# Temporary Contact Number based Contact Tracing

written on Thursday, April 9, 2020

I have already talked here before about privacy preserving contact tracing to fight Covid-19 but I figured I give an update to this. I have spent the last week now investigating different approaches to this and my view has changed quite a bit.

I strongly believe that contact tracing through phone apps is one of our best chances to return to normal and without losing our civil liberties. If you want to understand why, have a look at previous post about this topic.

## Two Fundamental Approaches

In the previous post I talked in favour of a partially centralized approach. This was largely because I felt that one of the inherent problems of any privacy preserving contact tracing system could be somewhat mitigated. That downside is that a person could always use any such contact tracing system in a way where they could determine that another person they met tested positive for covid-19 later. With a system that has support from a central authority this still cannot be prevented, but such behavior could be detected as abusive. However I am not quite convinced that this would just be security by obscurity and that the more correct way to deal with this is to just fundamentally communicate to users that this is an inherent property of the system.

So the disclaimer to any app has to be: if you do not want that other people discover when you will test positive for covid-19 you should not use any contact tracing apps. Which is also why I strongly believe that any such system absolutely needs to be voluntary.

So if I no longer believe in favour of the centralized approach, what do I prefer then? Quite simply put an approach based on temporary contact numbers, short TCNs. These protocols are fundamentally decentralized and give us some other benefits.

## Reality on the Ground

What makes application based contact tracing very interesting is that they take advantage of working on top of a widely deployed piece of hardware: smart phones. Specifically smartphones which support Bluetooth low energy (BLE). If you hold an AirPods case close to your iPhone you will notice that something happens on your screen. BLE is what enables that.

The downside of this is that BLE comes with some restrictions. The two most relevant ones are the payload size. BLE comes with different modes and different platforms call this in different ways but the most compatible and energy preserving modes restrict us to under 30 bytes of payload. That's not enough to make fancy public key cryptography work which would be necessary for centralized approaches to play to their advantages. This is also why systems that currently follow the centralized approach will typically exchange a short ID and the extra payload is then actually exchanged through the cloud or GATT. The former makes a system that could be somewhat decentralized much more centralized.

TCN based protocols instead will exchange just random identifiers instead. Most TCN based protocols currently suggest between 16 and 26 bytes of effectively random data which is easier to work with.

Another complexity is that at present iOS devices in background cannot discover each other. This limitation might be solvable by Apple and it appears various groups are currently in contact with Apple to see what can be done. Interestingly an iOS device with the app in background can be discovered by an Android device so there might be a way to fix this.

## TCN Strawman Protocol

The TCN strawman protocol is the most basic of all these protocols. It was first written down by the Co-Epi project and is very easy to explain.

1. all mobile phones randomly generate TCNs and remember and broadcast these.
2. all mobile phones check against a server which publishes TCNs that are known to be covid-19 positive.
3. all mobile phones check their local contact list against the downloaded list locally for an intersection.

Step 2 is the only one where a central system is necessary. For instance this could be the server of the Austrian Red Cross which publishes TCNs. Since the TCNs of encounters are only stored on the devices they have to get on contact with covid-19 tested positive individuals first.

The strawman protocol wouldn't work in practice at the peak of the infection because of the sheer data requirements. However there are various cryptographic tricks which are floating around to reduce the size of the data set.

## DP-3T

DP-3T is currently one of the most promising protocols here. It has a low cost variant which satisfies most of the qualities of the strawman protocol while reducing the amount of data greatly (to around 1.5MB of data per day for a peak infection rate of 40.000 infections a day). Additionally it comes with a protocol extension (âUnlinkable decentralized proximity tracingâ) which improves on the simple protocol in a few important aspects. Specifically it makes it significantly harder for an adversary to track or identify infected users at the cost of higher bandwidth requirements.

A simple version of the protocol is easily explained:

1. A device generates a secret key. Each day the user derives a new version of the secret key by feeding it into a ratchet like a SHA256 hash function.
2. Each day the device generates TCNs out of the day's secret key for instance by using a AES in counter mode. If for instance we want to switch TCNs every 15 minutes we would need to generate 4 * 24 * 16 bytes worth of TCNs to have enough for a day.
3. Devices now broadcast a random TCN for the day for 15 minutes each.
4. When a device encounters another person and they consider the contact long enough, they record the approximate time of day and the TCN encountered.
5. When a user tests covid-19 positive they upload the secret key of the first day of infection and generate a new secret key.
6. Other devices now download the secret key for that user and generate all possible TCNs locally and check for infection. They only need to generate 14 derivations of the secret key and the 96 TCNs for each day.

In the more complex version the device uploads seeds of the secret keys for all time windows in the infection window. On the backend server a cuckoo filter is created every 4 hours and the seeds are inserted. Because Cuckoo filters have a small probability of producing false positives parameters need to be selected appropriately to reduce this risk. The upside is that the sets of identifiers used by the same user are hidden.

## PEPP-PT and Local Governments

So this leads us to PEPP-PT. It would appear that PEPP-PT is evaluating DP-3T as the reference protocol and they are going to open source the code with the idea to support local authorities in implementing their own version. Officially they have not decided between centralized or TCN approaches yet, but there seems to be a high chance it will be the latter. The concept is also very simple. Simple enough that if you want to explain this system to others, there is also a nice little comic strip available that explains it.

If your local government is planning on implementing a covid tracing app it might be worth directing them towards Co-Epi. It already has an implementation of many of the same ideas in their GitHub repository. If they do want a centralized approach the Singaporean government Open Sourced their application under GPL3 under the name BlueTrace. It avoids largely unnecessary cloud infrastructure from what I can tell.