Secure multi-party computation (SMPC) enables organisations to collaborate on sensitive data analysis without directly sharing raw information. However, seemingly harmless aggregate outputs, particularly private set intersection (PSI), can leak individual-level information when analysed strategically over time.

Homomorphic encryption is a powerful cryptographic technique that allows computations to be performed on encrypted data without decrypting it first. This blog post will introduce the concept of homomorphic encryption and demonstrate implementations using Python. What is Homomorphic Encryption? Homomorphic encryption is a form of encryption that allows specific types of computations to be carried out on ciphertext.

In last post we covered, Privacy Preserving Measurement (PPM) and discussed how Distributed Aggregation Protocol (DAP) works. Today, we'll explore how to implement a simplified version of the DAP using Python with Prio3 as our Verifiable Distributed Aggregation Function (VDAF). This implementation will support multiple clients, demonstrating how DAP can aggregate data from multiple sources while maintaining privacy.

In 1982, Andrew Yao proposed the Millionaire Problem which discusses how two millionaires can learn who is richest one without disclosing their actual wealth. They solve this problem by comparing their wealth using secure two party computation to ensure that they learn only the richest one and nothing else is revealed. The problem was later generalised for secure multiparty computation by Goldreich et al in 1987.

Differential Privacy (DP) is a mathematical framework that protects individual privacy in data analysis while allowing useful insights to be extracted. It works by adding carefully calibrated noise to data or query results, ensuring that including or excluding any single individual's data doesn't significantly change the analysis outcomes.