Dorabella & D'Agapeyeff Ciphers - Solutions
Cryptanalysis - Main Stages
Cribbing
Not being skilled in the application of statistics in cryptanalysis, my analysis began with an assumption of what the underlying Plaintext at the start of the message might be (ie - a crib). I began with “Forli, Malvern” - Forli being the name of the house the Elgars were renting at the time the cipher is said to date from and this being the way Elgar routinely began his written correspondence. For this to be correct, I reasoned the underlying system had to be some sort of polyalphabetic substitution (Vigenère), with a second (fixed) substitution to convert cipher letters to hoop characters. I extended this beginning to "Forli, Malvern Link. A and Dai ???? met St Swithin". I subsequently changed St Swithin to St Stephen - but still couldn't get beyond char 39, concluding that some sort of system change had occurred at (or by) this point and that I would need to find a suitable crib to break into the 2nd half of the message. Referring to brief biographical notes I had made on the Elgars, and having spent several hours staring at chars 40-87, the breakthrough crib suddenly came to me - Brompton Oratory, where the Elgars were wed! Plugging this in at 54 - 68 gave me the vital 'aba' pattern at 60-62 (=ONO). [At this stage, I was dismissive of the full stop in the cipher after char 65]. Working backwards, I got back to char 40 with a highly promising "eighty six. Wed at Brompton Oratory." I belatedly noticed a 3-char repeat at 49-51 (WED) and 73-75 and concluded the text continued (from Oratory) but oWED - and embarrassingly had a spell in fantasy-land, including various stabs at 76-87: Pangrams, French, taxis - you name it - all of which were rightly mocked. However, I had by this stage enough bits of data to form more or less the entire 2 mixed alphabet sequences which are the sliding rows of Tables 1 and 2. I also felt I had sufficient evidence to conclude that I was dealing with a 'Polyalphabetical Encipherment By Groups', the group length being a fixed value of 8. [It took me a year or so to shift from this standpoint to one of variable length groups!]
Chaining or Mapping
For table 1, I reasoned that the Encipherer had stepped down the Table in a regular fashion and had been forced to change Table/Key/something, having got to the bottom of his page. [The actual structure was at this point still somewhat unclear in my mind.] I thus set about building a chain of my recoveries and then decimating the chain at the various non-factor distances (for alphabet length 24, the non-factor distances are 5, 7 and 11 and their reversals 19, 17 and 13), the hope being that the use of a rectangular transposition cage of any sort in the construction of the Mixed Alphabet would show through as likely heads/tails of columns occurring at some quasi-regular interval. This indeed proved to be the case and led me to (more or less) the final sequence now showing as CV1 - a 9-wide rectangle with the middle row offset by 1. [The final version as seen in CV1 is actually 10-wide, middle row offset by 2.]
For Table 2, I used a similar technique, the main difference here being that the stepping was NOT regular. Consequently, I struggled for some time to find the correct distances - the breakthrough coming when I recognised the 3-char repeat mentioned above. I reasoned that this meant 'same key and same plain' and that a full cycle of the Mixed Alphabet had been travelled. In other words, the distance X to Y to F (originally recovered as Z) to X was equal to 24. And from heads/tails properties, I concluded the steps were XtoY=9, YtoF=8, FtoX=7.
This gave me 2 Mixed Alphabets - but with no clear indication of their derivation. [I initially had Table 1 as derived from 'The Time Machine', published 1895 - but had to back off this idea.] A breakthrough of sorts came when I found that by taking every 5th letter of Mixed Alphabet 2, starting with G, I got the sequence "GET WHY I'M X. BOS". Announcing this huge find (!) to my wife, a crossword-puzzler, she remarked "surely it should be 'FORGET' etc". I ignored this suggestion - costing me 6 months in terms of recovery time!
Hoop Recoveries
One of the things I found difficult initially was forming a clear idea of the system construction and how it would work. A big break came with the recovery of the keyphrases from which the two hoop alphabets are formed - and the fact that there was an image reversal involved. Having solved the single-hoop keyphrases, the recovery of the spiral write-in pattern, the take-out by row (Part 1) and by column (Part 2) and the reversible T-blob image for the double and triple hoops soon followed. Now that I had the hoop alphabets recovered back to their initial phrase, I knew there had to be a similar stage of recovery possible for the 2 Vigenere tables. Also, the first signs of the X, Y conundrum were beginning to emerge (I initially thought it was X, Y and Z). I recalled advice given to me early on – ‘unpick carefully and hopefully all will become clear’. So I again unpicked characters 21-27 and belatedly asked myself “if the Plain is A.[=Alice] and ??????? met St Stephen, what or who is ??????? likely to be”? I tried ‘Eduardo’ against both keys available, with no luck. But it soon became clear what the answer was (see CV2) and this in turn led me to a better understanding of the system - principally, that it wasn't a Fixed length of Group but rather variable group lengths; also, there was a Running Key being used. Further breakthroughs in the Plaintext and Keys (and my appreciation of the overall system structure) quickly followed. Based on my findings, I have no doubt that the cipher message we see today is NOT from Elgar. If he did write in cipher to Miss Penny, then his original somehow got substituted for the message we have here (with or without Dora's connivance). The complexity of the underlying system suggests it was never intended for someone such as Dora, who apparently struggled to solve even a fairly simple anagram. Together with some of the Key and Plaintext content, it would seem to suggest a classroom training exercise for would-be cryptanalysts*, packed with examples of different cryptographic features and techniques, with students perhaps working (under supervision) in small groups and staged handouts being given to keep everyone moving at roughly the same speed. [Peter G. Brooks, moderator of the Elgar Cipher Group, informs me that there is good anecdotal evidence provided by a Canadian member of the Group, Mo Srivastava, that the message was, in fact, used at Bletchley Park. Mo wrote: "I was introduced to this by an old neighbour of mine, William Tutte, who was one of the Bletchley Park cryptographers during WWII. His colleagues at Bletchley Park knew of this cipher (it had been published shortly before the war) and used it as a vehicle for testing the analytical abilities of new staff ... they were interested in seeing how people thought through cryptography problems, and this particular cipher proved to be a fertile ground for doing so."] The reader will discover later in this solution that the eminent cryptographer who devised this system and message has left his signature!
* recruits to GC&CS, to be called up in the event of hostilities with Germany, probably to work on the Enigma problem. Indeed, Dorabella may well have been devised as a paper Enigma problem.
