To add to our list of challenge ciphers (Bellaso’s, d’Agapeyeff’s, Feynman’s, etc), here’s one I hadn’t seen before from Helen Fouché Gaines’ (1956) “Cryptanalysis: A Study of Ciphers and Their Solution”, which I found courtesy of Greg Ross’s Futility Closet website:-

```VQBUP PVSPG GFPNU EDOKD XHEWT IYCLK XRZAP VUFSA WEMUX GPNIV QJMNJ JNIZY KBPNF RRHTB WWNUQ JAJGJ FHADQ LQMFL XRGGW UGWVZ GKFBC MPXKE KQCQQ LBODO QJVEL.```

The cipher is the last in a series of exercises at the end of a chapter titled “Investigating the Unknown Cipher,” and she gives no hint as to its source. Of the exercises, she writes, “There is none in which the system may not be learned through analysis, unless perhaps the final unnumbered cryptogram.” The solution says simply “Unsolved.”

If you look at the book itself (p.217), all Gaines says is “Here is one which nobody has been able to decrypt:“. Hence it is not at all clear whether this is a composed challenge cipher (i.e. designed to confound) or an accidental challenge cipher (i.e. one found in the wild but never yet solved). I suspect the latter… but perhaps someone will know for sure either way.

Incidentally, the 1968 comment on this mentioned in the Futility Closet post is online here (it’s on p.5): just so you know, the authors there offer an [entirely fictional, I expect] “Nicodemus J. Grumbow award” for anyone solving it.

As far as the ciphertext itself goes, it has a flattish distribution (Q appears 9 times, while T & Y appear only twice each, all 26 letters are used), with a standard deviation of 1.52144, i.e. much flatter than a normal alphabet would present.

It has no repeated trigrams, while QJ & PN appear three times (DO, GW, QL, GG, VQ, PV, NU, NI and XR each appear twice). There are seven doubled letter-pairs, all appearing once only each (PP, GG, JJ, RR, WW, GG, QQ). There are a few visible patterns in the text that vaguely suggest some kind of structuring (JAJGJ, QCQQ, QLQ and QQL), but all of which might just be random.

As a result, it doesn’t appear to be a monoalphabetic substitution, nor a (conventional) polyalphabetic substitution (as there seems to be no obvious cycles, loops, or repeats). The cipher text is 125 characters long, which (as a mathematician) makes me idly wonder whether this was partly enciphered using some kind of a 5x5x5 three-dimensional transposition cipher, the sort of thing a Bond villain would gloat about in his/her evil monologue. I don’t believe for a minute that this is the case, of course, but I thought I’d mention it all the same. 🙂

Any thoughts? Is there anything that suggests to you what kind of a cipher this might be?

7 thoughts on “Helen Fouché Gaines’ challenge cipher…”

1. bdid1dr on January 21, 2013 at 5:03 pm said:

popup sass sos SSI (Social Security Insurance)

🙂

2. The spacing between QJ is 22, and 44. Maybe the key is 11 letters in length.

That is assuming some sort of polyalphabetic cipher, Vignere maybe.

Going to take another look at this tonight to see what I can come up with. Thanks for bringing this one to my attention Nick 🙂

3. Stu: ooh, I didn’t notice that at all – good catch, Stu! 🙂 A length-11 polyalpha would be well worth checking for…

4. If you divide it into pairs 18 of the 24 recurring digrams remain intact, this suggests pair for pair substitution to me, possibly some kind of Playfair with 1 or 3 nulls tacked on the end to complete the blocks of 5.

Tony

5. Anne-Lise Pasch on February 7, 2013 at 12:04 pm said:

If you break it into pairs into columns of 5, you get recurring digrams in the same columns. (XR in 1, PN in 2 and QL in 3)

VQ BU PP VS PG
GF PN UE DO KD
XH EW TI YC LK
XR ZA PV UF SA
WE MU XG PN IV
QJ MN JJ NI ZY
KB PN FR RH TB
WW NU QJ AJ GJ
FH AD QL QM FL
XR GG WU GW VZ
GK FB CM PX KE
KQ CQ QL BO DO
QJ VE L

6. Jim Melichar on January 18, 2014 at 3:35 am said:

This cipher reminds me so much of Kryptos K4 that I can’t bring myself to look at it.

7. Jim: 🙂