Anomalous Input-Output Bit Correlation in SHA-3-256: Evidence of Structural Bias in the Keccak Sponge Construction

We present empirical evidence of a statistically significant input-output bit correlation anomaly in SHA-3-256 (FIPS 202) that is not present in SHA-256. Specifically, when isolating a single input bit while randomizing all other input bits, SHA-3-256 exhibits output bit correlations exceeding 3 sigma at rates consistent with or slightly above random expectation. However, a positional dependency was observed: input byte position 8 (corresponding to the boundary of Keccak lane [1,0]) produced 4 correlated output bits with a maximum z-score of 4.30, while the SHA-256 control produced 0 correlated bits under identical conditions. While individual results remain within plausible statistical fluctuation, the positional structure of the anomaly — concentrated at lane boundaries — warrants further investigation and independent replication.