronic devices, leading to the recovery of the secret encryption key embedded within the device. Finally, with an understanding of how lost energy relates to EM radiation, we propose adiabatic charging as a solution to minimize EM leakage, thereby paving the way towards low-overhead EM SCA resilience.