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Open Source Paillier Libraries

The Confidential Computing team at Data61 has been looking at novel methods of using privacy preserving computation - with the lofty long term goal of increasing users' privacy while still allowing modern analytical insights.

One of the principals we've been relying on is partially homomorphic encryption - the ability to carry out some basic mathematical operations on encrypted data, usually this property is either addition or multiplication. Take a quick look at my previous post on Homomorphic Encryption. My team has looked at multiple homomorphic systems and settled on using the Paillier Crypto system for some of our confidential computing projects.

The homomorphic properties of the Paillier Crypto system are:
  • An encrypted number can be multiplied by a non encrypted scalar.
  • Encrypted numbers can be added together.
  • Encrypted numbers can be added to non encrypted scalars.
Everything else (such as multiplying encrypted numbers together) is either extremely difficult or impossible. Only positive integers are supported by the encryption system, so an encoding is required to use this system with floating point numbers.

Last year we published papers on using the Paillier cryptographic system to protect an individual's genome sequence while still using it for meaningful medical research. At Nicta Techfest 2014 we demonstrated the ability to privately calculate geographic proximity between cooperating parties - using the Paillier cryptosystem. Since then we've been implementing privacy preserving statistics and machine learning algorithms using the Paillier cryptosystem.

We have created a Python and Java version of the Paillier cryptosystem using an IEEE Float compatible encoding scheme. I'm proud to say they are both open source and available on github.

Python Paillier Github, Python Paillier documentationJavallier Github

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