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BoolTest: Polynomial randomness tester

Project description

BoolTest

Build Status

Boolean PRNG tester - analysing statistical properties of PRNGs.

Randomness tester based on our paper published at Secrypt 2017

How does it work?

BoolTest generates a set of boolean functions, computes the expected result distribution when evaluated on truly random data and compares this to the evaluation on the data being tested.

Pip installation

BoolTest is available via pip:

pip3 install booltest

Local installation

From the local dir:

pip3 install --upgrade --find-links=. .

The engine

BoolTest does the heavy lifting with the native python extension bitarray_ph4

Bitarray operations are performed effectively using fast operations implemented in C.

Experiments

First launch

The following commands generate two different files, random and zero-filled. Both are tested, the difference between files should be evident.

dd if=/dev/urandom of=random-file.bin bs=1024 count=$((1024*10))
dd if=/dev/zero of=zero-file.bin bs=1024 count=$((1024*10))

booltest --degree 2 --block 256 --combine-deg 2 --top 128 --tv $((1024*1024*10)) --rounds 0 random-file.bin
booltest --degree 2 --block 256 --combine-deg 2 --top 128 --tv $((1024*1024*10)) --rounds 0 zero-file.bin
  • The BoolTest with the given parameters constructs all polynomials of degree 2 from monomials {x_0, …, x_{255}}
  • Evaluates all polynomials on the input data (windowing), computes zscore from the computed vs reference data
  • Selects 128 best polynomials (abs(zscore))
  • Phase 2: Take the best 128 polynomials and combine them by XOR to the --combine-deg number of terms.
  • The resulting polynomials are evaluated again and results printed out.

Common testing parameters

We usually use BoolTest with the following testing parameters:

--top 128 --no-comb-and --only-top-comb --only-top-deg --no-term-map --topterm-heap --topterm-heap-k 256

The same can be done with the --default-params

Output and p-values

BoolTest returns zscores of the best distinguishers.

In order to obtain a p-value from the Z-score you need to compute a reference experiments, i.e., compute N BoolTest experiments on a random data and observe the z-score distribution. Z-score is data-size invariant but it depends on the BoolTest parameters (n, deg, k).

The most straightforward evaluation is to check whether z-score obtained from the real experiment has been observed in the reference runs. If not, we can conclude the BoolTest rejects the null hypothesis with pvalue 1/N.

To obtain lower alpha you need to perform more reference experiments, to obtain higher alpha integrate the z-score histogram from tails to mean to obtain desired percentage of the area under z-score histogram.

The file pval_db.json contains reference z-score -> pvalue mapping for N=20 000 reference runs.

BoolTest now supports adding pvalue database as a parameter --ref-db path-to-db.json If the database is not given, BoolTest tries to locate the default pval_db.json in the BoolTest installation directory and on the path.

If the database is found, BoolTest shows also OK/reject result for the best distinguisher, given the reference database contains the data for given (n, deg, k) parameters.

Example:

 - best poly zscore  -5.37867, expp: 0.0625, exp:   10240, obs:    9713, diff:  5.1464844 %, poly: [[64, 245, 207, 242]]
2019-12-13 20:25:17 PHX booltest.booltest_main[51363] INFO Ref samples: 40005, min-zscrore: 4.838657, max-zscore: 7.835336, best observed: 5.3786712268614005, rejected: False, alpha: 2.4996875390576178e-05

Halving method

We have implemented another evaluation method called halving, enabled with commandline option --halving. It needs twice more data than the default method, because of how it works:

  • The input file is divided to two halves
  • BoolTest runs as before on the first half, picks the best distinguisher
  • BoolTest runs the best distinguisher on the second half
  • As the best distinguisher selected to the second half “never seen” the second half and there is only one polynomial the p-value can be directly computed due to independence.

The best distinguisher results are essentially following Binomial distribution: Bi(number_of_blocks, probability_of_dist_eval_to_1).

To compute the p-value we run the Binomial test: scipy.stats.binom_test(observed_ones, n=ntrials, p=dist_probab, alternative='two-sided')

This method eliminates a need to have a pval_db.json database computed with the reference data for given parameters. The benefit is the halving method gives directly a p-value, without a need to run reference computations. The downside is the method needs twice more data and can give weaker results than the original BoolTest evaluation.

Example:

 - zscore[idx00]: -0.40825, observed: 00010200, expected: 00010240   idx:      0, poly: [[64, 245, 207, 242]]
2019-12-13 20:25:17 PHX booltest.booltest_main[51363] INFO Binomial dist, two-sided pval: 0.6868421673496484, pst: 0.0625, ntrials: 163840, succ: 10200

Java random

Analyze output of the java.util.Random, use only polynomials in the specified file. Analyze 100 MB of data:

booltest --degree 2 --block 512 --combine-deg 2 --top 128 --tv $((1024*1024*100)) --rounds 0 \
  --poly-file data/polynomials/polynomials-randjava_seed0.txt \
  randjava_seed0.bin

Input data

BoolTest can test:

  • Pregenerated data files
  • Use the CryptoStreams configuration files to generate input data on the fly, using CryptoStreams (library contains plenty round-reduced cryptographic primitives)

Cluster computation (Metacentrum)

  • Map / Reduce.
  • The booltest/testjobs.py creates job files
  • The booltest/testjobsproc.py processes result files
  • BoolTest job is configured via JSON file. Result of a computation is JSON file.
  • The booltest/testjobsbase.py performs job aggregation, i.e., more BoolTest runs in one shell script as job planning overhead is non-negligible. Useful for fast running jobs.
  • Works with PBSPro, qsub queueing algorithm

Example - generate jobs from CryptoStreams configurations

python ../booltest/booltest/testjobs.py  \
    --data-dir $RESDIR --job-dir $JOBDIR --result-dir=$RESDIR \
    --top 128 --matrix-size 1 10 100 --matrix-block 128 256 384 512 --matrix-deg 1 2 3 --matrix-comb-deg 1 2 3 \
    --no-comb-and --only-top-comb --only-top-deg --no-term-map --topterm-heap --topterm-heap-k 256 \
    --skip-finished --no-functions --ignore-existing \
    --generator-folder ../bool-cfggens/ --generator-path ../bool-cfggens/crypto-streams_v2.3-13-gff877be

For all CryptoStreams configuration files located under ../bool-cfggens/ it generates BoolTest tests with parameters:

input_size x block_size x deg x comb-deg
{1, 10, 100} x {128, 256, 384, 512} x {1, 2, 3} x {1, 2, 3}
  • Command generates PBSPro shell scripts to $JOBDIR, results are placed into $RESDIR.
  • For one configuration file which is typically round reduced crypto primitive it performs 3*4*3*3 = 108 tests.
  • When using CryptoStreams config files the config files have to specify the longest tested input, in this case, 100 MB.

Example - analyze input files

python ../booltest/booltest/testjobs.py  \
    --test-files ../card_prng/*.bin \
    --data-dir $RESDIR --job-dir $JOBDIR --result-dir=$RESDIR \
    --top 128 --matrix-size 1 10 100 --matrix-block 128 256 384 512 --matrix-deg 1 2 3 --matrix-comb-deg 1 2 3 \
    --no-comb-and --only-top-comb --only-top-deg --no-term-map --topterm-heap --topterm-heap-k 256 \
    --skip-finished --no-functions --ignore-existing

This example generates job to analyze input files (e.g., smartcard generated randomness)

Example - reference statistics

python ../booltest/booltest/testjobs.py  \
    --data-dir $RESDIR --job-dir $JOBDIR --result-dir=$RESDIR \
    --generator-path --generator-path ../bool-cfggens/crypto-streams_v2.3-13-gff877be \
    --top 128 --matrix-size 10 --matrix-block 128 256 384 512 --matrix-deg 1 2 3 --matrix-comb-deg 1 2 3 \
    --no-comb-and --only-top-comb --only-top-deg --no-term-map --topterm-heap --topterm-heap-k 256 \
    --skip-finished --ref-only --test-rand-runs 1000 --skip-existing --counters-only --no-sac --no-rpcs --no-reinit

Computes 1000 independent AES round 10 runs, each with different seed in the counter mode. Tests BoolTest in various configurations.

Reference data

Reference data extracted from the pval_db.json for standard parameters are displayed in the table below. The z-score distribution does not change with data length for random data.

The table shows minimal and maximal observed z-score with given number of samples for given BoolTest parameters run on a random data. If your test gives z-score outside of the interval the null hypothesis is rejected with the given alpha.

block deg comb-deg samples alpha min max mean stddev
128 1 1 40006 2.5e-05 1.791114 5.259500 2.829184 0.392369
128 1 2 40006 2.5e-05 3.248292 5.891956 3.969550 0.295748
128 1 3 40007 2.5e-05 4.148908 6.873527 4.785917 0.252568
128 2 1 40007 2.5e-05 2.970847 5.874507 3.892347 0.336373
128 2 2 40007 2.5e-05 4.318940 7.185170 5.283498 0.304000
128 2 3 40007 2.5e-05 4.861234 7.625240 5.768929 0.294646
128 3 1 40005 2.5e-05 3.927999 7.458227 4.708559 0.289679
128 3 2 40003 2.5e-05 5.773050 8.525327 6.559734 0.265691
128 3 3 40008 2.5e-05 6.708463 9.213692 7.617935 0.283725
256 1 1 40007 2.5e-05 2.032139 5.473894 3.043441 0.370599
256 1 2 40007 2.5e-05 3.223516 6.321811 3.969150 0.294976
256 1 3 40007 2.5e-05 4.139409 6.393366 4.787687 0.254152
256 2 1 40004 2.5e-05 3.371045 6.680122 4.220396 0.312306
256 2 2 40005 2.5e-05 4.838657 7.835336 5.659828 0.296378
256 2 3 40008 2.5e-05 5.225983 7.678057 6.050640 0.288560
256 3 1 40006 2.5e-05 4.432665 6.699031 5.129937 0.263808
256 3 2 40007 2.5e-05 6.376655 8.765264 7.140519 0.245438
256 3 3 40009 2.5e-05 7.434249 9.683502 8.246235 0.262657
384 1 1 40006 2.5e-05 2.228137 5.488184 3.164776 0.358101
384 1 2 40008 2.5e-05 3.214039 5.821200 3.969855 0.297057
384 1 3 40007 2.5e-05 4.125450 6.395214 4.787421 0.249821
384 2 1 40006 2.5e-05 3.555668 6.394131 4.402679 0.295179
384 2 2 40007 2.5e-05 5.022725 7.760645 5.858194 0.289895
384 2 3 40006 2.5e-05 5.338075 8.195091 6.201193 0.284553
384 3 1 40008 2.5e-05 4.626479 6.880511 5.362216 0.250799
384 3 2 40006 2.5e-05 6.757955 8.914936 7.452872 0.234911
384 3 3 40006 2.5e-05 7.785775 10.147881 8.587092 0.255603
512 1 1 40007 2.5e-05 2.317317 5.418879 3.244575 0.347515
512 1 2 40005 2.5e-05 3.182516 6.602836 3.970192 0.295726
512 1 3 40004 2.5e-05 4.184326 6.618015 4.788764 0.250334
512 2 1 40008 2.5e-05 3.742041 6.213365 4.529020 0.287930
512 2 2 40005 2.5e-05 5.088407 8.296912 5.994227 0.285201
512 2 3 40008 2.5e-05 5.521000 8.581706 6.303711 0.283522
512 3 1 40005 2.5e-05 4.878445 7.012645 5.522388 0.242736
512 3 2 40007 2.5e-05 6.978223 9.254703 7.668983 0.229045
512 3 3 40007 2.5e-05 8.052672 10.753842 8.816430 0.249750

Reference z-score distributions

Z-score distribution plot for block length 128 bit Z-score distribution plot for block length 256 bit Z-score distribution plot for block length 384 bit Z-score distribution plot for block length 512 bit

Installation

Scipy installation with pip

pip install pyopenssl
pip install pycrypto
pip install git+https://github.com/scipy/scipy.git
pip install --upgrade --find-links=. .

Virtual environment

It is usually recommended to create a new python virtual environment for the project:

virtualenv ~/pyenv
source ~/pyenv/bin/activate
pip install --upgrade pip
pip install --upgrade --find-links=. .

Deployments

For various deployment information see Deployments.md.

Python 3.5+

BoolTest does not work with lower Python version. Use pyenv to install a new Python version. It internally downloads Python sources and installs it to ~/.pyenv.

git clone https://github.com/pyenv/pyenv.git ~/.pyenv
echo 'export PYENV_ROOT="$HOME/.pyenv"' >> ~/.bashrc
echo 'export PATH="$PYENV_ROOT/bin:$PATH"' >> ~/.bashrc
echo 'eval "$(pyenv init -)"' >> ~/.bashrc
exec $SHELL
pyenv install 3.7.1
pyenv local 3.7.1

The recommended version is Python 3.5+

SECRYPT 2017

For SECRYPT 2017 related experiments check out SECRYPT2017.md

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