Analyzing RSA and Paillier Encryption Schemes: Secure Multiplication in Homomorphic Environments

Homomorphic encryption stands as a cornerstone in modern cryptography, facilitating computations on encrypted data while safeguarding privacy. Within this realm, RSA (Rivest-Shamir-Adleman) and Paillier encryption are notable schemes. RSA encryption, leveraging the challenge of factoring large prime numbers, supports Homomorphic operations but grapples with computational overhead in multiplication tasks. In contrast, Paillier encryption simplifies multiplication by transforming it into addition. A comprehensive comparative analysis between RSA and Paillier encryption underscores their distinct advan-tages. While RSA encryption boasts widespread adoption and robustness, Paillier encryption excels in efficiency and security for homomorphic multiplication operations. However, the choice between the two hinges on specific application requirements. Balancing factors such as computational complexity, security guarantees, and practical considerations becomes imperative. Ultimately, selecting the most suitable encryption scheme en-tails a thorough assessment of these factors to ensure optimal performance and security in the given context.