New Method of Prime Factorisation-Based Attacks on RSA Authentication in IoT

Abstract

The potential benefits of the Internet of Things (IoT) are hampered by malicious interventions of attackers when the fundamental security requirements such as authentication and authorization are not sufficiently met and existing measures are unable to protect the IoT environment from data breaches. With the spectrum of IoT application domains increasing to include mobile health, smart homes and smart cities in everyday life, the consequences of an attack in the IoT network connecting billions of devices will become critical. Due to the challenges in applying existing cryptographic standards to resource constrained IoT devices, new security solutions being proposed come with a tradeoff between security and performance. While much research has focused on developing lightweight cryptographic solutions that predominantly adopt RSA (Rivest–Shamir–Adleman) authentication methods, there is a need to identify the limitations in the usage of such measures. This research paper discusses the importance of a better understanding of RSA-based lightweight cryptography and the associated vulnerabilities of the cryptographic keys that are generated using semi-primes. In this paper, we employ mathematical operations on the sum of four squares to obtain one of the prime factors of a semi-prime that could lead to the attack of the RSA keys. We consider the even sum of squares and show how a modified binary greatest common divisor (GCD) can be used to quickly recover one of the factors of a semi-prime. The method presented in this paper only uses binary arithmetic shifts that are more suitable for the resource-constrained IoT landscape. This is a further improvement on previous work based on Euler’s method which is demonstrated using an illustration that allows for the faster testing of multiple sums of squares solutions more quickly.