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

2025-12-23

AI Summary

The “dual-capacitor paradox” obscures the physical origin of energy dissipation and its link to electromagnetic side-channel analysis (EM SCA) leakage during cryptographic operations. Method: This work establishes a quantitative pathway between EM radiation intensity and cryptographic key leakage rate by unifying circuit-level energy conservation, analytical RC/RLC transient modeling, electromagnetic radiation theory, and empirical EM SCA validation. Contribution/Results: We demonstrate that non-adiabatic energy dissipation—occurring predominantly during transient capacitor charging/discharging—is the dominant source of EM radiation and the fundamental physical enabler of key recovery. Leveraging this insight, we propose a low-overhead, adiabatic-charging-based countermeasure paradigm. Implemented on an FPGA, it achieves 27 dB suppression of EM radiation and reduces key recovery success rate to near-random guessing levels (≈0.4%), outperforming state-of-the-art protections. This work bridges circuit physics and side-channel security, enabling physically grounded, efficient EM leakage mitigation.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Adversarial Attacks & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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.

Problem

• Connects capacitor charging energy loss to electromagnetic side-channel leakage.
• Proposes adiabatic charging to minimize electromagnetic leakage in digital circuits.
• Links lost energy to secret encryption key recovery in electronic devices.

Innovation

• Adiabatic charging reduces electromagnetic side-channel leakage
• Connects capacitor energy loss to electromagnetic radiation analysis
• Analytically proves energy dissipation in RC and RLC circuits