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MIXMAX

MIXMAX is a matrix-recursive pseudo-random number generator based on Kolmogorov K-systems and Anosov C-systems. It uses a special NxN matrix multiplication in a Galois field to generate extremely high-quality random numbers with exceptional statistical properties and very long periods.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Deterministic PRNG
Security status	🎓 Educational Only
Complexity	Advanced
Inventor	Konstantin Savvidy, George Savvidy
Year	2015
Origin	🌐 International
Source	algorithms/random/mixmax.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 2048 bytes (16384 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Original Paper: The MIXMAX random number generator (CPC 2015)
• Spectral Test of MIXMAX Generators (Chaos 2018)
• Official Implementation (HEPForge)
• ROOT CERN Implementation
• Wikipedia: MIXMAX generator

References

• A Priori Tests for MIXMAX (arXiv 2018)
• TestU01 Statistical Testing Suite
• Savvidy’s Research Papers

Test vectors

5 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Seed [1,2,3,4]: First 4 outputs (32 bytes) - Verified against C# implementation

Field	Value
seed	00000001000000020000000300000004
outputSize	32
input	null
expected	6379afc57b50bf572c9062f116e0458ad22a0a30e848249ba286b8c5a633b27a

Vector 2 — Seed [0]: First 3 outputs (24 bytes) - Zero seed with SplitMix64 initialization

Field	Value
seed	0000000000000000
outputSize	24
input	null
expected	05bc6a4a6d369615b1d0a961f181c7420294730f6fbef9ae

Vector 3 — Seed [1]: First 5 outputs (40 bytes) - Single-byte seed propagation

Field	Value
seed	0000000000000001
outputSize	40
input	null
expected	ff4a6538e039e776dea700280bdc6e54 b67e275ac7959c340dcf790540c41f19 b13744fcb2dff6ee

Vector 4 — Seed [42]: First 4 outputs (32 bytes) - Common test seed value

Field	Value
seed	000000000000002a
outputSize	32
input	null
expected	462494ab7e4722b7233c616cc59dcf723d3137eccf3befadb59766ee350e766e

Vector 5 — Seed [123456789]: First 3 outputs (24 bytes) - Large seed value test

Field	Value
seed	00000000075bcd15
outputSize	24
input	null
expected	8506a0fdac78f9caefb5db32389c75de1d094a706b95537f

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