Probing RSA's weak spots: Dissecting timing attacks and Euclidean method exploitations

Abstract

The RSA encryption system, a cornerstone of numerous cryptographic frameworks, has long enjoyed a reputation for robustness. However, its strength is inherently tethered to the meticulous selection and management of its foundational prime numbers, p and q. This study delves into a nuanced vulnerability that surfaces when p and q assume particularly large values. Within this context, we illuminate how the Euclidean method can be weaponized to swiftly decipher RSA-encrypted messages, unveiling the original plaintext with surprising efficiency. Intriguingly, our analysis also uncovers that harnessing parallel computation for the Euclidean method expedites decryption exponentially, accentuating this vulnerability. Such revelations cast a spotlight on a delicate balancing act between computational prowess and cryptographic fortitude. The insights gleaned from our research emphasize the paramount importance of judicious prime selection in the RSA framework. They also caution about the unforeseen pitfalls that might lurk behind algorithmic enhancements in cryptographic contexts. Through this investigation, we aspire to catalyse a critical re-evaluation of RSA's real-world deployments and champion a more circumspect, continually adaptive approach to designing cryptographic systems.