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Advanced library for randomization, hashing and statistical analysis (devoted to chaos machines). :microscope:

2 years after

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Features | Overview | Installation | User Guide | Contributing | License

Got a question? Join us on stackoverflow or chat on IRC.

Advanced library for randomization, hashing and statistical analysis (devoted to chaos machines).

Libchaos is a computing library written in the C++ language to help with the development of software for scientific research. The library tries to be as general as possible, modern and easy-to-use.

Project goal is to implement & analyze various algorithms for randomization and hashing, while maintaining simplicity and security, making them suitable for use in your own code. Popular tools like TestU01, Dieharder and Hashdeep are obsolete or their development has been stopped. Libchaos aims to replace them.

The library implements wide range of chaos machines, which present the idea of creating a universal scheme with modular design and customizable parameters, which can be applied wherever randomness and sensitiveness is needed (pseudo-random oracle).

std::string hash = chaos::password<CHAOS_MACHINE_XORRING64, 500, 50, 95>("my password", "private salt");
// hash == "EA79560A7E0937EC66BDBE22EAFDC96AA5D7AFE4E970C3C856B7D92632EAA8EEC828E61E59E024922F58D4045BC053E"

It turns out that a pseudo-random function can be easily enriched by a chaotic system, creating something completely new. What's interesting is that this scheme allows specification by three parameters: execution time, period/memory required, initial secret key.

Getting Help

If you have questions about the library, please be sure to check out the API documentation. If you still have questions, reach out to us on IRC or post a question on stackoverflow (using the libchaos tag).

Reporting Bugs

Please open a GitHub Issue and include as much information as you can. If possible, provide sample code that illustrates the problem you're reporting. If you're seeing a bug only on a specific repository, please provide a link to it if possible.

Do not open a GitHub Issue for help, only for bug reports.


Ready In Progress TODO
Chaos machines Statistical tests & functions Entropy pools (different seeding scenarios)
Pseudo-random number generators Adapter for truely random generators (dynamical reseeding) Gnuplot/R utilities & analysis
Signatures for algorithms (portability on various architectures) Ranking for algorithms (speed/quality) Javascript API
STL compatibility Hashdeep fork (named chaosdeep) Seed recovery (attacks)



Each software problem requires different tools and algorithms to solve it effectively and achieve best results. Engineer's problem is how to decide which method will suit his needs best.

Example Instructions
#include <iostream>
#include <chaos.h>  // library header

// initialize chaos machine (64-bit version)

int main(void) {
  machine.set_space(100000); // 2^6400000 period length
  machine.push(0x8a5cd789635d2dff);    // add some data
  machine.push(0x284600e3f30e38c3);     // and other...
  while (true) putc_unlocked(machine.pull(), stdout);
Just copy, paste it into new file and prompt:

$ g++ -std=c++11 -lchaos
$ ./a.out | xxd -l 1024
See it run! Have fun.

This project offers very convenient interface for practical use, not just research. In the next section, there is a list of recommended algorithms and their strengths, period lengths, and speeds.

Example Instructions
#include <iostream>
#include <chaos.h>  // library header

// initialize PRNG (by Sebastiano Vigna)

int main(void) {
  prng.seed(0x8a5cd789635d2dff); // initialize with seed
  while (true) putc_unlocked(, stdout);
Notice that you can use CHAOS_PRNG_* and CHAOS_MACHINE_* algorithms. See the table below and read the library user guide to understand the difference.

Chaos Machines (theory/pdf)

In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracle. It was designed specifically to combine the benefits of hash function and pseudo-random function.

Name Input Output Period Quality Speed
CHAOS_MACHINE_NCG proof of concept uint32_t uint32_t (216n,232n) high 4.38007M
CHAOS_MACHINE_XORRING32 uint32_t uint32_t 232n high 33.0828M
CHAOS_MACHINE_XORRING64 uint64_t uint64_t 264n high 31.6051M

Machines can be used to implement many cryptographic primitives, including cryptographic hashes, message authentication codes and randomness extractors.

Pseudo-Random Number Generators

PRNGs are algorithms for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. Generated sequence is not truly random, because it is completely determined by a relatively small set of initial values, called the seed.

Name Seed Output Period Quality Speed
CHAOS_PRNG_KISS uint32_t [2] uint32_t 2119.5 high 99.9175M items/s
CHAOS_PRNG_ABYSSINIAN uint32_t [2] uint32_t 2126 high 165.754M items/s
CHAOS_PRNG_XOROSHIRO128PLUS uint64_t uint64_t 2128 high 178.426M items/s
CHAOS_PRNG_XOROSHIRO1024STAR uint64_t uint64_t 21024 high 165.289M items/s
CHAOS_PRNG_XORSHF96 uint32_t [3] uint32_t 296 - 1 high 185.148M items/s

STL Comparison

Library competes with PRNGs from standard library. Benchmarks confirms that libchaos is faster and offers more...

Benchmark                                Time           CPU Iterations                   Speed (Travis)
B__STL_MINSTD_RAND__Next               333 us        333 us       2108   1.46467GB/s   46.8694M items/s
B__STL_MT19937__Next                   229 us        229 us       3074   2.13247GB/s    68.239M items/s
B__STL_MT19937_64__Next                260 us        260 us       2683   1.87711GB/s   60.0674M items/s
B__STL_RANLUX24__Next                 2326 us       2327 us        295   214.828MB/s   6.71339M items/s
B__STL_RANLUX48__Next               118524 us     118598 us          6   67.4546MB/s   2.10796M items/s
B__STL_KNUTH_B__Next                  1083 us       1084 us        641   461.418MB/s   14.4193M items/s


The library needs a C++ compiler that supports C++11. You will need g++ 4.7 or newer to get started, so be sure to have an up-to-date compiler.

TODO. Add this library to Homebrew. Then simply $ brew install libchaos to install this package on OS X. This is an idea for the future, to be realized when the library has a stable version.

Basic Installation

$ git clone [email protected]:maciejczyzewski/libchaos.git
$ cd libchaos && ./

Manual Installation

We welcome patches. If you plan to contribute a patch, you need to build library and its own tests, which has further requirements:

$ git clone --recursive [email protected]:maciejczyzewski/libchaos.git
$ mkdir libchaos/build && cd "$_"
$ make && make install

Uninstalling Library

CMake creates a file called install_manifest.txt when executing the install target. This contains a list of all installed files.

$ make uninstall # where is install_manifest.txt

User Guide

This page gives a good introduction to libchaos. It assumes you already have library installed. If you do not, head over to the installation section. More complicated examples are in examples/ directory.

Warning. This project is at an early stage of development. The list of core features is not ready. Only main modules are documented. If you have some ideas, feel free to contribute.


Directory structure and contents:

Directory Purpose
deps/ Contains non-installed 3rd-party code that library depends on.
cmake/ Miscellaneous helper code.
include/chaos/engines/ Implementations of chaos machines.
include/chaos/generators/ Implementations of pseudo-random number generators.
include/chaos/ Core library abstractions.
tests Benchmarks and tests (using Google Test and Google Benchmark).


List of implemented algorithms is in the ALGORITHMS file.

CHAOS_MACHINE_* gen; // @1: for CMs
CHAOS_PRNG_* gen;    // @2: for PRNGS

Chaos Machines


gen.set_time(4);      // time parameter
gen.set_space(1000);  // memory parameter (period length)
                      // initial secret key
gen.set_key({0x84242f96eca9c41d, 0xa3c65b8776f96855, 0x5b34a39f070b5837,
             0x4489affce4f31a1e, 0x2ffeeb0a48316f40, 0xdc2d9891fe68c022,
             0x3659132bb12fea70, 0xaac17d8efa43cab8, 0xc4cb815590989b13,
             0x5ee975283d71c93b, 0x691548c86c1bd540, 0x7910c41d10a1e6a5,
             0x0b5fc64563b3e2a8, 0x047f7684e9fc949d, 0xb99181f2d8f685ca});

For pushing a blob:

gen.push(a); // @1: using function (fastest)
gen << a;    // @2: using operator

For getting a block:

gen.pull();  // @1: using function (fastest)
gen >> a;    // @2: using operator
gen();       // @3: STL style (for API)

For clearing to initial state:


Pseudo-Random Number Generators

For seeding:

gen.seed(a); // @1: using function (fastest)
gen << a;    // @2: using operator

For getting a number:;  // @1: using function (fastest)
gen >> a;    // @2: using operator
gen();       // @3: STL style (for API)

Password Salting

For salting passwords:

std::string hash =
        CHAOS_MACHINE_XORRING64,   // machine algorithm
        time_parameter,            // computational consumption
        space_parameter,           // memory required/space-hardness
        output_size                // length of hashed password
    >(password, salt);

Example usage:

std::string hash = chaos::password<CHAOS_MACHINE_XORRING64, 200, 50, 40>(
    "some secret password", "my private salt");
// hash == "C6EB731977A6CB785196BAF11CA8BEC02CDEAFE8"


Have you ever been fascinated by chaotic maps, fractals or something connected with disorder or randomness? Join us or support by sharing!

Our work flow is a typical GitHub flow, where contributors fork the libchaos repository, make their changes on branch, and submit a Pull Request (a.k.a. "PR"). Pull requests should usually be targeted at the master branch.

Please include a nice description of your changes when you submit your PR; if we have to read the whole diff to figure out why you're contributing, you're less likely to get feedback and have your change merged in. Life will be a lot easier for us if you follow this pattern (i.e. fork, named branch, submit PR). If you use your fork's master branch directly, things can get messy.

Before wrapping up a PR, you should be sure to:

  • Write tests to cover any functional changes.
  • Update documentation for any changed public APIs.
  • Add to the file information describing any major changes.

Testing & Benchmarking

To execute tests you need to build library manualy with option -DLIBCHAOS_ENABLE_TESTING=ON.

    - b_<filename>.cc               # for benchmarking      |       BENCHMARK(TEST_NAME)
    - t_<filename>.cc               # for testing           |       TEST(TEST_NAME, CASE_NAME)

After make build, repository should contains programs named as: bchaos and tchaos (separately for benchmark and test), because tests are required while benchmarks are optional.

Future Ideas

If you are starting to work on a particular area, feel free to submit a PR that highlights your work in progress (and note in the PR title that it's not ready to merge). These early PRs are welcome and will help in getting visibility for your fix, allow others to comment early on the changes and also let others know that you are currently working on something.


See LICENSE file in this repository.

Top Contributors



-   v1.0 zip tar