Cryptographically Keyed Gaussian-Distributed Spread-Spectrum for Enhanced Covert Communications: Design, Implementation, and Simulated Performance in ITU Channel Models

Gaussian-Distributed Spread-Spectrum (GDSS) achieves noise-like statistics for low probability of detection (LPD),
yet the original design leaves a practical traffic-analysis surface: synchronisation bursts built from repeatable pseudo-
noise (PN) and predictable timing can correlate across sessions. Masking drawn from thermal noise is statisti-
cally Gaussian but not cryptographically secret against a determined adversary with long captures. This preprint
documents Cryptographically Keyed GDSS (GR-K-GDSS), implemented as the GNU Radio out-of-tree module
gr-k-gdss, which replaces hardware-noise masking with ChaCha20-driven Box–Muller Gaussian masks, derives
independent subkeys via HKDF-SHA256 from a BrainpoolP256r1 ECDH shared secret, and randomises sync PN
and timing per session. Session nonces concatenate a 32-bit session identifier and 64-bit transmit sequence in
big-endian form. The reference transmit chain (example flowgraph) chains microphone input, Codec2 vocoder,
ChaCha20-Poly1305 payload protection (via gr-linux-crypto), SOQPSK modulation (gr-qradiolink), and
the keyed spreader. The despreader implements acquisition, tracking, and locked states with coarse-fine code search,
early-prompt-late timing, adaptive correlation thresholds, SNR estimation, and phase-based frequency error track-
ing; keys arrive on a GNU Radio PMT set_key port. Simulated IQ tests in the repository report cross-session
standard-GDSS sync correlation 1.0000 versus 0.1028 for keyed bursts (≈9.7× reduction). Unit tests: 37 passed (1
skipped) at time of generation (the project README may still quote an older snapshot such as 30 passed; the suite
has expanded). IQ statistical checks: 29/29 passed on generated files. Section 7 reports statistical bit-error simu-
lations (NumPy/SciPy Monte Carlo for standard and keyed GDSS, DSSS analytical reference, simplified VHF/HF
channels); they are not over-the-air measurements. LDPC overlays use ideal SNR shifts (∼5 dB) consistent with
prior GDSS/LDPC studies rather than bit-true decoder output. Limitations include absence of formal indistinguisha-
bility proofs for ChaCha20+Box–Muller versus thermal noise, lack of cryptographic forward secrecy under static
long-term ECDH keys unless augmented, and quantum vulnerability of BrainpoolP256r1 to Shor’s algorithm. Oper-
ational guidance for RTL-SDR DC offset and IQ imbalance appears in project USAGE.md. All claims are contingent
on expert review. This text is also posted on the IACR Cryptology ePrint Archive as Report 2025/108456 (archive
record 21 March 2026)