Defending against Power Analysis Attacks: A Novel Approach with Factorial Expansions in Elliptic Curve Cryptography

Power analysis attacks have emerged as a significant threat to the security of elliptic curve cryptography (ECC), necessitating the development of countermeasures that can safeguard against such attacks without compromising computational efficiency. This paper introduces an innovative approach that integrates signed factorial expansions (SFE) with random masking techniques for scalar multiplication, a critical operation in ECC. The proposed method encodes large scalar values into smaller integers and incorporates randomization to resist a variety of power analysis attacks effectively. By conducting simulations, we demonstrate that the algorithm not only maintains high computational efficiency but also exhibits excellent performance in resource-constrained cryptographic chips, which are typically vulnerable to such attacks. The algorithm's resilience is attributed to the randomization of scalar multiplication operations, which obscures the correlation between operation and power consumption, thereby thwarting attempts at key recovery by an attacker. Our simulation results validate the algorithm's ability to defend against simple power analysis (SPA), differential power analysis (DPA), zero-value register-based power analysis (RPA), zero-value point-based power analysis (ZPA), and double attack (DA) methods. This work not only enhances the security of ECC implementations but also provides a practical solution for cryptographic systems with limited resources, offering a promising direction for future research and applications in the field of cryptography.