Bellaso-Challenges-2-bar

The challenges of Giouan Battista Bellaso were one of the top unsolved crypto mysteries. Norbert Biermann has now published the last two parts of the solution.

When I wrote my article series about the top 25 unsolved crypto mysteries in 2013 (in German), a series of cryptograms from Italy ranked number 11: Giouan Battista Bellaso’s challenges from 1555 and 1564. These ten challenges are the oldest crypto excercises known in the codebreaking community.

 

Bellaso’s challenges

Bellaso published three of the challenges in his book Noui et singolari modi di cifrare (1555), the seven others in Il uero modo di scriuere in cifra (1564).

On his webpage, Nick Pelling presents transcriptions of all ten cryptograms. For instance, here’s the first one from the first book:

Frzf  polh  hebx  ghqf  xtou  ulfh  gihm  qbgn* yoep  rpmi  porn  zngy
gzop  zctm  qdfl  hian  bxbu  dqmt  dnul  ayxm  cars  gsgc  xrch  omdo
cgmh  hxpc  bom*f rntr  oyqz  zhim  hsph  mphr  xrfh  omd’a updq  bedp
rhxe  flfg  dqlb  dcdq  cxrf  glmb  pctq  pnpy  fdeo  zcxt  braz  bude
qpyh  gnfp  beinu ndqa  ngxn  bloc  auyu  btos  iblx  fbyid fxyh  mctf
tmoz  fhlb  aich  oqep  luzi  ucxe  nctb  ghpz  lbxu  flzs  myxt  nbon*
loge  nxhq  xyef  nzgh  ryrd  myrf  qfao  dqse  tryr  cqtx  ddbx  nscu
hpnq  qscq  hqry  gnsp  huam  pfpn  fdcg  tbsn  lman  smlb  zcmb  easa
qemb  udoa  cxph  rsqgf yrnf  fgep  itia  amsy  acih  sxth  tsfd  cxph
lyni  rupt  ygdr  enqn  nfhi  enbe* engc  monb  qogt  rszy  clcx  aldu
ayix  ttis  phms  asbl  cpix  gnsr  tyeo  qxrf  yedx  mtgix rhcm  xuhf
sghr  opbg  slbo  cecu  flhb  npfc  e*rep gdqv  bzpr  haum  prpc  doxd
qylp  hqfq  dimtu ibgs  xelc  hgsh  zumh  qbxa  xcqt  pilb  ocud  slgl
hgdh  uhpd  hbxe  fltq  yayg  bdcle gmtn  umni  utpl  tufq  bdzo  sfzb
yezd  xnqc  opcy  pyhq  efso  zsbm  ornd  hudc  nulr  ryrn  pxlnu tgdaz

In the 1990s, Italian crypto historian Augusto Buonafalce made Bellaso’s challenges known to a wider audience. In January 2006, he presented them in a Cryptologia article. In 2009, Nick Pelling published the challenges on his blog. Among Pelling’s readers was Tony Gaffney (now also a reader of Klausis Krypto Kolumne), who is known as a great codebreaker.

This is what happened next:

  • March 31, 2009: Tony Gaffney reports the solution to challenge #6 from the second book.
  • March 19, 2009: Tony posts two more solutions: #1 and #2 from the second book.
  • April 27, 2009: Tony solves #7 from the second book.
  • May 5, 2009: Tony publishes solutions #3 and #4 from the second book.

Six of ten challenges were solved now. The story continued in 2016:

Now, two challenges (#2 and #3 from the first book) remained unsolved. Here is a scan of these two ciphertexts:

Bellaso-Challenges-Book1_2-3

 

The last two mysteries solved

Last year, Norbert told me that he had solved challenges #2 and #3 from Bellaso’s first book, too. However, I could not announce this success, as Norbert planned to publish his work in Cryptologia. On February 12, 2018, Norbert’s solution description was made available on the Cryptologia website.

This means that, after almost 500 years and over 20 years after their rediscovery by Augusto Buonafalce, Bellaso’s challenge ciphers are now completely solved. Congratulations to Norbert and Tony! I am very proud that my blog played a role in the solution of this mystery.

 

How Norbert solved the challenges

Giouan Battista Bellaso is known as one of the inventors of polyalphabetic encryption. In his publications, he suggested the use of substitution tables that looked like this one:

Bellaso-Table-2

Using this table to encrypt the message CRIPTO with the keyword TEST works as follows:

  • The C is encrypted with the ST table (because ST contains T, which is the first letter of the keyword). C encrypts to R.
  • The R is encrypted with the EF table (because EF contains E, which is the second letter of the keyword). R encrypts to F.
  • The I is encrypted with the ST table (because ST contains S, which is the third letter of the keyword). I enccrypts to Z.
  • The P is encrypted with the ST table (because ST contains T, which is the fourth letter of the keyword). P encrypts to A.
  • The T is encrypted with the ST table (because ST contains T, which is the first letter of the keyword). T encrypts to E.

This means that CRIPTO encrypts to RBZAEC. All in all, this method is very similar to the Vigenère Cipher, which was introduced a few decades later.

It comes as no surprise that Bellaso used this encryption technique for the first two challenges in his first book. The third ciphertext is encrypted in a similar way.

Norbert Biermann solved the three ciphertexts from Bellaso’s first book with a technique that is certainly familiar to many readers of this blog: hill climbing. To be more precise, he used simulated annealing, which is a hill climbing variant. For instance, here’s the table Norbert’s hill climbing program found for the second challenge of the first book:

Bellaso-Challenges-table-2

The keyword of the first challenge is actually a key poem (Eclogue 3 by Virgil, verse 28–31). For his second challenge, Bellaso used an excerpt from Psalm 50. The third ciphertext is not based on a keyword.

 

The cleartexts

Here’s the cleartext of Bellaso’s first ciphertext (book #1):

Al magnifico et illustre Signor Pompeo Avogaro parente et compare suo osservandissimo.
Tra tutte le inventioni del mondo ho sempre giudicato la inventione degli
caratteri essere la più degna anzi singolare; mediante la quale si parla insieme
anchor che di luntano come se di appresso. Si fusse cosa in vero sopra mondo
non meno utile che ingegnosa? Il primo honore appo questa inventione darei
à la cifra con il cui mezzo non solamente di luntano l’uno l’altro si parla, ma
che di più ciò si fa a malgrado d’ogni uno senza essere intesi da alcuno fuori
che dove si vuole; il che quanto sia utile anzi necessario al mondo per le varie
occorrenze et sottilità degli huomini. Ne ponno fare gli principi testimonio
chiarissimo perciò che la maggior parte delle più importanti cose loro si
spediscono con le cifre.

Here’s cleartext #2:

Al Signor Vincenzo Maggio, philosofo eccellentissimo, suo cugino osservandissimo.
Finito che ho l‘ufficio della consolaria de’ quartieri per levarmi alquanto
della mente le grandi confusioni et contrarietà de’ dottori legisti moderni.
Gli quali hanno di modo con gli loro scritti involuppate le leggi nelle ciance
loro, che non le leggi, ma le passioni, cavillationi, et vani sottilità dilettosi, et
avaritia per consultori fanno hoggidì le sentenze; et se il foco non gli provede,
stemo male et per l‘avenire peggio.
Ho pigliato in mano le meccaniche del vostro de ingegno divino Aristotele et
insieme considerate alcune sue questioni. Ho composto per capriccio una
arghena de rote diciotto. Tredici de’ quali son talmente proportionate insieme,
che finiscono il loro circuito tutte in un punto. Otto pesi ne levano cento; laonde
credo, che li antichi Romani usassino simili instrumenti per tirare et levare quelle
pietre, le quali a vederle et pensare a che modo fussino mosse, ci fanno stupire.

Here’s the third cleartext:

Hoc sermone eruditionem omnibus commendabat Diogenes, quod diceret
eam iuvenibus adferre sobrietatem, senibus solatium, pauperibus divitias,
divitibus ornamentum: propterea quod ætatem, suapte sponte lubricam
coerceat ab intemperantia, senectutis incommoda honesto solatio mitiget,
pauperibus sit pro viatico, non enim egere debent eruditi.
Aristoteles dicebat eruditionem in prosperis esse ornamentum, in
adversis refugium. Parentes qui liberos suos recte instituissent, aiebat multo
honorabiliores esse iis qui tantum genuissent, quod ab his contigisset vivere,
ab illis etiam bene vivere.

Again, congratulations to Norbert Biermann on this great codebreaking work!


Further reading: The Top 50 unsolved encrypted messages: 27. Ferdinand III’s encrypted letters

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Kommentare (15)

  1. #1 Thomas
    17. Februar 2018

    Norbert:
    Congratulations on this milestone in cipher history. Fantastic work!

  2. #2 Thomas
    17. Februar 2018

    What do 26, 27 and 28 stand for in the second cleartext? Maybe a typing error?

  3. #3 Gerd
    17. Februar 2018

    Looking at Bellaso’s tables, it seems that the tables are symmetric for encryption and decryption, and a letter is never encrypted in its own. Can someone confirm this? Is it a posssible weakness that can be used for breaking the code?
    Gerd

  4. #4 Klaus Schmeh
    17. Februar 2018

    >Looking at Bellaso’s tables, it seems that the tables are
    >symmetric for encryption and decryption, and a letter is
    >never encrypted in its own. Can someone confirm this?
    Yes, this is correct.
    It is certainly a weakness.

  5. #5 Klaus Schmeh
    17. Februar 2018

    >What do 26, 27 and 28 stand for in the second
    >cleartext? Maybe a typing error?
    Sorry, these numbers refer to footnotes. I have corrected this.

  6. #6 CS
    17. Februar 2018

    In the example (encrypting CRIPTO using the keyword TEST), is there a mistake in the encryption of “R”?
    It is said that it should be encrypted by the EF table (as R is the second letter of CRIPTO and E is the second letter of TEST). However, in the EF table, R should be encrypted by F, shouldn’t it? The R=B encryption is found in the QR table.

  7. #7 Norbert
    17. Februar 2018

    @Klaus
    Thanks for the article. Wow, you shoot faster than your shadow! I just wanted to inform you about the publication this weekend …

    @Klaus, Thomas
    Thanks for the congratulations :-)

    @Gerd

    a letter is never encrypted in its own

    This is true for the encryption system which was used by Bellaso for the first and second challenge of 1555 and which Klaus outlines above. (The two ciphertexts have independent alphabets and differ in the way the keyphrase is applied).

    Moreover, as the eleven reciprocal alphabets (see “Table 4” above) are all built by simply shifting the lower row, it is obvious that any letter of the upper row can encrypt only to one of the eleven letters of the lower row, and vice versa. Of course, this weakens the cipher significantly.

    However, the third challenge uses a completely different system in which a letter might indeed encrypt to itself. This system uses non-reciprocal alphabets with two homophones per vowel and three homophones for the word divider symbol “y”. Sounds unspectacular so far, but the cipher uses a total of four alphabets which are completely independent from each other. After each occurrence of a word divider in the plaintext, the alphabet is changed (which results in irregular periods). Double letters are (in all challenges) generally reduced to singles which, in combination with the homophones, makes pattern search a difficult if not impossible task.

  8. #8 Norbert
    17. Februar 2018

    The solutions quoted by Klaus are transcriptions with re-established double letters etc. The “raw” plaintext of the second challenge, for example, looks like this:

    alsi gnor yuic enzo ymag ioyp hilo sofo ...

  9. #9 George Lasry
    17. Februar 2018

    Congratulations, Norbert. A very impressive landmark achievement!

    Any chance to see you in Uppsala in June?

  10. #10 Klaus Schmeh
    18. Februar 2018

    @CS: You’re right, I corrected it.

  11. #11 Tony
    18. Februar 2018

    Great job Norbert – well done

  12. #12 Thomas Ernst
    Latrobe
    18. Februar 2018

    @ Norbert: your solution is a beautiful crypto-analytical masterwork, as you certainly know yourself! Am sending my heartfelt congratulations!!

  13. #13 Nils Kopal
    Kassel
    19. Februar 2018

    Great job Norbert :-) Well done!

  14. #14 Norbert
    21. Februar 2018

    George, Tony, Thomas Ernst, and Nils: Thank you very much for your posts. Your compliments and warm words mean a lot to me. By the way: yes, I am planning to come to Uppsala in June :-).

    As I was expecting the paper to be published at some point in the summer, the online publication and Klaus’s blog article only a few days later caught me off guard and, in a way, ill-prepared. Needless to say, few readers of this blog will want to spend money for having access to the paper. As far as I know, I am entitled to put online (for free access) a pre-print version of it, and I will certainly do so in the near future. Yet, there are a couple of problems to be solved first (for example, the webspace of a University of Arts might not be the right place). For the time being, I can only offer my contingent of free eprints to the readers of this blog. There are some forty views remaining at the moment:

    http://www.tandfonline.com/eprint/PPcNCsHM8EFXPSvUZUc9/full

    Feel free to use this link as long as it is working: first come, first serve (but please, be fair and and don’t click on “reload page” forty times).

  15. #15 George Lasry
    2. März 2018

    Norbert: Really happy to see you in June. Congratulations again!