Mathematical Techniques for Private Computing: Strengthening Data Privacy in Cloud-Based Systems

Abstract

This paper investigates sophisticated mathematical methodologies for privacy of data within cloud-based situations, particularly on secure private computing. In addition, with the use of cloud infrastructures to store and process sensitive data courting more risk for organizations in terms of potential breaches leading of unauthorized access or privacy infringements. To cope with these issues, we investigate recent cryptographic approaches such as fully homomorphic encryption, multi-party computation and differential privacy for secure computations over encrypted data preserving the confidentiality properties. Homomorphic encryption allows specific mathematical operations to be executed on ciphertexts and the results can then later (with a particular protocol) decrypt into correct outcomes. Multi-party computation allows for collective calculations of different parties while further keeping private inputs from individual participants. Differential Privacy adds a statistical noise mechanism that protects against privacy leakage from aggregate datasets. The paper then describes how these techniques are implemented in practice, studies their computational efficiency and discusses security/performance trade-offs. Cases studies and simulations present their applicability for cloud environments, promoting a more privacy aware approach to data security in the field of computing with these mathematical methods. The study based on the Moebius technique reveals just how fundamental mathematical advances will be for making secure cloud-based systems in years to come.