fract 3.2.3

A Hyperchaotic, Quantum-Resistant, Minimalist Cryptographic Hash
Documentation

FRACT-256

A Hyperchaotic, Quantum-Resistant, Minimalist Cryptographic Hash implementation in Rust.

Overview

FRACT is a cryptographic hash function that leverages hyperchaotic dynamical systems on finite modular lattices to achieve provable diffusion, natural quantum resistance, and exceptional performance. By eschewing traditional S-boxes and large constant arrays in favor of coupled chaotic maps with positive Lyapunov exponents, the design achieves cryptographically secure avalanche effects through deterministic chaos.

Features

  • Minimal Design: Only 8 arithmetic operations per round, zero lookup tables
  • High Performance: Targeting ~4 cycles/byte on standard hardware
  • Quantum Resistant: Non-algebraic structure resists quantum algorithms
  • Sponge Construction: 256-bit state with 128-bit rate and capacity
  • Hybrid Logistic-Tent Map: Chaotic primitive on ℤ₂₆₄
  • Hyperchaotic Lattice: Four coupled chaotic maps for enhanced diffusion
  • Deterministic: All operations are fixed-point integer arithmetic and rust wrapping arithmetic enforced hash stay determinisitc accross all machines.

Foundation

READ WHITEPAPER -> https://www.pawit.co/whitepapers/fract-whitepaper.pdf

:: license is creative commons attribution 4.0 international Author: Pawit Sahare ( @morphym ).

Metrics

notes:

There are modification made to have some states to be public; new function 'from state' all these are for https://github.com/morphym/zk-disorder ; these are made on branch 'zk-disorder'.

>

Install binary

cargo install fract

Then, Enjoy a, Fast. Minimal. Hyperchaotic, Quantum-Resistant, Hash.

princee@princee:~$ fract

    ╔══════════════════════════════════════════════════════════════╗
    ║                                                              ║
    ║    ░██████╗░█████╗░░█████╗░██╗░░██╗░█████╗░████████╗░█████╗░  ║
    ║    ██╔════╝██╔══██╗██╔══██╗██║░░██║██╔══██╗╚══██╔══╝██╔══██╗  ║
    ║    █████╗░░███████║██║░░╚═╝███████║███████║░░░██║░░░██║░░╚═╝  ║
    ║    ██╔══╝░░██╔══██║██║░░██╗██╔══██║██╔══██║░░░██║░░░██║░░██╗  ║
    ║    ██║░░░░░██║░░██║╚█████╔╝██║░░██║██║░░██║░░░██║░░░╚█████╔╝  ║
    ║    ╚═╝░░░░░╚═╝░░╚═╝░╚════╝░╚═╝░░╚═╝╚═╝░░╚═╝░░░╚═╝░░░░╚════╝░  ║
    ║                                                              ║
    ║    Hyperchaotic · Quantum-Resistant · Fast Cryptographic Hash ║
    ║                                                              ║
    ║    Author: @morphym                                          ║
    ║    Version: 0.1.0                                            ║
    ║                                                              ║
    ╚══════════════════════════════════════════════════════════════╝

Usage: fract [OPTIONS] [FILE]...
       fract bench [OPTIONS]

Run 'fract --help' for detailed usage information.
princee@princee:~$ fract cat 
c3405751cd163e953f04744da9eb4bd411930a2b3de066c3c9e2ca905b33aa99  cat
princee@princee:~$

Benchmark

To run local benchmark in your machine

fract bench

Result: On a 4 vCPU machine:

princee@princee:~$ fract bench
=== Fract Benchmark ===
Data size: 1048576 bytes
Iterations: 100
Mode: 256-bit
Method: single-pass

Total time: 1.439969279s
Throughput: 69.45 MiB/s
Last hash: 60e1a1235112e7d3

=== Additional Stats ===
Bytes processed: 104857600
Nanoseconds per byte: 13.73
Cycles/byte (est. at 3GHz): 41.20
princee@princee:~$

Core

These are core mathematical foundation; not all are stated here; read whitepaper for comprehensive mathematical specification.

Hybrid Logistic-Tent Map (HLTM)

The core chaotic primitive is defined on ℤ₂₆₄:

f(x) = { 4x(1 - x) mod 2^64          if x < 2^63
       { 4(2^64 - x)(x - 2^63) mod 2^64  if x ≥ 2^63

This exhibits a Lyapunov exponent λ ≈ 0.693, guaranteeing exponential divergence.

Coupled Hyperchaotic Lattice Φ

For state S = (s₀, s₁, s₂, s₃) ∈ (ℤ₂₆₄)⁴:

Φ(S) = {
  s₀' = f(s₀) ⊕ (s₁ ≫ 31) ⊕ (s₃ ≪ 17)
  s₁' = f(s₁) ⊕ (s₂ ≫ 23) ⊕ (s₀ ≪ 11)
  s₂' = f(s₂) ⊕ (s₃ ≫ 47) ⊕ (s₁ ≪ 29)
  s₃' = f(s₃) ⊕ (s₀ ≫ 13) ⊕ (s₂ ≪ 5)
}

All operations use modular arithmetic with constant-time behavior.

note: whitepaper contain more information on all mathematical impl.

Usage

Read: https://github.com/morphym/fract/blob/master/usage.md

API Reference

Fract

The main hasher struct that implements the sponge construction.

Methods

  • new() -> Self - Creates a new hasher instance
  • update(&mut self, data: &[u8]) - Absorbs data into the state
  • finalize(self) -> [u8; 32] - Finalizes and returns 256-bit hash
  • hash(data: &[u8]) -> [u8; 32] - One-shot hashing (256-bit)
  • hash512(data: &[u8]) -> [u8; 64] - One-shot hashing (512-bit)

Convenience Functions

  • hash_to_hex(data: &[u8]) -> String - Returns 256-bit hash as hex string
  • hash512_to_hex(data: &[u8]) -> String - Returns 512-bit hash as hex string

Security Considerations

NOTE: This is an experimental implementation of a novel cryptographic design. The security claims in the whitepaper have not yet been independently verified through third-party cryptanalysis.

Claims

  • Classical Preimage Resistance: 2²⁵⁶
  • Classical Collision Resistance: 2¹²⁸ (birthday bound on 128-bit capacity)
  • Quantum Preimage Resistance: 2²⁵⁶ (with 512-bit output)

Future Works.

  1. No third-party cryptanalysis has yet been performed
  2. The aggressive round count (R=8) may need increase for conservative deployments
  3. Algebraic attacks using modular arithmetic decomposition have not yet been thoroughly analyzed

Implementation information.

  • Language: Pure Rust, #![no_std] compatible
  • Constants: Only 4 IV words (256 bits of √2)
  • Memory: Zero lookup tables, entirely ALU-bound
  • Timing: Constant-time operations using wrapping_* intrinsics
  • Dependencies: Only hex crate for hex encoding functions

Performance

Target performance characteristics:

  • Throughput: ~4 cycles/byte
  • Latency: 48 cycles for 16-byte input
  • Code Size: <1 KB
  • Vectorization: Four u64 lanes enable SIMD execution

Testing

Run the test suite:

cargo test

Run the demo:

cargo run --example demo

References

  • Whitepaper: fract.pdf - Comprehensive mathematical specification
  • Based on chaos theory and hyperchaotic dynamical systems
  • Sponge construction as described in the Keccak/SHA-3 standard

License

MIT License

Author

@morphym- Morphy Moretti {Pawit Sahare}.

Citation

Pawit, S. (2025). FRACT- A Hyperchaotic, Quantum Resistant, Fast Cryptographic Hash.
  Pawit Sahare. 
https://doi.org/10.5281/zenodo.17983496

https://pawit.co/works/fract
.