Detecting movement using motion vectors & Functional ENcryption

Detecting movement using motion vectors & Functional ENcryption - post blog
Monday, January 6, 2020

Extended version in Kudelski Security

Author: Johan Cattin (Kudelski Security)

We have already discussed what Functional ENcryption is in a previous post and mentioned we are building a prototype leveraging FE to detect motion. Let’s take a look at how this is possible.

As we explained previously, FE is relatively new, and existing schemes are either relatively constrained in their function evaluation, or impractical. However, one type of FE scheme has been around for a while and is dealing with interesting beasts: vectors! We are thinking of the “Inner Product Functional Encryption Schemes”, obviously. We skipped it last time, but it might be good to start with a quick:

Math recap: inner products and vectors

Alright, first things first, what is a vector?

A vector can be different things (that are often related), but the one that interests us today is the mathematical and physical definition of a vector. (And no, it’s not just one-dimensional arrays!)

Detecting motion in a video using vectors

First, let’s start with video codecs and video encoding.

When you are recording a video and handling it on a computer, it wouldn’t be practical to have the raw data from the camera sensor. Instead, videos are encoded using “codecs”, so that the video stream can be optimized in different ways. One of the most interesting ways to optimize a video stream is to compress it, in order to have smaller files (or using less bandwidth if it’s just a stream). The different codecs are using different methods to achieve this, and overall video encoding and compression is a very interesting field. But today we will focus on one standard way to do it: MPEG-4, aka H.264, one of the most used compression standard for video.

Functional Encryption

If you need a refresher, you can read our previous post on Functional Encryption.

Among the different existing FE schemes, the Inner Product family is very likely to provide us with the perfect scheme. In fact, Inner Product with Function Hiding schemes are perfectly suited to our needs! The function hiding feature allows both vectors of the inner product to remain secret, whereas in “classical” inner product schemes only one vector is kept secret.

The prototype we are working on at Kudelski Security for the FENTEC project is designed for the IoT world. The choice of a particular Function-Hiding Inner Product FE implementation will be dictated by its computational complexity. Basically, the fastest the better.