Mini hash/KL diagnostic
Measures divergence from uniformity on toy SHA-256 prefixes.
View script
idle
Mathematical atlas
PT mathematics / information
exploration
Cryptography and one-way functions
Reading easy/hard asymmetry as controlled loss of persistent structure.
Plain
The idea
A one-way function is easy to compute forward, but hard to invert. Intuitively, it keeps the result while dispersing the path.
PT gives a natural language for this: the forward map preserves enough structure to produce an output, while inversion must reconstruct persistence lost into entropy.
hash → D_KL faible
Standard
Standard reading
In a hash function, many inputs lead to fixed-size outputs. The information budget contracts; inversion requires recovering erased structure.
The page should remain a conceptual application unless scripts actually measure sieve or structural signatures.
Takeaways
- Cryptography illustrates persistence vs entropy very well.
- Do not claim a general security proof.
- Scripts can provide experimental demonstrations.
Technical
Technical formulation
The PT_Cryptographie and sha256-sieve-structure projects can support an experimental page: residue spectra, survivor classes, KL measures, collisions, and robustness tests.
The canonical status must remain careful: PT reading of informational asymmetry, not a general proof of cryptographic security.
GitHub repositories to publish: Igrekess/PT_Cryptographie, Igrekess/sha256-sieve-structure; monograph ch04_gft.
Formulas
$f:x\mapsto y\quad\text{easy},\qquad f^{-1}(y)\quad\text{hard}$
$\Delta D_{KL}\downarrow\Rightarrow\text{inverse structure less accessible}$
public code
Code and scripts
The links below point to public resources or planned GitHub repositories. No local working path is exposed to the reader.
GitHub
Igrekess/PT_Cryptographie
GitHub repository to publish before this can become a download link.
GitHub
Igrekess/sha256-sieve-structure
GitHub repository to publish before this can become a download link.