F-BLEAU

F-BLEAU is a tool for estimating the leakage of a system about its secrets in a black-box manner (i.e., by only looking at examples of secret inputs and respective outputs). It considers a generic system as a black-box, taking secret inputs and returning outputs accordingly, and it measures how much the outputs "leak" about the inputs. It was proposed in [2].

F-BLEAU is based on the equivalence between estimating the error of a Machine Learning model of a specific class and the estimation of information leakage [1,2,3].

This code was also used for the experiments of [2] on the following evaluations: Gowalla, e-passport, and side channel attack to finite field exponentiation.

Getting started

F-BLEAU takes as input CSV data containing examples of system's inputs and outputs. It currently requires two CSV files as input: a training file and a validation (or test) file, such as:

0, 0.1, 2.43, 1.1
1, 0.0, 1.22, 1.1
1, 1.0, 1.02, 0.1
...

where the first column specifies the secret, and the remaining ones indicate the output vector.

It runs a chosen method for estimating the Bayes risk (smallest probability of error of an adversary at predicting a secret given the respective output), and relative security measures.

The general syntax is:

fbleau <estimate> [options] <train> <test>

Estimates

Currently available estimates:

log k-NN estimate, with k = ln(n), where n is the number of training examples.

log 10 k-NN estimate, with k = log10(n), where n is the number of training examples.

frequentist (or "lookup table") Standard estimate. Note that this is only applicable when the outputs are finite; also, it does not scale well to large systems (e.g., large input/output spaces).

Bounds and other estimates:

nn-bound Produces a lower bound of R* discovered by Cover and Hard ('67), which is based on the error of the NN classifier (1-NN).

--knn Runs the k-NN classifier for a fixed k to be specified. Note that this does not guarantee convergence to the Bayes risk.

Example

This example considers 100K observations generated according to a Geometric distribution with privacy level nu=4 (see [2] for details); the true value of the Bayes risk is R*=0.456 computed analytically. The observations are split into training (80%) and test sets (examples/geometric-4.train.csv and examples/geometric-4.test.csv respectively).

One can run fbleau to compute the log estimate as follows:

$ fbleau log examples/geometric-4.train.csv examples/geometric-4.test.csv
mapped vectors into 191 unique IDs
mapped vectors into 191 unique IDs
Random guessing error: 0.913
Estimating leakage measures...

Final estimate: 0.47475
Multiplicative Leakage: 6.037356321839082
Additive Leakage: 0.43825000000000003
Bayes security measure: 0.5199890470974808
Min-entropy Leakage: 2.593916950824318

Minimum estimate: 0.47355
Multiplicative Leakage: 6.051149425287359
Additive Leakage: 0.43945
Bayes security measure: 0.5186746987951807
Min-entropy Leakage: 2.5972092105949125

NOTE: depending on your machine's specs this may take a while. fbleau is designed to effectively exploit many CPUs, albeit with low RAM requirements; further optimisations are in the works.

One should look at the Minimum estimate (i.e., the minimum value that the Bayes risk estimate took as the size of the training examples increases), rather than at the Final estimate: indeed, the estimates do not guarantee a monotonically decreasing behaviour.

For the frequentist estimate:

$ fbleau frequentist examples/geometric-4.train.csv examples/geometric-4.test.csv
mapped vectors into 191 unique IDs
mapped vectors into 191 unique IDs
Random guessing error: 0.913
Estimating leakage measures...

Final estimate: 0.5621
Multiplicative Leakage: 5.033333333333335
Additive Leakage: 0.3509
Bayes security measure: 0.6156626506024097
Min-entropy Leakage: 2.3315141437165607

Minimum estimate: 0.56205
Multiplicative Leakage: 5.033908045977013
Additive Leakage: 0.35095
Bayes security measure: 0.6156078860898139
Min-entropy Leakage: 2.3316788631368333

Further options

It is often useful to know the value of an estimate at every step (i.e., for training size 1, 2, ...). fbleau can output this into a file specified by --verbose=<logfile>.

By default, fbleau runs for all training data. However, one can specify a stopping criterion, in the form of a (delta, q)-convergence: fbleau stops when the estimate's value has not changed more than delta (--delta), either in relative (default) or absolute (--absolute) sense, for at least q steps (--qstop).

fbleau can scale the individual values of the system's output ("features") in the [0,1] interval by specifying the --scale flag.

By default, fbleau uses a number of threads equal to the number of CPUs. To limit this number, you can use --nprocs.

An option --distance is available to select the desired distance metric for nearest neighbor methods.

Further options are shown in the help page:

fbleau -h

Install

The code is written in Rust, but it is thought to be used as a standalone command line tool. Bindings to other programming languages (e.g., Python) may happen in the future.

Install rustup, which will make cargo available on your path. Then run:

cargo install fbleau

You should now find the binary fbleau in your $PATH (if not, check out rustup again).

If rustup is not available on your system (e.g., some *BSD systems), you should still be able to install cargo with the system's package manager, and then install fbleau as above. If this doesn't work, please open a ticket.

TODO

Currently, the code provided here:

• is based on frequentist and nearest neighbor methods; in the future we hope to extend this to other ML methods; note that this does not affect the generality of the results, which hold against any classifier,
• computes one estimate at the time (i.e., to compute multiple estimates one needs to run fbleau several times); this can change in the future.

Short term

• return various leakage measures (instead of just R*)
• resubstitution estimate

Mid term

• predictions for multiple estimators at the same time
• get training data from standard input (on-line mode)

Maybe

• other ML methods (e.g., SVM, neural network)
• Python and Java bindings

References

[1] 2017, "Bayes, not Naïve: Security Bounds on Website Fingerprinting Defenses". Giovanni Cherubin

[2] 2018, "F-BLEAU: Practical Channel Leakage Estimation". Giovanni Cherubin, Konstantinos Chatzikokolakis, Catuscia Palamidessi.

[3] (Blog) "Machine Learning methods for Quantifying the Security of Black-boxes". https://giocher.com/pages/bayes.html