Paillier Shines a Light On a New World of Computing

We need to move to an information world where every single data element is be encrypted at every point, no matter if it is at rest, in motion, or in process. The in-process part is our greatest challenge, and only homomorphic encryption will solve this problem. In the future our data processors may operate on encrypted values.

The Paillier cryptosystem is one method which supports partially homomorphic encryption, where two encrypted values can be added together, and the decryption of the result gives the addition. We thus use and public key to encrypt the values, and a private key to decrypt the result. So, rather than try and lay out the maths on the page, here is the screen shot of the method from the Wikipedia:

So, I’ll show you how we decode these scribbles, and code it with some simple code, and reveal the magic of homomorphic encryption. If you just want to watch, here’s a demo: