The d’Agapayeff Cipher, continued…
In a recent post, I mentioned the idea that the d’Agapeyeff cipher might involve a diagonal transposition on the 14×14 grid cryptologists suspect it may well have been based upon. To test this out a bit, I wrote a short C++ program (which I’ve uploaded here) which turns the number pairs into characters (for convenience) and prints out all four diagonal transpositions (forward, reverse, forward boustrophedon, reverse boustrophedon) starting from each of the four corners.
Because the number of doubled and tripled letters is a simple measure of whether a transposition is likely to be plausible or not, I counted those up as well. The next metric to calculate would be the unique letter adjacency count (i.e. how many unique pairs of letters appear for each ordering)… but that’s a task for another day.
Interestingly, transpositions starting from the top-left corner (and their reverse-order reflections in the bottom-right corner) have no triple-letters at all, as well as far fewer double-letters (9/10/11 compared to 13/14/15) than transpositions that start from the top-right. Though intriguing, I don’t know if this is statistically significant: I haven’t determined what the predicted doublet and triplet count would be for a totally randomised transposition, perhaps calculating that too that would be a good idea.
For any passing cryptologers, here is the ASCII version of the d’Agapeyeff cipher (as output by the C++ code) when arranged as a 14×14 grid (in numerical order but without J), followed by the 16 diagonal transpositions with their associated double & triple counts. My guess is that the top left corner reverse diagonal transposition (the second one down, starting “KBDMIDPIK…”) is most likely to be the correct transposition, but we shall see (hopefully!) if this is true…
D I I M O N L C L L I I M B
D K N M O Q K I E N K K K S
C E E L C L K P K K D B M R
P I C M K I N L E L O P D P
D P P C M G B N B L L G L D
C K M L D N C M P L C C C Y
I L Q Q O C P O E D P E B T
B B P Q P Q I Q G K D E K F
E N B D I L M O B M D Q L S
E B D O O Q N P I Q L E G I
N N P M N D B G B E B N K R
G C M M G G N M P O K M L N
G O B M N K L D K I P L B R
*** Top left corner ***
Forward order…
KDBDIMCKIPPENMQDIEMOBCPCLONQIKPMCQLDBLMCKLKCLEBQLMIKILDE
NPQDGNPELQNBBQONBLKNIIGNDDPCCNEKKIPGCPOIQPMBLDKMOOMMOLIO
PLOBKBBMNQMQELLPMSMGDNOGDCGDRNGBPBKPCLPKNGIMDECDLMBQDEBY
DPELQKTKOBELFIKNGSPMKILLRBNR
–> number of doubles = 11, number of triples = 0
Reverse order…
KBDMIDPIKCQMNEPBOMEIDQNOLCPCDLQCMPKILCKLKCMLBDLIKIMLQBEQ
LEPNGDQPNEIINKLBNOQBBNPIKKENCCPDDNGOMKDLBMPQIOPCGBKBOLPO
ILOMMOSMPLLEQMQNMBRDGCDGONDGMPLCPKBPBGNDCEDMIGNKYBEDQBML
TKQLEPDFLEBOKSGNKIIKMPRLLNBR
–> number of doubles = 9, number of triples = 0
Simple boustrophedon (forward then reverse)…
KBDDIMPIKCPENMQBOMEIDCPCLONQDLQCMPKIBLMCKLKCLDLIKIMLQBEE
NPQDGNPELQIINKLBNOQBBNGNDDPCCNEKKIPOMKDLBMPQIOPCGOMMOLIO
PLOBKBSMPLLEQMQNMBMGDNOGDCGDRPLCPKBPBGNKNGIMDECDYBEDQBML
DPELQKTFLEBOKIKNGSIKMPLLRNBR
–> number of doubles = 10, number of triples = 0
Reverse boustrophedon (reverse then forward)…
KDBMIDCKIPQMNEPDIEMOBQNOLCPCIKPMCQLDLCKLKCMLBEBQLMIKILDQ
LEPNGDQPNENBBQONBLKNIIPIKKENCCPDDNGGCPOIQPMBLDKMOBKBOLPO
ILOMMOBMNQMQELLPMSRDGCDGONDGMNGBPBKPCLPDCEDMIGNKLMBQDEBY
TKQLEPDKOBELFSGNKIPMKIRLLBNR
–> number of doubles = 9, number of triples = 0
*** Top right corner ***
Forward order…
OPBIMSQIKRDIKMPLLKBDDDLNDPLYQCEKOGCTBLIKLLCBFQNKPELCEKSP
OQKLBLPELIMMOLNNPDDQGRBIMCIBMEKDEKNKINLKGCOGMLNLRDKEMMNP
QBQBMBDECCDCIOIEKLCIPLOQMPBOPPPMQPLNGPIDKQQIQBMKCLPDODND
IBBONGLBNDMGKEBPMNENMMNCBGOG
–> number of doubles = 14, number of triples = 2
Reverse order…
OBPSMIRKIQPMKIDDDBKLLYLPDNLDTCGOKECQFBCLLKILBSKECLEPKNQI
LEPLBLKQOPRGQDDPNNLOMMNKEDKEMBICMIBRLNLMGOCGKLNIKBMBQBQP
NMMEKDLKEIOICDCCEDPOBPMQOLPICIPGNLPQMPPKMBQIQQKDDNDODPLC
LGNOBBIKGMDNBNMPBEMMNEBCNOGG
–> number of doubles = 15, number of triples = 1
Simple boustrophedon (forward then reverse)…
OBPIMSRKIQDIKMPDDBKLLDLNDPLYTCGOKECQBLIKLLCBFSKECLEPKNQP
OQKLBLPELIRGQDDPNNLOMMBIMCIBMEKDEKNRLNLMGOCGKLNIKDKEMMNP
QBQBMBLKEIOICDCCEDCIPLOQMPBOPIPGNLPQMPPDKQQIQBMKDNDODPLC
IBBONGLKGMDNBEBPMNMMNENCBOGG
–> number of doubles = 13, number of triples = 0
Reverse boustrophedon (reverse then forward)…
OPBSMIQIKRPMKIDLLKBDDYLPDNLDQCEKOGCTFBCLLKILBQNKPELCEKSI
LEPLBLKQOPMMOLNNPDDQGRNKEDKEMBICMIBKINLKGCOGMLNLRBMBQBQP
NMMEKDDECCDCIOIEKLPOBPMQOLPICPPMQPLNGPIKMBQIQQKDCLPDODND
LGNOBBIBNDMGKNMPBEENMMBCNGOG
–> number of doubles = 14, number of triples = 0
*** Bottom right corner ***
Forward order…
RNBRLLIKMPSGNKIFLEBOKTKQLEPDYBEDQBMLDCEDMIGNKPLCPKBPBGNR
DGCDGONDGMSMPLLEQMQNMBBKBOLPOILOMMOOMKDLBMPQIOPCGPIKKENC
CPDDNGIINKLBNOQBBNQLEPNGDQPNEDLIKIMLQBELCKLKCMLBDLQCMPKI
QNOLCPCBOMEIDQMNEPPIKCMIDBDK
–> number of doubles = 11, number of triples = 0
Reverse order…
RBNLLRPMKIIKNGSKOBELFDPELQKTLMBQDEBYKNGIMDECDNGBPBKPCLPM
GDNOGDCGDRBMNQMQELLPMSOMMOLIOPLOBKBGCPOIQPMBLDKMOGNDDPCC
NEKKIPNBBQONBLKNIIENPQDGNPELQEBQLMIKILDBLMCKLKCLIKPMCQLD
CPCLONQDIEMOBPENMQCKIPDIMDBK
–> number of doubles = 9, number of triples = 0
Simple boustrophedon (forward then reverse)…
RBNRLLPMKISGNKIKOBELFTKQLEPDLMBQDEBYDCEDMIGNKNGBPBKPCLPR
DGCDGONDGMBMNQMQELLPMSBKBOLPOILOMMOGCPOIQPMBLDKMOPIKKENC
CPDDNGNBBQONBLKNIIQLEPNGDQPNEEBQLMIKILDLCKLKCMLBIKPMCQLD
QNOLCPCDIEMOBQMNEPCKIPMIDDBK
–> number of doubles = 10, number of triples = 0
Reverse boustrophedon (reverse then forward)…
RNBLLRIKMPIKNGSFLEBOKDPELQKTYBEDQBMLKNGIMDECDPLCPKBPBGNM
GDNOGDCGDRSMPLLEQMQNMBOMMOLIOPLOBKBOMKDLBMPQIOPCGGNDDPCC
NEKKIPIINKLBNOQBBNENPQDGNPELQDLIKIMLQBEBLMCKLKCLDLQCMPKI
CPCLONQBOMEIDPENMQPIKCDIMBDK
–> number of doubles = 9, number of triples = 0*** Bottom left corner ***
Forward order…
GOGBCNMMNENMPBEKGMDNBLGNOBBIDNDODPLCKMBQIQQKDIPGNLPQMPPP
OBPMQOLPICLKEIOICDCCEDBMBQBQPNMMEKDRLNLMGOCGKLNIKNKEDKEM
BICMIBRGQDDPNNLOMMILEPLBLKQOPSKECLEPKNQFBCLLKILBTCGOKECQ
YLPDNLDDDBKLLPMKIDRKIQSMIBPO
–> number of doubles = 14, number of triples = 2
Reverse order…
GGONCBENMMEBPMNBNDMGKIBBONGLCLPDODNDDKQQIQBMKPPMQPLNGPIC
IPLOQMPBOPDECCDCIOIEKLDKEMMNPQBQBMBKINLKGCOGMLNLRBIMCIBM
EKDEKNMMOLNNPDDQGRPOQKLBLPELIQNKPELCEKSBLIKLLCBFQCEKOGCT
DLNDPLYLLKBDDDIKMPQIKRIMSPBO
–> number of doubles = 15, number of triples = 1
Simple boustrophedon (forward then reverse)…
GGOBCNENMMNMPBEBNDMGKLGNOBBICLPDODNDKMBQIQQKDPPMQPLNGPIP
OBPMQOLPICDECCDCIOIEKLBMBQBQPNMMEKDKINLKGCOGMLNLRNKEDKEM
BICMIBMMOLNNPDDQGRILEPLBLKQOPQNKPELCEKSFBCLLKILBQCEKOGCT
YLPDNLDLLKBDDPMKIDQIKRSMIPBO
–> number of doubles = 13, number of triples = 0
Reverse boustrophedon (reverse then forward)…
GOGNCBMMNEEBPMNKGMDNBIBBONGLDNDODPLCDKQQIQBMKIPGNLPQMPPC
IPLOQMPBOPLKEIOICDCCEDDKEMMNPQBQBMBRLNLMGOCGKLNIKBIMCIBM
EKDEKNRGQDDPNNLOMMPOQKLBLPELISKECLEPKNQBLIKLLCBFTCGOKECQ
DLNDPLYDDBKLLDIKMPRKIQIMSBPO
–> number of doubles = 14, number of triples = 0
December 22nd, 2009 at 3:24 pm
Hi,
I stumbled across your site looking for stuff on the D’agapeyeff cipher. I have now subscribed!!
I’m tinkering with the D’agapayeff cipher and was very interested by your posts.
I just don’t know if we’re giving Mr D’agapeyeff too much credit? The book itself is fairly basic and you would assume the challenge at the end would be at a similar level? Obviously “Basic” is not the same as “Easy to crack”!
One of your comments in particular intrigued me. You say that triple letters in a row are extemely rare in English, but D’agapeyeff fields two of them in his cipher. I’m not so sure it’s that rare. I mean, even the few small lines in this paragraph have three english “Triples” in them!!!
Thanks for your posts and website. I look forward to receiving the email updates.
Scott
December 22nd, 2009 at 4:23 pm
If it was that simple, I’m sure that he would have remembered how he did it.
I think it more likely that it was a series of simple transformations, and that we’re actually pretty much on the right line. For example, the triples are a good indication (a) that there probably is some kind of transposition going on
, and (b) that there probably isn’t any polyalpha going on. 
December 31st, 2010 at 3:16 am
Leaving a short note about this cipher.
I’ve been working on it for a couple months now – off and on.
I believe the pattern in the cipher is “man-made”. The 6-0s are nulls. The thought first came to me due to the zeros being used both as padding and as part of the 5×5 polybius square. That just did not sit right with me.
What is is left is a series of 1s 2s 3s 4s and 5s written over a 14×14 grid. These have been transposed.
Simply put, I believe that D’Agapeyeff unknowingly used the ADFGX cipher. He’s illustrated a version of it using the letters ABCDE on pg 124-126 of his original book.
Mono-alphabetic substitution followed by fractionated transposition over 14 columns could easily stand up for 70 years, even without the ciphertext being disguised.
Simple enough encryption and well within what D’Agapeyeff taught in his book. He had several mentions of adding nulls to a ciphertext to make cryptanalysis more difficult.
Cheers,
Jim