The emergence of cloud computing has completely reshaped the way data is being stored and processed, providing scalable and cost-effective responses to the needs of data storage and processing. Nevertheless, there have been serious privacy and security issues that arose through the migration of sensitive data into a cloud setting. Privacy-preserving cryptographic methods came to the fore as a great remedy, allowing computations without revealing the underlying data and thus contributing to maintaining privacy. This article delves into the realm of privacy-preserving cryptography for cloud computing, exploring three key techniques: two of which are homomorphic encryption and secure multi-party computation (SMC), and the latter, which is called differential privacy. Homomorphic encryption allows calculations to be done on the encrypted data, thus preserving the secrecy of the data despite the involvement of the cloud in the process. SMC is such a phenomenon that enables the parties to compute a given function collectively without disclosing the private inputs, thus making it possible to encrypt data transmission from the parties. Differential privacy offers a rigorous basis of mathematics for maintaining the privacy of individuals in the patterns of a statistical database in the process of privacy-preserving analytics. The article provides a clear explanation of the fundamentals, practical examples, and technical issues of these privacy-preserving methods. It underlines the essence of finding the right compromise between personal data protection and good computing speed, and it also tells us about the necessity of the widespread implementation of these tools for a more transparent and safer cyber world.