Towards A More Private Data World — Adding and Subtraction with Homomorphic Encryption
Meet Pascal
In 1999, as part of his PhD, Pascal Paillier created a wonderful public key encryption method that allows us to add, subtract and scalar multiply encrypted values [1]:
It was a slow-burner of a paper that took a while to take hold:
But, now, in a world which is starting to respect the privacy of data, we see it making its full impact, with 573 citations in 2022. Why the impact now? Well, many of the methods proposed for homomorphic encryption are based on lattice methods, but they tend to have heavy requirements for processing. And, so, Paillier encryption is much more efficient, and can easily process addition, subtraction, and scalar multiplication. In machine learning, for example, there are many operations that are just additions and subtractions, so it is well matched to the requirements for privacy-preserving machine learning.
The Paillier method
The Paillier cryptosystem is thus a partial homomorphic encryption (PHE) method, and here two encrypted values can be added together, and the…
