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Build Status Maven Central License: MIT


Library for secure statistics and linear algebra on data held by multiple parties without sharing the data with the other parties.

Table of Contents

About The Project

FRESCO-stat is a library for secure numerical computations, statistics and linear algebra using the FRESCO framework. FRESCO uses secure multi-party computation to enable computations to be performed on data distributed among multiple parties without each party seeing the other parties' data.

There is no assumption on how the data is distributed among the parties -- the data may for example be divided horizontally, where each party has a different set of data entries, or vertically, where each party has different attributes for the same entries, or any combination of the two. Or one party could know the model parameters and other parties the data used to fit the, model eg. in regression or machine learning.

The library supports both simple descriptive statistics and more complicated analysis and regression, including linear and logistic regression and survival analysis using Cox regression.

The library has five function libraries:

  1. Statistics
    • Descriptive statistics
      • Sample mean
      • Sample standard deviation
      • Sample variance
      • Sample median
      • Simple and multi-dimensional histograms
      • Frequency table
      • Sample correlation
      • Sample percentiles
    • Regression
      • Simple and multivariate linear regression
    • Statistical tests
      • One- and two-sample t-test
      • ꭓ²-test
      • F-test
      • Kruskall-Wallis test
      • Wilcoxon signed rank test
      • Breusch-Pagan test
      • Durbin-Watson test
      • Jarque-Bera test
    • Outlier detection
      • Mahalanobis distance
    • Survival analysis
      • Cox regression
    • Anonymization methods
      • k-anonymization
      • Differentially private histograms
      • Differentially private linear regression
  2. Sampling from various distributions
    • Bernoulli distribution
    • Categorical distribution
    • Exponential distribution
    • Irwin-Hall distribution
    • Laplace distribution
    • Normal distribution
    • Rademacher distribution
    • Uniform distribution
  3. Linear Algebra (see also the fixed library in FRESCO for basic linear algebra functions)
    • Back- and forward substitution
    • Gram-Schmidt process
    • Inverse of triangular matrices
    • Moore-Penrose pseudo inverse
    • QR-algorithm for eigenvalue computation
    • QR-decomposition
  4. Machine learning
    • Logistic regression with gradient descent
    • Multilayer perceptron
  5. Filtered statistics
    • Same as Statistics but with the option of obliviously filtering what samples from a data set will be used in an analysis.

The libraries are used similarly to computation directories in FRESCO by calling e.g.

Statistics.using(builder).chiSquare(observed, expected);

to perform a ꭓ²-test on a dataset.

Note that it is not uncommon to experience overflows during computation, which will appear as very large outputs. This may be avoided by normalizing the input data and/or using a bigger modulus in FRESCO.


Build the project and the documentation using Maven:

mvn clean install
mvn javadoc:javadoc

The Javadoc can be found online or in the target/apidocs folder.

The library may be included in other projects by including it as a Maven dependency.



If you want to help out developing new features for FRESCO-stat or fix a bug you've stumbled upon, it may be done as follows:

  1. Fork the Project
  2. Create your Feature Branch (git checkout -b feature/MyFeature)
  3. Commit your Changes (git commit -m 'Add MyFeature')
  4. Push to the Branch (git push origin feature/MyFeature)
  5. Open a Pull Request


Distributed under the MIT License. See the licence for more information.


The library is developed and maintained by the Security Lab at the Alexandra Institute. If you have found a bug, have questions about the usage of the library, or you are missing functionality, feel free to contact us at


Library for secure computation of statistics using the FRESCO framework







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