30-Character HFGCS Broadcast Messages Are Not Uniform Ciphertext: Field Structure and a Dated Format Revision

1.Introduction

The High-Frequency Global Communications System broadcasts short fixed-length base32 strings over shortwave as Emergency Action Message traffic.RFC 4648 base32: the letters A–Z plus the digits 2–7. 0, 1, and 8 are excluded as confusable with O, I, and B — a practical alphabet for traffic read aloud, character by character, over HF voice. To an observer without key material they appear as opaque 150-bit messages, and a natural null is that each is the output of an IND-CPA-secure AEAD primitive — statistically indistinguishable from uniform random base32.

This paper evaluates that null from ciphertext alone, and rejects it three ways. The base32 marginal is not uniform: M and 5 are under-represented by ~40% at nearly every body position, in every prefix cell, at a rate stable across the whole window. Superimposed on that stable deficit, the Group 1 message carries positional structure that is not stable: a change-point analysis dates a single format revision to 1 October 2024 which removes one mid-body field (positions 19–21), while the post-revision format carries a deficit-exempt slot of its own at positions 16–17 — in the marginal channel only — that the pre-revision format lacks. And a revision-invariant constraint makes the final six characters near-certainly pairwise distinct. The layout is thus versioned — five regions on each side of the revision, but not the same five — and no region is identified with a specific primitive; the observations establish the regions and the dated change, not their cryptographic meaning.

2.Corpus and the October 2024 revision

The corpus is 10,899 transcribed Group 1/Group 2 broadcasts of length 30, collected 2022-01-25 to 2026-07-29. Retaining the earliest instance of each distinct string (first-broadcast itemization, to approximate independence against operational retransmission) gives N = 5,881 unique messages: 3,917 Group 1 and 1,964 Group 2. The finest key partition the data supports is one prefix (PR), a rotating identifier active for weeks to months. All statistics below derive from this single load.

2.1The change-point

Group 1 is not temporally homogeneous. Ordering its 3,917 unique messages by broadcast time and searching every temporal split for a discrete change in positional structure — the maximum-likelihood change-point over the message-by-message character-equality matrix, prefix excluded because prefix rotation correlates with time — returns one dominant break, with likelihood-ratio 320. The maximum-likelihood split falls between consecutive messages at 00:33z and 00:57z on 2024-10-02 — the evening of 1 October 2024 US local, hours after the C6 prefix replaced 3E. That is a point estimate, not a resolution: the only near-certain per-message marker, a repeat within positions 19–21, appears in about one new-format message in 10, so the split can be moved 14 messages earlier or 7 later before the likelihood ratio reaches 20:1 — anywhere from 25 September to 3 October. Every instant inside that bracket is about equally consistent with the data, and we suspect the change took effect at 00:00z on 1 October 2024, the start of the UTC day on which the prefix changed (1.4:1 against, relative to the split).Bounded, not observed: the first message individually recognizable as new-format aired at 01:43z on 3 October, 7 messages after the split. The per-format tables split at 2024-10-02 01:30z; moving that cutoff anywhere inside the bracket changes no reported statistic beyond rounding. Permuting the message order destroys the break (p < 0.0002 over 4,999 shuffles), confirming it is a property of the time-ordering.

We therefore treat Group 1 as two formats: a pre-revision format (N = 2,587, 2022-01-25 to 2024-10-02) and a post-revision format (N = 1,330, 2024-10-02 onward), and report every positional statistic below for each. Pooling the two averages a hard pre-revision constraint against its absence and describes neither. The same analysis on Group 2 finds no significant change-point (p ≈ 0.49), so it is treated as one population. Procedure: analysis/eam_epoch_sweep.py; this paper is generated end-to-end by analysis/eam_30char_format_render.py.

3.First-order symbol distribution

Under the uniform null, each base32 symbol occurs at rate 1/32 = 3.125% at every body position. Across all Group 1 body characters (109,676), M and 5 instead occur at 1.929% and 1.952%, aggregate z of -22.8 and -22.3z counts standard deviations from expectation. |z| ≈ 3.3 clears this paper’s multiple-comparison threshold; |z| ≈ 20 is beyond any accident of sampling.; a matched CSPRNG control stays within ±2.The control: a same-size corpus drawn from a cryptographic random generator and pushed through the identical pipeline — what every table below looks like when nothing is there. Every other symbol is near uniform.

3.1Persistence across prefixes and across the revision

The deficit is not stratum mixing. It appears in every prefix cell (Table 3), and it survives the revision: restricted to the full-deficit body positions, M occurs at 1.646% pre-revision and 1.88% post-revision (5 at 1.733% and 1.884%) — a ~45% shortfall on both sides. The pre/post gap is only ~2σ (M) and not clearly significant, so at most the deficit softened marginally after the revision. Whatever produces the bias operates uniformly across prefixes and persists through the format change; unlike the positional structure below, it is essentially not versioned.

4.Position-wise bias profile

If the deficit reflects format structure it should concentrate at specific positions. It does. Two regions break from the body-wide deficit — and they differ in whether they survive the revision.Marginal properties such as this deficit bind the population, not the message: no single broadcast can violate a rate. The per-message rules come later (§5–§6).

5.Equality-suppression profile

An independent probe: the rate at which two positions carry the same symbol (1/32 under the null, regardless of the marginal).A doublet: the same character at both positions of a given pair within one message. This is the channel where the revision is sharpest.

5.1The trailing constraint is a no-any-duplicate rule, and it is permanent

Extending the probe to all C(30,2) position pairs, the trailing suppression is not limited to adjacent pairs: every one of the fifteen pairs within 25–30 shows a ~15-fold equality deficit. The six trailing characters are near-certainly all mutually distinct — a stronger rule than "no adjacent repeats."Chance rate for six independent base-32 characters to be all-different: 31/32 × 30/32 × 29/32 × 28/32 × 27/32 ≈ 61% — the birthday problem in a 32-symbol year. Group 1 sits at 97%. Table 6 shows it holds in every prefix cell, including post-revision cells, confirming revision-invariance.

6.Within-key structural probes

Conditional on the marginal deficit and the equality constraints, does the message behave like a strong pseudorandom function within one prefix? Three probes — pairwise mutual information, LZMA compressibility, and inter-message differential structure — say yes. Each prefix cell is retired and replaced faster than the interval to the revision, so no cell straddles 1 October 2024: these within-cell results hold in both formats.

Mutual information at the terminal pair sits within the shuffle null (Table 7); LZMA ratios for the prefix cells sit at the synthetic-random floor (0.668); and modular differences between date-ordered consecutive messages are uniform once retransmissions are de-duplicated. These rule out simple failure modes (stuck RNG, short-period PRG, table lookup) but cannot on their own establish cryptographic provenance.

7.Synthesis: two dated region models

The evidence is incompatible with a single uniform-output generator across all 150 bits, and the region layout is versioned. Before 1 October 2024 the Group 1 message has five distinguishable regions:

a prefix P (positions 1–2); a head slot X (3–4) exempt from the deficit; the main body B, carrying the full deficit and running 5–24 but interrupted at 19–21 by the mid-body field T; T is the three characters marked in both the marginal and equality channels, while positions 22–24 on its far side are statistically ordinary body (per-position z ≈ −5, Table 4); and the trailing all-distinct region R (25–30). The two B segments are one behaviour split by the embedded field. The revision deletes T — positions 19–21 lose both signatures and merge in — but the post-revision body is not contiguous either: positions 16–17 form a deficit-exempt slot X₂ (§4, z = +8.6) that the pre-revision format lacks. The symbol is chosen by behaviour: X₂ is marked in the marginal channel only, with adjacent-pair equality at chance — the equality probe of §5, which pinned T, is blind to it — so it is a second slot of the head-slot class (X), not the mid-body field relocated. T has no successor. The post-revision layout is:

The prefix, head slot, and trailing region are common to both layouts; what differs is the embedded structure — a three-position two-channel field at 19–21 before; a two-position marginal-only slot at 16–17 after. We name regions by behaviour, not primitive: the M/5 body deficit (~40% overall) is inconsistent with the uniform output of a standard authenticator, so the natural reading of T as part of a truncated tag — it spans bits 91–105, straddling the 96-bit width common to such tags — is ruled out by the statistics of the surrounding region. That T was removed on a datable evening without disturbing the others is itself an argument against a fixed cryptographic component — a truncated authenticator does not come and go by operational schedule.

8.Conclusion

The 30-character Group 1 message is not uniform-output encryption. It carries a stable M/5 body deficit (~40% overall), a permanent head slot and trailing all-distinct field, and — until the start of October 2024 — a mid-body field at positions 19–21 whose two independent signatures switched off together; from then on the format carries a marginal-only exempt slot at 16–17 (X₂, z = +8.6), a second slot of the head-slot class. The single free-standing observation needing no interpretation and no format qualifier is the ~15-fold suppression of pairwise equality across the final six characters, in every prefix and both formats. Natural next steps: a bit-offset scan across the 150 bits, cross-length comparison, and the same change-point analysis applied to other length/group cohorts. Group 2 carries none of this structure and shows no revision; the two groups are not producing output with the same internal format.

Prepared 2026-07-29. Supersedes the version of 2026-04-17, eam_30char_format_analysis_v0.html, which treated Group 1 as one stationary population and so overlooked the 1 October 2024 format revision (§2.1). Its positional statistics pool the two formats: the mid-body field at 19–21 was reported at the pooled pair-equality z ≈ −7 (Table 5) rather than z ≈ −9 before the revision and chance after; the post-revision deficit-exempt slot at 16–17 (X₂, §4) was not detected; and the revision-invariance of the head slot and of the trailing all-distinct field (§5.1) could not be established.