Fast Fully Homomorphic Evaluation of Neural Networks in the Cloud

In order for Fully Homomorphic Encryption (FHE) to be deployed in real-world applications, still today --- even if a theoretical solution has been around for almost 10 years --- it is required to increase the efficiency of used algorithms. As the interactions of parameters and components of nowadays lattice-based realizations of FHE are non-trivial, schemes once set up to meet a multitude of design constraints, often end up having high requirements. Too high for some "killer"-application as run-times may pose a prohibitive hurdle.

In this blog-post, I'd like to present a use-case where an Fully Homomorphic Encryption (FHE) scheme achieves unprecedentedly fast classification of encrypted data, and makes scale-invariant homomorphic evaluation of neural networks (NN) possible.

Are privacy-preserving services in the Cloud relevant?

At this point, I think, I can skip philosophizing about the ubiquitous utility of machine learning, as we can see its impact everyday all around us. On the other hand the quest for privacy-preserving application of machine learning algorithms to user data is becoming a central topic of discussions recently. It is expected that the General Data Protection Regulation (GDPR), a result of the call for European law (which could serve as paragon internationally) to protect its citizens, its economy, will push forward innovation in this direction too.

Simply put, users of Machine Learning as a Service (MLaaS) in the Cloud, want to only share & upload encrypted images as input to the companies' powerful, pre-trained cognitive models.

Clearly, encrypting content ensures data confidentiality, assuming the associated private key of the  public-key encryption scheme never leaves the user’s trusted device. (As a side note; recent news reports suggest that such an assumption for user controlled devices are not always guaranteed. The Cloud operating on FHE encrypted data on the other hand is not possibly vulnerable to leak private user data through the whole class of cache attacks, i.e. Meltdown and Spectre.)

Let's briefly look at the problem setting.

To overcome conflicting interests of confidentiality and utility of data in the Cloud-based scenario, Fully Homomorphic Encryption can help the user to receive a useful answer to their encrypted question in a privacy-preserving way. Hence, the cloud needs to support homomorphic computations on the FHE encrypted inputs and send back the still encrypted result of this delegated operation in a reasonable time. In principal, only the legitimate user can decrypt the output using their secret key. The cloud service cannot deduce information from the random looking inputs, intermediate or final results, but can still charge the user for providing the service, e.g. classifying an image in this example.

Let's briefly look at the task.

First step when approaching a solution of how to use FHE for NN is defining minimal requirements of the concrete task and knowing what can be considered practical FHE.
We want to showcase fast homomorphic evaluation of a pre-trained NN to classify a depicted shape without leaking privacy of the input data at an 80 [bit] security level, e.g. images of handwritten digits from the MNIST dataset.
The output, given in less than two seconds, shall be encrypted scores assigned to each possible output and the highest score, decrypted by the user, is the most probable label of the input image.

A depiction of how input is propagated in order to evaluate a discretized deep neural networks with an arbitrary depth $d$ of hidden layers to arrive at a classification. Each neuron performs operations $f_i$; a function linearly depending on values of the incoming wires and weights followed by a non-linear operations. The latter is typically referred to as ``activation''.

As deep neural networks with $d$ hidden layers give good results in practice, we target this type with a scale-invariant FHE scheme.

Let's look at the problem solution.

In an attempt to bringing forth FHE in practice, our C++ code builds on top of an existing Fast Fully Homomorphic Encryption Library over the Torus (TFHE) and introduces a new framework for homomorphic evaluation.

To increase the efficiency, which is an important step paving the way to practicality, the underlying FHE scheme needs to be parametrized once for a given network.
Secondly, a security analysis is another crucial step in vetting the algorithms, ensuring their use maturely resists state-of-the-art cryptanalysis and fulfills the targeted security level.

The main capability of our scheme is that when evaluating a single neuron, the output value can readily be used for the next operation as it is bootstrapped to ensure low error propagation.

Close-up on a single neuron.

We apply the activation function directly to the weighted sum of inputs according to the network's wires, i.e. computing $y = f(x) = sign( \langle x, w\rangle )$, with fixed weights for the neuron and sign as activation.

Scale-invariance means that privacy-preserving evaluation of deep neural networks do not longer pose a hurdle, as computations carried out by every neuron in the network is independent of the total number of neurons and layers and hence scales linearly.

With this approach, we can report the performance result of an experiment to classify 10000 encrypted images from the MNIST dataset with more than 96% accuracy on average taking less than 1.7 seconds, using the TFHE library as a starting point.

Running an experiment on a trained neural net with 784:100:10--topology deployed in the Cloud.

An uploaded encrypted test image is input to the homomorphic evaluation of our scheme that classifies a depicted shape (without leaking privacy of the input data). The evaluation of the neural network outputs the encrypted scores $S_i$ assigned to each digit $i$. The highest score, decrypted by the user, is the most probable label of their image.

I'd like to stress that the good performance of this scale-able approach is not limited to homomorphic evaluation of neural networks with one hidden layer, as depicted above, but can be applied to deep neural networks, that in practice could be composed of possibly a hundred hidden layers or an even broader class of cognitive models.

For a detailed, formal description I refer to the full version of the paper or you may try out the proof-of-concept implementation code, available online that shows how to obtain these research results, applying our generic framework to a trained NN and MNIST dataset inputs as a demonstration.

Let's look at directions for future work and open-questions.

Finally, mentioning limits on the functionality of our FHE scheme, and pointing out the applicability to other well-specified domains rounds off this treatment here.

To comfort a potential concern for the service providers that their users might be sending malicious requests, to evaluate private networks with our framework is not dealt with at the moment, although it is in principal possible.
They could either try to learn the company's intellectual property (the weights and the topology of the neural network itself), or try to derive sensitive information encoded therein (which could be a breach into the privacy of the training dataset).
In this latter case a statistical databases studied in the differential privacy literature can be used in the training phase.

An open question is how further performance gains can be achieved by refining the algorithms. Also listing all general cognitive models that are possible is interesting.

So long, stay tuned for faster solutions and more general demonstrations!

WhatsApp backdoor? Should I be worried?

WhatsApp Backdoor!!! 

Let's start this blog entry with that title and it is very easy to get reader's attention (Especially in the security community) with big bold letters and saying that there is a backdoor. I say this because it was exactly what happened on January 13th (Friday the 13th, maybe it is correlated) when The Guardian released the news. After that, the security community/websites and others started a big debate about it. In fact, some hours after the release from the Guardian others websites started saying that it isn't a backdoor such as: Gizmodo, Open Whisper System blog and others' websites.

Well, we are going to give some "conclusions about the subject" later. First, let's explore more about it.

What is a backdoor?

If we talk about computer systems or cryptography, we are going to have something like this definition: "A backdoor is a method, often secret, of bypassing normal authentication in a product, computer system, cryptosystem or algorithm etc. Backdoors are often used for securing unauthorized remote access to a computer, or obtaining access to plaintext in cryptographic systems." In other words, it is an easy way to obtain access.

Are backdoors common?

Unfortunately, yes it appears in the news and computer systems more than we want. Also, after the Snowden revelations the term backdoor is very common in the non-academic area. However, it does not mean that people become more worried.

What is the real problem?

Perfect, we learned about backdoors. Now, let's explain the problem with WhatsApp. Let's see an hypothetical case, imagine that you have a smartphone and for some reason (fall in a lake, you have been abducted by E.T. and forget your phone in the spaceship) you don't have access to your smartphone anymore. Fortunately, you can recover your phone number, buy a new smartphone and reinstall Whatsapp. However, when you reinstall WhatsApp, it generates a new key. However, now we have a problem what the app should do with the messages that you received when you were offline. The app could just drop the messages and never deliver or it could ask for your contacts to encrypt with the new key. According to the Guardian this approach is the backdoor:
"WhatsApp’s implementation automatically resends an undelivered message with a new key without warning the user in advance or giving them the ability to prevent it."

I, personally, say that it is a mistake that WhatsApp just show a notification saying that the key change and automatically resends.

Is it exploitable?

I will say: Yes, it is.
Let's see how it is possible to exploit.

In fact, it consists in exploit another vulnerability, it is present in the SS7 protocol. The Signalling System No. 7 (SS7) is a set of telephony signaling protocols developed in 1975, which is used to set up and tear down most of the world's public switched telephone network (PSTN) telephone calls. It also performs number translation, local number portability, prepaid billing, Short Message Service (SMS), and other mass market services.

The SS7 vulnerabilities are known since 2008. However, it had the attention from media in 2014, Tobias Engel at CCC showed how it is possible to exploit SS7 vulnerabilities. You can check exactly how in this link. In the video, he shows that it is possible to change the phone number between cellphones. In the same congress and right after Tobias, Karsten Nohl showed how to read "others SMS", the talk can be followed in this link.

What is the SS7 vulnerability?

Let see very quickly the structure of a GSM network, the next figure shows it.

So, if you are inside of the SS7 network, you can just start listen the network and as we saw in the videos it is possible to change somethings such as your number.

Since it is possible to change your number and the verification from whatsApp can be done by call or a SMS verification. What happened if I have access to SS7 network and change my number to any other number and I reinstall WhatsApp and pass the verification?

According to the policy of WhatsApp, my smartphone is going to generate a new key and all the new messages are going to be encrypted with this new key. I didn't create a new attack here, it has been done before as this youtube video shows:

It is valid to say that this attack can be used in others messengers. However, others apps have another policy, e.g.  Signal drops the messages until you "recheck" the new key.

 If you are interested to see the how messengers handle this key problem, there is a nice blog entry at Medium.

Conclusions? 

The news from Guardian is not a real backdoor, it is a known problem about handling with keys and the news was more like a "click bait". However, the good thing about all of this history are the discussions in different communities and an alert to people take care about their privacy.

All this incident makes us to start doing some social and technical questions, such as:
Should we accept the news from the media as truth?
Why the hell we continue to use a system from 1975?
Can we create a better way to handle with keys?


 In addition, I should say that if you are looking for more privacy to your life. You should check Privacy Tools, in this case, the section about "Encrypted Instant Messenger".