d'Agapeyeff cryptogram revisited

           ''Codes of this kind can be solved without difficulty.'


                           Alexander d'Agapeyeff (1902-1955)
















The d'Agapeyeff cipher belongs to the ten most wanted ciphers to solve. d'Agapeyeff published his challenge cipher in 1939 in his book Codes and Ciphers, a textbook on the history of cryptography. The book has been republished in 1949 as a revised and reset edition. In his next edition in 1952 the challenge cipher he removed the cipher and it did not reappear in later editions of the book.

*His name is often misspelled as d'Agapayeff.


This is the ciphertext (p. 144):


75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
82858 47582 81837 28462 82837 58164 75748 58162 92000


One might question, what would be the reason to delete the challenge cipher. There are no reports that the cipher had been broken. Couldn't the cryptogram be deciphered because of mistakes and was this the reason to remove it from future editions ? He could easily have corrected mistakes, if any. He didn't do in his revised edition of 1949 either. Was the cipher too difficult for the general reader of his book ? Apparently yes, because in the last seventy years no one managed to decipher the challenge cryptogram, but this can not be a good reason to remove the cipher from future editions. One might expect, that he would replace it by an easier to solve cryptogram, but he did not do so. d'Agapeyeff himself kept silent about the reason. He just said, that he had forgotten the key, but we do not know, if he spoke the truth. His son Alex d'Agapeyeff, who was co-founder of CAP, didn't know either.


My attention to the d'Agapeyeff cipher was drawn by Nick Pelling's newsletter and site Cipher Mysteries, which I regularly consulted to learn more about an other (supposed) cipher, the Beinecke MS 408 or Voynich MS. I found it annoying that such a simple cipher as the d'Agapeyeff's had not been solved in seventy years since 1939, bought the book and started to read, more to convince myself about the difficulty than aiming to solve the problem myself as I was no cipher specialist like Pelling's contributors. Besides it was strongly believed, that the answer could be found in d'Agapeyeff's book, especially in the preceding chapters, where he gives a description of various ciphers and a method to resolve them. After all, d'Agapeyeff's book was a tutorial to lear about methods to encrypt and decrypt.


Dictionary code


When I looked at the challenge page I found three ciphers, two of them resolved and the last one the challenge cipher, upon which the reader could test his skills. As it would be very useful to find the type of the challenge cipher and the method to resolve it, I went through the preceding chapters as follows:


1. invented alphabets p. 103 -
2. mono-alphabetic transposition p. 105 p. 121 (resolved)
3. poly-alphabetic transposition, Vigénère cipher  p. 113 p. 133 (resolved)
4. dictionary code / Mansfield method p. 114 p. 140
5. cryptographic machines p. 116 -
6. syko (cipher machine) p. 117 -
7. musical code p. 120 -


From the above scheme it is most likely that the challenge cipher (p. 144) will be a dictionary code as the other two examples have been resolved by the author himself, and both the description and the solution of the dictionary code have been extensively explained. As far as I know the possibility of a dictionary code for the d'Agapeyeff challenge cipher has not yet been investigated. Code specialists tend to confine themselves to most complicated transposition and substition ciphers, which is of course their core business. But of course d'Agapeyeff as a former geographer was a generalist too.The dictionary code is more for generalists like me. Yet Alexander d'Agapeyeff in his book pays much attention to the dictionary code, which he calls a highly specialized form of substitution system, which involves the use of modified dictionaries known as code books, both for commercial and military purposes.


What dictionary ?


If the challenge cipher indeed is a dictionary code, the question may be answered, why the cipher has been removed from the future editions from 1952 onwards against speculations. d'Agapeyeff refers to the Concise Oxford Dictionary, current edition (3rd edition, 1934-August 1951, several times reprinted), edited by H.W. Fowler and H.G. Le Mesurier. (p. 115). In August 1952 the 3rd edition of the Concise Oxford Dictionary has been replaced by the brandnew 4th edition. I don't know, if d'Agapeyeff then changed the data on p. 115 to the new 4th edition with a new pagination and texts, but the new 4th edition could certainly be a good reason to remove the cipher from the later editions of his book from 1952 onwards as the relation between cipher and dictionary unfortunately had been broken.



Concise Oxford Dictionary (1934-1951)


Mansfield method


If the task would only be to look up the page and lemma in the Concise Oxford Dictionary the d'Agapeyeff cipher would not be much of a challenge, upon which his readers could exercize their skills. So I wonder, if he didn't want his readers to use the Mansfield method (1936)* to find the right page and lemma. As the Mansfield Progressive Dictionary is not available either, one should make one's own progressive dictionary by listing and numbering the digraphs AA, AB, AC, AD, etc. The use of the Mansfield method may be an other reason to remove the challenge cipher from d'Agapeyeff''s book, because the outcome of the Mansfield method to resolve the challenge cipher will  equally be related to the 3rd edition of the Concise Oxford Dictionary.


* Mansfield (Louis C.S.), The Solution of Codes and Ciphers. 1936.


A very British mystery indeed.


Both the description of the dictionary code (p. 114-116) and the method to resolve a dictionary code with the Mansfield method (p. 140-143) are closely related to the 3rd edition of the Concise Oxford Dictionary (1934-1951). When the 3rd edition was replaced by the 4th edition (August 1951) with new pagination and lemmata, the relation was broken. As this was an obvious reason to remove the challenge code from future editions of Codes and Ciphers (1952 onwards), this may well indicate, that the challenge code is a dictionary code, to be resolved with the Mansfield's method. This complies with the order of the three ciphers on p. 144 of Codes and Ciphers, which are a. mono-alphabetic substitution (p. 128), b. poly-alphanetic substition or Vigénère cipher (p. 135) and c. (in my opinion) dictionary code annex Mansfield's method (p. 140) as a cryptogram upon which the reader is invited to test his skills. If any other cipher would have been used as a challenge cipher, there would have been no need to remove it from future editions of Codes and Ciphers, because such ciphers would be self-explaining without help of external sources. 


Menno Knul


14 juli 2014







William F. Friedman presents the fundamental operations for the solution of practically every cryptogram:


(1) The determination of the language employed in the plain text version.

(2) The determination of the general system of cryptography employed.

(3) The reconstruction of the specific key in the case of a cipher system, or the reconstruction of, partial or complete, of the code book, in the case of a code system or both in the case of an enciphered code system.

(4) The reconstruction or establishment of the plain text.                                                        

William F. Friedman (1891-1969)


In some cases, step (2) may proceed step (1). This is the classical approach to cryptanalysis. It may be further reduced to:


1. Arrangement and rearrangement of data to disclose non-random characteristics or manifestations ( i.e. frequency counts, repetitions, patterns, symmetrical phenomena)

2. Recognition of the nonrandom characteristics or manifestations when disclosed (via statistics or other techniques)

3. Explanation of nonrandom characteristics when recognized. (by luck, intelligence, or perseverance)


Much of the work is in determining the general system. In the final analysis, the solution of every cryptogram involving a form of substitution depends upon its reduction to mono-alphabetic terms, if it is not originally in those terms.






The Beinecke MS 408 or Voynich MS, which generally is thought to be a cipher text, learns that the four basic operations should be preceded by:


(0) The identification of the script to decide, if we deal with a code or not.


The same applies to selfmade scripts like the one of Giovanni de la Porta, Hildegard von Bingen, obsolete scripts and non-alphabet scripts, but it applies as well to Chinese, Japanese, Cyrillic and other scrpts and transcripts. As for the Beinecke MS 408, which is taken for a coded book since 1916, I doubt so, because the script, which has not yet been identified, shows all characteristics of a common script and the subjects (herbarium, astrologium, balneum) treated in the book were openly available  in the usual languages (Latin, Italian, Spanish or in Arab languages). Yet the Beinecke MS 408 is listed as a coded book. However, methods used in cryptography can well be adopted to identify the characters of the Beinecke MS 408 (Voynich MS).




Alexander d'Agapeyeff I (1902 St.Petersburg (Russian Federation) - March, 22nd, 1955 Maugersbury (Fairford, England ) was a Russian born, jewish, carthographer, who  settled in the United Kingdom. In September, 1924 he married in Stow, Suffolk (Engeland) with Josephine Christian Pasey-Adams (1895-1983), daughter of Edward Charles Passay-Adams (1859- ) and Josephine Christian Morris (1872- ). During World War II he was R.A.F. Wing Commander.





1939 Alexander d'Agapeyeff, Codes and Ciphers, Oxford University Press, 1939 (Meridian Books), reprint 1949, revised 1952 (Geoffrey Cumberlege), 1960 (Compass Books), 1971 (Gryphon Books), 1974 (Gale Reserch Co.), 2005 (Gale Research Co),2008 (subtitel: A History of Cryptography) (Hesperides). The d'Agapeyeff cryptogram has been published in the 1939 and 1949 editions, but has been removed from 1952 onwards.


1945 Alexander d'Agapeyeff and E.C.R. Hadfield, Maps. Londen, N.Y., Oxford University Press, 2nd. ed. 1945


Burial place: Stow-on-the-Wold Cemetery, Stow-on-the-Wold, Gloucestershire, England


His son


His son Alexander (Alex) d'Agapeyeff II was director of Consultants in Information Technology (CIT). Alex d'Agapeyeff was co-founder of CAP.The Times death notices [31 March] inform us of the passing, on 26 March, 2003, of Alex d'Agapeyeff, OBE, FCA, FBCS.





In 1981, the Prime Minister, Mrs Thatcher, visited the BCS as part of her promotion of government IT policy. The photograph shows the president, Frank Hooper, next to Mrs Thatcher. On her right is Peter Hall, his predecessor. At the head of the table is the Duke of Kent and I am on his right. The only other woman in the room is Steve Shirley, later our president, and on her right is Alex d'Agapeyeff. The Prime Minister's interest was critical. Her visit to the BCS was both symbolic and purposeful: to hear the views of the professionals and to enlist their support.


His grandson


His grandson Alex d'Agapeyeff III was qualified from the University of London in 1998 and has been a consultant in anaesthesia and intensive care at Gloucestershire Royal Hospital since 2010. Practice: Gloucestershire Royal NHS Trust Gloucester Royal Hospital Great Western Road GLOUCESTER GL1 3NN, and Tetbury Hospital Trust Ltd Malmesbury Road TETBURY GL8 8XB. Special duty: Organ donation.







The D'Agapeyeff cipher is an as-yet unbroken cipher that appears in the first edition of Codes and Ciphers, an elementary book on cryptography published by the Russian-born English cryptographer and cartographerAlexander D'Agapeyeff in 1939.


Offered as a "challenge cipher" at the end of the book, it was not included in later editions, and D'Agapeyeff is said to have admitted later to having forgotten how he had encrypted it.


The ciphertext is:


75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
82858 47582 81837 28462 82837 58164 75748 58162 92000

Use of nulls in ciphertext


It is possible that not all the ciphertext characters are used in decryption and that some characters are nulls. Evidence for this is given by the author on p. 111 of the text under the sub-section heading Military Codes and Ciphers:


"The cipher is of course easily made out, but if every third, fourth, or fifth letter, as may be previously arranged, is a dummy inserted after a message has been put into cipher, it is then extremely difficult to decipher unless you are in the secret."


While the index of coincidence for the D'Agapeyeff cipher is 1.74 when taken in pairs horizontally (eg, '75' '62' '82'), the letter frequency distribution is too flat for a 196 character message written in English.

Additionally, D'Agapeyeff left two ciphers for the reader to solve. Each are approximately 100 characters in length and have an index of coincidence much higher than what is expected for English plaintext.


Polybius square in Codes and Ciphers


Alexander D'Agapeyeff made extensive use of the Polybius square throughout the examples in his text. Including walking the reader through solving most of a Polybius square based cipher from a friend in his cryptanalysis section of the book. This ciphertext consisted of 178 characters:




When deciphered with a Polybius square, the plaintext contains several typos and reads:


"The new plan of attack includes operations by three bombr squadrons over factory arya southwest o the river"


C V N * T E
E B P K * *





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