Distributional Signatures in ML-KEM Ciphertext: A Black-Box Statistical Measurement

We present the first black-box statistical characterization of ciphertext output from the three NIST post-quantum cryptographic standards: ML-KEM (FIPS 203), ML-DSA (FIPS 204), and HQC. Using CASI (Causal Amplification Security Index), a composite metric derived from four position-aware statistical strategies, we measure the distributional distance of PQC output from uniform random across nine parameter configurations at scale (500,000 samples), with stability confirmed over five independent replications. Our central finding is a compression isolation experiment on ML-KEM that separates two signal components: (1) the non-uniformity of LWE coefficient distributions after Compress_d, and (2) byte-alignment artifacts from bit-packing. Contrary to initial expectation, the bit-packing masks the distributional signal rather than creating it. When ML-KEM coefficients are re-encoded in uniform 16-bit representation with randomized padding, the Crypto-CASI increases from 5.3 to 10.1 (ML-KEM-512) and from 1.5 to 15.5 (ML-KEM-1024), while uniform random coefficients in the same format produce Crypto-CASI ≈ 1.0. This demonstrates that Compress_d serves a dual function in ML-KEM: reducing ciphertext size (its designed purpose) and incidentally masking the distributional signature of Module-LWE noise. The masking effect is strongest for ML-KEM-1024 (d_u=11), which reduces a raw signal of 15.5 to 1.5 in the encoded output. HQC (code-based KEM) shows no detectable signal at any security level, serving as a negative control. These findings have no implications for the IND-CPA security of ML-KEM but provide the first quantitative measurement of post-compression distributional properties across NIST PQC standards. Key results: Compression isolation proves LWE coefficient distribution is the signal source, not bit-packing; Compress_d masking quantified across all three ML-KEM parameter sets; HQC indistinguishable from random at all security levels; ML-DSA signatures show expected structural patterns from rejection sampling. All experiments reproducible via open-source live-casi tool.