Moshe Rubin
(mosher@mountainvistasoft.com)

This Progress Report is a compilation of Chaocipher-related information since Progress Report #26 (February 2019).

Here's a brief listing of items:

- Chaocipher mentioned in Craig P. Bauer's book "Unsolved!"
- Wolfram Function Repository has a Chaocipher function
- Chaocipher mentioned in Mike Barlow's "Computer Supplement #5"
- Ken Hannigan's paper on John F. Byrne and his connection to Wicklow, Ireland
- Rosetta Code: Chaocipher implemented in many programming languages
- Roaming Zenith: An alternate way of displaying permuted Chaocipher alphabets
- Chaocipher hypothesis re "no hits < 7" is finally proven
- Call for someone solving "no hits < 7" in the Crypto Forum
- Perl Weekly Challenge #25: Implement Chaocipher
- Off-the-wall link between Chaocipher and the Zodiac ciphers
- What is the reference here to Chaocipher?!
- Fascinating Chaocipher pt/ct challenge: find the starting alphabets
- Musings regarding Chaocipher research

Chapter 8, entitled "A Challenge Cipher", tells the story of Major General Joseph O. Mauborgne (1881-1971). Mauborgne had an illustrious army career, rising prominently in the Army Signal Corps between the years 1914-1941. He served as the army's twelfth chief signal officer from October 1937 until he reached the mandatory retirement age in 1941.

In 1914, Mauborgne made his reputation when, as a young first lieutenant, he achieved the first recorded solution of the Playfair cipher, then used by the British as their field cipher. In World War I he independantly invented the one-time pad.

In 1915, between these two events, Mauborgne, now a 1st Lieutenant, submitted a challenge cipher message to the director of the Army Signal School. The message was in a new system invented by Mauborgne, and he felt the system was far superior to the Playfair or the M-94 cipher wheel system. He suggested that members of the Signal Corps should be given the chance to solve it. Lou Kruh, a well-known collector of cryptological items and a prolific cryptographic author, published Mauborgne's challenge cipher in the American Cryptogram Association's "The Cryptogram" and in Cryptologia, but no solution was ever submitted by a solver.

When investigating the 1915 challenge cipher presented by Kruh, Bauer wanted to see Mauborgne's original letter. Unfortunately, the New York Public Library could no longer find the original. In his chapter 8, Bauer brings several examples of inaccuracies in Kruh's articles, and opines that Kruh may have introduced errors into the transcription of Mauborgne's cipher. One such inaccuracy relates to Lou Kruh's and Cipher Deavours's 1990 article in Cryptologia.

You can read the relevant portions of Chapter 8 describing Kruh's writing about Chaocipher. Bauer bases his doubts about Kruh's accuracy on Jeff Calof's excellent paper in Cryptologia entitled "Chaocipher Exhibit 5: History, Analysis, and Solution of Cryptologia's 1990 Challenge".

"... is
a general multi-paradigm computational language developed by Wolfram
Research. It emphasizes symbolic computation, functional programming,
and rule-based programming and can employ arbitrary structures and
data. It is the programming language of the mathematical symbolic
computation program Mathematica."

The Wolfram Language syntax is overall similar to the M-expression of 1960s LISP, with support for infix operators and "function-notation" function calls.

The Wolfram Function Repository is a public resource that hosts an expanding collection of contributed standalone functions suitable for immediate use in any Wolfram Language computation. Two of the standalone functions in the repository are the "ChaoCipher" and "ChaoDecipher" high-level functions for encipering and deciphering Chaocipher messages, respectively.

Computer Supplement #5, published in January/February 1988, presented an article entitled "Have you tried the Chaocipher?"

I have been interested in J.F.Byrne for
many years, not because of any interest in ciphers, but originally as
part of research I was undertaking while a student in the 1970s on the
life of Francis Sheehy-Skeffington, a contemporary of Byrne’s,
and more recently in connection with the history of my local parish of
Dunganstown, Co Wicklow. As you will be aware, J. F. Byrne wrote
extensively in his memoir, Silent Years, about the time he spent with
the Fogarty family in Carrigmore, Co. Wicklow. In 1993 and 1994
as part of a local history project in the parish, I co-operated with
Fr. Jim Murphy in taping a series of interviews with Michael Fogarty of
Carrigmore, the grandson of the man in whose house J.F. Byrne spent the
summers of his early life. I later published an article about
life in this area in the 1890s, based in part on Michael
Fogarty’s inherited memories and J.F. Byrne’s memoir.
I am hoping now to write a little more for a local history society
about Michael Fogarty, who died in 2005, about his memories or
previous generations, and what he had been told about visitors to
Carrigmore, including J. F. Byrne, Francis Sheehy Skeffington and James
Joyce (although I am almost certain that Michael Fogarty was mistaken
and that Joyce was never a visitor to Carrigmore).

This first email led to numerous fascinating and eye-opening revelations over the years, as we both shared the information we had about John F. Byrne. I must admit that carrying on such interesting correspondences, with someone as erudite and enthusiastic as Ken, has been a high point for me in my historical research into John F. Byrne's life.

Ken's paper was first published locally in the Wicklow Journal. However, as is the way of excellent research articles, it was picked up on by the prestigious Dublin James Joyce Journal, and the editors invited him to submit a version of it to their journal. With Ken's permission, you can read his paper "James Joyce, John Francis Byrne and their Contemporaries: the Wicklow Connections." It is a scholarly, but a most readable, personal, and intimate account of John Francis Byrne's life in Ireland, and it contains many references to Chaocipher.

One of its pages is dedicated to the Chaocipher algorithm, and solutions for coding the algorithm can be found in 26 different programming languages, from Arc, C, and C# to Tailspin, Visual Basic .NET, and zkl.

Left Alphabet (ct)
Right Alphabet (pt) CT <- PT

HXUCZVAMDSLKPEFJRIGTWOBNYQ PTLNBQDEOYSFAVZKGJRIHWXUMC O W

ONYQHXUCZVAMDBSLKPEFJRIGTW XUCPTLNBQDEOYMSFAVZKGJRIHW A E

ADBSLKPEFJRIGMTWONYQHXUCZV OYSFAVZKGJRIHMWXUCPTLNBQDE H L

HUCZVADBSLKPEXFJRIGMTWONYQ NBDEOYSFAVZKGQJRIHMWXUCPTL Q L

QUCZVADBSLKPEHXFJRIGMTWONY NBEOYSFAVZKGQDJRIHMWXUCPTL H D

HFJRIGMTWONYQXUCZVADBSLKPE JRHMWXUCPTLNBIEOYSFAVZKGQD C O

CVADBSLKPEHFJZRIGMTWONYQXU YSAVZKGQDJRHMFWXUCPTLNBIEO N N

NQXUCVADBSLKPYEHFJZRIGMTWO BIOYSAVZKGQDJERHMFWXUCPTLN Y E

YHFJZRIGMTWONEQXUCVADBSLKP RHFWXUCPTLNBIMOYSAVZKGQDJE N I

NQXUCVADBSLKPEYHFJZRIGMTWO MOSAVZKGQDJERYHFWXUCPTLNBI X S

XCVADBSLKPEYHUFJZRIGMTWONQ AVKGQDJERYHFWZXUCPTLNBIMOS T B

TONQXCVADBSLKWPEYHUFJZRIGM IMSAVKGQDJERYOHFWZXUCPTLNB S E

SKWPEYHUFJZRILGMTONQXCVADB RYHFWZXUCPTLNOBIMSAVKGQDJE Z T

ZILGMTONQXCVARDBSKWPEYHUFJ LNBIMSAVKGQDJOERYHFWZXUCPT J T

JILGMTONQXCVAZRDBSKWPEYHUF LNIMSAVKGQDJOBERYHFWZXUCPT R E

RBSKWPEYHUFJIDLGMTONQXCVAZ RYFWZXUCPTLNIHMSAVKGQDJOBE R R

RSKWPEYHUFJIDBLGMTONQXCVAZ YFZXUCPTLNIHMWSAVKGQDJOBER H T

HFJIDBLGMTONQUXCVAZRSKWPEY LNHMWSAVKGQDJIOBERYFZXUCPT J H

JDBLGMTONQUXCIVAZRSKWPEYHF MWAVKGQDJIOBESRYFZXUCPTLNH B A

BGMTONQUXCIVALZRSKWPEYHFJD VKQDJIOBESRYFGZXUCPTLNHMWA Y N

YFJDBGMTONQUXHCIVALZRSKWPE HMAVKQDJIOBESWRYFGZXUCPTLN H W

HIVALZRSKWPEYCFJDBGMTONQUX RYGZXUCPTLNHMFAVKQDJIOBESW Q E

QXHIVALZRSKWPUEYCFJDBGMTON SWYGZXUCPTLNHRMFAVKQDJIOBE K L

KPUEYCFJDBGMTWONQXHIVALZRS NHMFAVKQDJIOBRESWYGZXUCPTL S L

SPUEYCFJDBGMTKWONQXHIVALZR NHFAVKQDJIOBRMESWYGZXUCPTL O S

OQXHIVALZRSPUNEYCFJDBGMTKW WYZXUCPTLNHFAGVKQDJIOBRMES U A

UEYCFJDBGMTKWNOQXHIVALZRSP GVQDJIOBRMESWKYZXUCPTLNHFA J I

JBGMTKWNOQXHIDVALZRSPUEYCF OBMESWKYZXUCPRTLNHFAGVQDJI Y D

HXUCZVAMDSLKPEFJRIGTWOBNYQ PTLNBQDEOYSFAVZKGJRIHWXUMC O W

ONYQHXUCZVAMDBSLKPEFJRIGTW XUCPTLNBQDEOYMSFAVZKGJRIHW A E

ADBSLKPEFJRIGMTWONYQHXUCZV OYSFAVZKGJRIHMWXUCPTLNBQDE H L

HUCZVADBSLKPEXFJRIGMTWONYQ NBDEOYSFAVZKGQJRIHMWXUCPTL Q L

QUCZVADBSLKPEHXFJRIGMTWONY NBEOYSFAVZKGQDJRIHMWXUCPTL H D

HFJRIGMTWONYQXUCZVADBSLKPE JRHMWXUCPTLNBIEOYSFAVZKGQD C O

CVADBSLKPEHFJZRIGMTWONYQXU YSAVZKGQDJRHMFWXUCPTLNBIEO N N

NQXUCVADBSLKPYEHFJZRIGMTWO BIOYSAVZKGQDJERHMFWXUCPTLN Y E

YHFJZRIGMTWONEQXUCVADBSLKP RHFWXUCPTLNBIMOYSAVZKGQDJE N I

NQXUCVADBSLKPEYHFJZRIGMTWO MOSAVZKGQDJERYHFWXUCPTLNBI X S

XCVADBSLKPEYHUFJZRIGMTWONQ AVKGQDJERYHFWZXUCPTLNBIMOS T B

TONQXCVADBSLKWPEYHUFJZRIGM IMSAVKGQDJERYOHFWZXUCPTLNB S E

SKWPEYHUFJZRILGMTONQXCVADB RYHFWZXUCPTLNOBIMSAVKGQDJE Z T

ZILGMTONQXCVARDBSKWPEYHUFJ LNBIMSAVKGQDJOERYHFWZXUCPT J T

JILGMTONQXCVAZRDBSKWPEYHUF LNIMSAVKGQDJOBERYHFWZXUCPT R E

RBSKWPEYHUFJIDLGMTONQXCVAZ RYFWZXUCPTLNIHMSAVKGQDJOBE R R

RSKWPEYHUFJIDBLGMTONQXCVAZ YFZXUCPTLNIHMWSAVKGQDJOBER H T

HFJIDBLGMTONQUXCVAZRSKWPEY LNHMWSAVKGQDJIOBERYFZXUCPT J H

JDBLGMTONQUXCIVAZRSKWPEYHF MWAVKGQDJIOBESRYFZXUCPTLNH B A

BGMTONQUXCIVALZRSKWPEYHFJD VKQDJIOBESRYFGZXUCPTLNHMWA Y N

YFJDBGMTONQUXHCIVALZRSKWPE HMAVKQDJIOBESWRYFGZXUCPTLN H W

HIVALZRSKWPEYCFJDBGMTONQUX RYGZXUCPTLNHMFAVKQDJIOBESW Q E

QXHIVALZRSKWPUEYCFJDBGMTON SWYGZXUCPTLNHRMFAVKQDJIOBE K L

KPUEYCFJDBGMTWONQXHIVALZRS NHMFAVKQDJIOBRESWYGZXUCPTL S L

SPUEYCFJDBGMTKWONQXHIVALZR NHFAVKQDJIOBRMESWYGZXUCPTL O S

OQXHIVALZRSPUNEYCFJDBGMTKW WYZXUCPTLNHFAGVKQDJIOBRMES U A

UEYCFJDBGMTKWNOQXHIVALZRSP GVQDJIOBRMESWKYZXUCPTLNHFA J I

JBGMTKWNOQXHIDVALZRSPUEYCF OBMESWKYZXUCPRTLNHFAGVQDJI Y D

We will call this presentation the "stationary zenith" permuting method. This method reflects John F. Byrne's two-wheel physical model, because at each enciphering step the alphabets rotate and shift up to the stationary zenith position.

It turns out there is another, cryptographically identical method for permuting the alphabets which we call the "roaming zenith" method. The beauty of the "roaming zenith" permuting method is that it enables you to see, right before your eyes, the slow diffusion and entropy of the Chaocipher alphabets.

For a clear description of both methods, see the page entitled "Two ways to permute and display Chaocipher alphabets".

Chaocipher Progress Report #26, uploaded in Febraury 2019, announced the amazing fact that the lower bound of hits occurring was not nine (9), but rather seven (7). In other words, the phenomenon could be described as:

"Hits never occur at a distance less than 7"

Additional research showed that, when exhaustively iterating through a subset of possible encipherings, that seven (7) was indeed the theoretical minimum. In other words, hits could never occur at a distance of 6, 5, 4, 3, 2, or 1.

In February 2019, a challenge was uploaded to the Tapatalk Crypto Forum. The challenge was for readers to mathematically prove that seven (7) was indeed the theorectical minimum distance. At the time, no one took up the challenge.

I recently decided to "bite the bullet", and succeeded in proving the assertion. The proof can be read here.

The Perl & Raku Weekly Challenge website presents a weekly challenge to be solved in the Perl/Raku programming language. Weekly challenge #25, posted on 8 September 2019, stated the following challenge:

This challenge led to a flurry of activity trying to solve it. Subsequent posts and links touched upon Chaocipher card simulations, Pokemon sequences, and more.

https://perlweeklychallenge.org/blog/review-challenge-025/

https://github.com/LaurentRosenfeld/Perl-6-Miscellaneous/blob/master/Challenges-in-Perl6/Chaocipher.md

https://perlweeklychallenge.org/blog/meet-the-champion-025/

https://raku-musings.com/pokemon-chiao.html

https://github.com/LaurentRosenfeld/Perl-6-Miscellaneous/blob/master/Challenges-in-Perl6/Chaocipher.md

https://perlweeklychallenge.org/blog/meet-the-champion-025/

https://raku-musings.com/pokemon-chiao.html

Here's a zany monologue that tries to connect James Joyce, John F. Byrne, and Chaocipher to the Zodiac ciphers. Here is a quote from the end of the section:

Byrne had included
a whole raft of enciphered text in his book along with the plaintext
equivalent – his aim was to allow someone the realistic chance to
crack his cipher, after all. But, as a fail-safe, he encoded a final
section to which there was no plaintext provided. This would allow a
successful claimant to decipher the section and prove they had won the
prize.

That section was 17 letters long, one short of Zodiac’s version. I struggle to believe that this is just Zynch. In my opinion there is a strong likelihood that Zodiac got inspiration for his final 18 letters in the z408 from Byrne’s Chaocipher. If that is true then those 18 letters almost certainly do have some meaning to decipher.

That section was 17 letters long, one short of Zodiac’s version. I struggle to believe that this is just Zynch. In my opinion there is a strong likelihood that Zodiac got inspiration for his final 18 letters in the z408 from Byrne’s Chaocipher. If that is true then those 18 letters almost certainly do have some meaning to decipher.

Beats me how anyone could consider such a connection, but it makes for amusing reading.

Hiding data,
cracking codes, finding hidden messages. We welcome posts that aren't
as suitable for /r/crypto, such as basic cipher-cracking challenges and
discussions of simple data hiding.

On 10 July 2020, someone posted what he called "Challenges no. 2 (classical ciphers)". In this post he offered cryptographic challenges of different types. What interests us is cipher #4:

Clicking on the black area in "About #4" we see:

What we have here is a delightful challenge: given a Chaocipher ciphertext and its corresponding plaintext, can you derive the starting alphabets? This is precisely how the starting alphabets of Exhibit #1 were found. For a technical explanation of how to do this, see George Lasry's on-line "A Methodology for the Cryptanalysis of Classical Ciphers with Search Metaheuristics", section 8.3 ("Related Work – Prior Cryptanalysis").

Here, for easy access, are the ciphertext and plaintext:

Ciphertext:

RWTJQ
CBRAN SDDIJ IWPMT XTSSM BPQWW QLHTG ATWNL CZCHH WXSYS KEYZV ZITCA HZPZE
QNBXT YQCBB VOBBI WTTWE GVCVE RLVUH XJXHT BEMPZ VONCX JPQRN BXTIK GBPQQ
ZHPWX XELXA LFPXY KZYDS FAWNP WEOHO EPDVQ FFOGE RHZSP XRJLK BIKIU APPRN
ILKSQ OTQPM GCAKK JJ

Plaintext:

OKAYS
OTHIS ISJUS TATES TBASI CALLY BECAU SEIHA VENOI DEAWH ETHER THISI SSOLV
ABLEG IVENT HEREL ATIVE LYLIT TLEAM OUNTO FCIPH ERTEX THERE AGAIN THERE
STHER EISPA DDING SOITI SATLE ASTAL ITTLE LONGE RINTH EHOPE THATT HISHE
LPSWI THDEC RYPTI ON

If anyone succeeds in determining the starting alphabets, please send me a description of the method used and the starting alphabets, so I can highlight your solution on this site.

Good luck on this real-world cryptanalytic challenge!

P.S. Use ROT-13 to decrypt the text "V sbyybjrq gur ehyrf".

Besides the obvious answer of its being an intellectual challenge, I believe Chaocipher research, and research of other crypto-systems, has more far-reaching value. To date, this website has stimulated both historicak and cryptologic interest in other, sometimes unrelated, areas. Here is a list of my thoughts and observations on this topic:

- Even before the Chaocipher algorithm was discovered and revealed, amateur cryptanalysts were highly challenged to come up with a model that would match observations. This was the best cryptanalytic exercise, sharpening our general understanding of techniques for tackling difficult cipher challenges.
- It has impacted historical research:
- A large corpus of historical correspondences was collected and published. This affords a history buff to read about personages like Willam F. Friedman, Hebert O. Yardley, Parker Hitt, Rear Admiral (ret.) Dundas Preble Tucker, and others.
- Chaocipher research has led to fruitful fact sharing (e.g., see Ken Hannigan's article above) that enrichen the wider historical picture.
- Craig Bauer's research on Mauborgne's 1915 cipher (see above) benefitted from Jeff Calof's Chaocipher Exhibit #5 research.

- Chaocipher afforded Geroge Lasry, the indefatiguable cryptanalytic researcher, to add another cryptosystem to his impressive Ph.D thesis, "A Methodology for the Cryptanalysis of Classical Ciphers with Search Metaheuristics" (see Progress Report #26). Chaocipher enabled Lasry to test his thesis, for which Lasry capitalized on the invaluable observation that Chaocipher's ciphertext alphabet sequence does not add much security to the system. His findings and observation will hopefully fuel cryptanalytic techniques in the future.
- Investigating the "no hits < 7" phenomenon discussed above, we presented a method of proof that could be used when investigating other cipher systems beyond Chaocipher.
- As mentioned in my October 2011 paper "John F. Byrne's Chaocipher Revealed" (pages * and *), the PURPLE cipher system and Chaocipher shared several significant similarities. As I wrote then "Although a moot point today, had Friedman observed similarities between Chaocipher and Purple, he might have entertained the possibility that Byrne had sold his idea to the Japanese. Regardless of what we know today, documenting and studying Byrne’s Chaocipher within the organization would have been a correctthing to do, notwithstanding the heavy load on Friedman and his team ." Studying seemingly unimportant or unrelated cryptosystems may help break others.
- The Chaocipher concept has fired the imaginations of others to create similar system (e.g., Aaron Toponce's performing Chaocipher using playing cards) or to write the Chaocipher algorithm in a large number of different programming languages.

Copyright (c) 2020 Moshe Rubin

Created: 4 August 2020