---
id: H16
title: Statistically detectable input–output correlations vanish after a small number of steps
axis: C
kind: sha256
statement: With N = 20 000 samples, the number of (input bit, output bit) pairs with |corr| > 4/√N is large for s ≤ 4 and
  zero for s ≥ s** (to be measured), identical to the random-oracle control; output-byte chi-square tests are uniform beyond
  s**.
motivation: C1/C3.
assumptions: Single-block random messages.
expected_contribution: Bias figure.
related_work:
- nist2015fips180
possible_counterexamples: Residual correlations at 64 steps.
verification_strategy: experiments/reduced_round_sha256/bias_test.py
computational_budget: minutes
status: running
classification: pending
evidence: []
verdict: pending
---

# H16 — Statistically detectable input–output correlations vanish after a small number of steps

With N = 20 000 samples, the number of (input bit, output bit) pairs with |corr| > 4/√N is large for s ≤ 4 and zero for s ≥ s** (to be measured), identical to the random-oracle control; output-byte chi-square tests are uniform beyond s**.