Tool
Chaos-based PRNG
Convert any of five chaotic maps into a deterministic byte stream keyed by a seed and a parameter. Visualise byte uniformity (histogram + lag plot), check Shannon entropy + χ² uniformity, then download the bytes as raw binary or a hex dump.
Byte histogram
Lag plot byte_n vs byte_{n+1}
Statistics
| Shannon entropy (bits/byte) | 7.7497 / 8.0000 |
| Mean (expected 127.5) | 131.265 |
| Std dev (expected ≈ 73.9) | 89.062 |
| χ² (uniform, 255 d.o.f.) | 32373.94 (p ≈ 0.0000) |
First 32 bytes: ff 00 02 0a 29 8a fe 06 1a 5e ed 43 c6 b3 d7 89 fe 05 16 51 dd 77 fe 05 14 4b d4 8f fc 0f 3a b3
The same (map, seed, parameter) tuple deterministically reproduces the full stream. Treat (seed, parameter) as the symmetric key.
Diagnostic interpretation
- Histogram should be roughly flat at the expected level (256 bins, height ≈ N/256).
- Lag plot should be a uniform speckled square. Visible lines or curves mean strong correlations.
- Shannon entropy ≈ 8.0 bits/byte for ideal randomness.
- χ² with 255 d.o.f. should be near 255 (p ≈ 0.5). χ² ≫ 290 or p ≪ 0.01 means the byte distribution is non-uniform.
Pair this tool with /tools/nist to run the full SP800-22 sub-suite on the bit stream.
Cross-link: feed the bytes (or just use the same parameters) into /tools/nist to run the full NIST SP800-22 sub-suite.
FAQ