I ran 60 cryptanalysis experiments on SHA-256. Here's what I found.

Noctarion — Sun, 26 Apr 2026 13:01:35 +0000

TL;DR

SHA-256 cannot be broken. No shortcut for mining exists. But proving that produced 7 novel findings.

Setup

60 independent experiments
19 mathematical frameworks
5,000–1,000,000 hash evaluations per experiment
All signals Bonferroni-corrected and scale-verified (real signals scale as √N)

The 7 Novel Findings

1. Double-SHA-256 is NOT two independent hashes (9.56σ)

Bitcoin's SHA-256d has measurable cross-hash anti-correlation. W[8-15] in the second hash is ALWAYS constant padding — only 30 unique carry patterns exist vs theoretical 2^64.

Not exploitable (r=0.03), but real and never documented.

2. |HW(a)-16| → leading zeros: 20.48σ

The strongest signal in 60 experiments. Absolute deviation of working variable 'a' Hamming weight from 16 predicts output quality at 20.48σ. Invisible to standard linear analysis. Post-computation only.

3. Round 8 is the "insulator" — 17× drop

R0-2: 100% deterministic
R3: carry breaks control (→22%)
R4: nonce enters
R6-7: 26 trackable channels
R8: 💥 ALL 26 destroyed — 17× drop in ONE round
R16-64: perfect white noise

This is WHY every neural net, every evolutionary algorithm, every ML approach fails.

4. Nonce identity preserved (26.25σ) — but useless

Nonce tracking survives all 64 rounds. But nonce→quality correlation = 0.84σ (noise).
Count ⊥ Position. Two completely orthogonal channels.

5. Mixing: 85% linear + 15% nonlinear

Ch, Maj: <1% contribution each
ADD carries: 13%
Rotations Σ0, Σ1: 85%

Ch/Maj = algebraic protection. Rotations = actual mixer.

6. First algebraic mining impossibility proof via Z3

Nonces [0..31] proven IMPOSSIBLE for LZ≥8 at 4-round SHA-256. Algebraically, not probabilistically.

7. Groebner basis: 2^71 worse than brute force

64-round Groebner: ~2^103. Mining brute force: 2^32. The "just solve the polynomial equations" approach is 2 billion billion billion times harder.

All 19 Frameworks — 0 Exploitable Signals

Statistics, Neural Networks, Evolutionary, Spectral, Z3/SAT, Control Theory, FEM, Information Theory, Higher-Order Differentials, Cube Attack, Rebound, ANF, Multi-Variable, Side-Channel, Wang Differentials, p-adic, Tropical Geometry, Groebner, Representation Theory.

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