Skip to main content

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

Comments

Popular posts from this blog

Matplotlib in Django

The official django tutorial is very good, it stops short of displaying
data with matplotlib - which could be very handy for dsp or automated
testing. This is an extension to the tutorial. So first you must do the
official tutorial!
Complete the tutorial (as of writing this up to part 4).

Adding an image to a view

To start with we will take a static image from the hard drive and
display it on the polls index page.
Usually if it really is a static image this would be managed by the
webserver eg apache. For introduction purposes we will get django to
serve the static image. To do this we first need to change the
template.



Change the template
At the moment poll_list.html probably looks something like this:


<h1>Django test app - Polls</h1> {% if object_list %} <ul> {% for object in object_list %} <li><a href="/polls/{{object.id}}">{{ object.question }}</a></li> {% endfor %} </ul> {% else %} <p>No polls are available.</p> …

Homomorphic encryption using RSA

I recently had cause to briefly look into Homomorphic Encryption, the process of carrying out computations on encrypted data. This technique allows for privacy preserving computation. Fully homomorphic encryption (FHE) allows both addition and multiplication, but is (currently) impractically slow.

Partially homomorphic encryption just has to meet one of these criteria and can be much more efficient.
An unintended, but well-known, malleability in the common RSA algorithm means that the multiplication of ciphertexts is equal to the multiplication of the original messages. So unpadded RSA is a partially homomorphic encryption system.

RSA is beautiful in how simple it is. See wikipedia to see how to generate the public (e, m) and private keys (d, m).

Given a message x it is encrypted with the public keys it to get the ciphertext C(x)with:

C(x)=xemodm
To decrypt a ciphertext

Bluetooth with Python 3.3

Since about version 3.3 Python supports Bluetooth sockets natively. To put this to the test I got hold of an iRacer from sparkfun. To send to New Zealand the cost was $60. The toy has an on-board Bluetooth radio that supports the RFCOMM transport protocol.



The drive protocol is dead easy, you send single byte instructions when a direction or speed change is required. The bytes are broken into two nibbles: 0xXY where X is the direction and Y is the speed. For example the byte 0x16 means forwards at mid-speed. I was surprised to note the car continues carrying out the last given demand!

I let pairing get dealt with by the operating system. The code to create a Car object that is drivable over Bluetooth is very straight forward in pure Python:

importsocketimporttimeclassBluetoothCar:def__init__(self,mac_address="00:12:05:09:98:36"):self.socket=socket.socket(socket.AF_BLUETOOTH,socket.SOCK_STREAM,socket.BTPROTO_RFCOMM)self.socket.connect((mac_address,1))def_write(self,data_byte):…