The Madsen cryptogram: An unsolved encrypted text from a book about the CIA

Jozef Krajcovic

I think a book-derived Vigenère keyword is certainly worth testing, but the basic statistics of the ciphertext make a conventional short-period Vigenère solution rather difficult to reconcile with the data.

Using the 112-letter transcription

GQOWEXLGRNNYDDDPFECPODHCTCWRBCQJFTGEMMTNLVSSLHMJSTTBVWYLLZVRREIKZYYKFYOKRTOCPVYTCMWUFSZOHAANIENBDOZAAZVCFBHXHYEO

I obtain a global index of coincidence of

IC = 0.0357143.

That is actually below the random-alphabet expectation of approximately 1/26 = 0.03846, and far below the approximately 0.065–0.067 expected for ordinary English.

This also makes the ordinary Friedman estimate rather unhelpful. Using the standard approximation

k ≈ 0.027N / [ (N-1)IC – 0.038N + 0.065 ],

with N = 112 and IC = 0.035714, gives a formally negative value, about -13.3. Obviously a negative key length has no physical meaning; it simply tells us that the observed IC is too low for the assumptions behind the usual Friedman model. In other words, there is no positive short-key Vigenère signal in the global IC.

I also computed the mean IC of the Vigenère columns for candidate periods 2 through 20:

| Period | Mean column IC |
| —–: | —————-: |
| 2 | 0.03442 |
| 3 | 0.03048 |
| 4 | 0.03704 |
| 5 | 0.03610 |
| 6 | 0.03429 |
| 7 | 0.02619 |
| 8 | 0.02747 |
| 9 | 0.03587 |
| 10 | 0.03212 |
| 11 | 0.04500 |
| 12 | 0.03611 |
| 13 | 0.03144 |
| 14 | 0.02296 |
| 15 | 0.02778 |
| 16 | 0.02679 |
| 17 | 0.04650 |
| 18 | 0.03757 |
| 19 | 0.03509 |
| 20 | 0.01833 |

Periods 11 and 17 are the only conspicuous local maxima, but neither is close to what one would normally hope to see if the columns were approximately monoalphabetic encryptions of English. Moreover, by periods 17–20 the individual columns contain only about five to seven letters, so their IC estimates have enormous sampling variance. I therefore would not regard the peak at 17 as evidence for a 17-letter key.

I have also run direct optimisation against periodic Vigenère, Variant Beaufort and Beaufort forms. Short periods do not yield coherent English. At periods around 17–20 the optimiser can manufacture isolated English-looking fragments, but this is exactly where the number of independently adjustable Caesar shifts becomes large relative to a ciphertext of only 112 letters. The resulting candidates fail global linguistic consistency and behave like overfitting rather than a genuine plaintext.

The autokey possibilities I tested were also negative. Plaintext-autokey and related Vigenère/Beaufort recurrences, including word-reset variants, did not produce a consistent solution. Attempts to explain the text with simple feedback relations likewise failed.

There is another statistic that I think deserves particular attention. The ciphertext contains eleven adjacent identical pairs:

NN, DD, DD, MM, SS, TT, LL, RR, YY, AA, AA.

With 111 adjacent positions, a simple uniform 26-letter model gives an expectation of

111/26 ≈ 4.27

such equalities. The probability of seeing 11 or more under the corresponding simple binomial model is only about 0.0038, or 0.38%.

That does not mathematically exclude Vigenère, because the ciphertext is not required to be a perfect IID random sequence. But it is an unusual feature. A conventional long-key polyalphabetic cipher tends to randomise plaintext doubles rather than systematically preserve or create them, so the combination

IC ≈ 0.0357 + eleven ciphertext doubles

is something any proposed solution ought to explain.

For that reason I would distinguish two Vigenère hypotheses:

1. A normal short repeating keyword: the statistical evidence currently looks poor.

2. A specific long or irregular book-derived key: still testable, but the evidence would have to come from the key itself rather than from the IC. A candidate taken from the title page, dedication, introduction, a recurrent proper name, “Alpha/Omega”-type clue, etc. could simply be tried directly against all possible alignments and Vigenère/Beaufort orientations.

The important criterion would be that the proposed key decrypts essentially the entire 112-letter message into coherent English. With a text this short, isolated words such as THE, WILL, OVER, etc. are not enough; long-period optimisers generate such fragments quite easily by chance.

So I would definitely be interested in any specific keyword candidates you derive independently from the book. Those can be tested much more decisively than an unconstrained Vigenère search.