Robustness Analysis of Zero-Knowledge Proofs using QRP for IoT Devices

We attempt to study the time complexity and asymptotic security of the method in order to robustly analyze the security mechanism. Security analysis studies allow us to determine whether an algorithm is efficient or not. Security analysis studies also help us check whether algorithms tolerate different attacks on them or not. This research paper presents the robustness analysis of the zero knowledge proofs (ZKP) technique using the quadratic residuosity problem (QRP) as a superior alternative for Internet of Things (IoT) devices. If we want to achieve the main security issues (attacks on confidentiality, authentication, integrity, and availability) for IoT devices, then we need to know the security strength of the security mechanism we implement for it. The zero-knowledge proofs technique has been used with the QRP problem, and it is analyzed and compared with Elliptic Curve Cryptography (ECC) in order to see how they are correlated with each other. This study helps us know whether ZKP using QRP can address the security issues of IoT devices in a better way or not. The final covariance and correlation results show that both ZKP using QRP for the square root modulo n problem (SQROOT) and ECC are highly correlated with one another. Asymptotic time complexity and the graph of ZKP using QRP for the SQROOT algorithm compared to ECC clearly show that QRP for the SQROOT algorithm has not as good a time complexity as ECC but can address the security issues required by IoT devices.