Last updated: 22 July 2010

*Introduction*
Exhibit 1

In 1918 John F. Byrne invented a cryptographic system that he later presented to the US Navy in the belief that it was "absolutely indecipherable by anyone except the persons for whom the message is intended". To protect his invention he never made the workings of his system known to the public at large. In July 2010 the algorithm behind Chaocipher was finally revealed. As a somewhat obsessive puzzle solver I had to try my hand at breaking the cipher.

What follows is a very brief description of how the Chaocipher
system works, followed by my method for cracking the cipher with
particular reference to Byrne's challenges. For more details on the
history and workings of Chaocipher, read Moshe Rubin's
*Chaocipher Revealed: The Algorithm*
available from his very informative
*Chaocipher Clearing House*
website.

Chaocipher is based on *two rings* that are *rotated* to find the
cipher-text symbol corresponding to a plain-text symbol, and then
*permuted* to modify the mapping between plain and cipher
alphabets. On the mechanical device that Byrne envisioned, these
rings were adjacent to one another and engaged at a point on their
outside edges. In the explanation below I will draw the rings
concentrically, both to save space and to aid understanding of the
algorithm implemented by Byrne's device. The *inner* ring is known as
the *plain-text* ring and the *outer* as the *cipher-text* ring. To
encipher a symbol simply look up the plain-text on the inner ring
and record the corresponding symbol on the outer ring. After each
encipherment the rings are permuted. This is the chaotic part of
Chaocipher—it ensures that the *mapping between alphabets
changes* slightly at each step, and completely after a lot of
steps.

**Figure 1 ** How to encipher one symbol and then permute the rings.

In the figure above is a colour-coded version of the Chaocipher
rings with shuffled plain-text and cipher-text alphabets. The
alphabets are initially in a random order. The figure shows
the steps involved in enciphering the symbol **P**.

- Find the plain-text symbol,
**P**, on the inner ring and encipher it to the corresponding cipher-text symbol on the outer ring,**C**. - Rotate the rings simultaneously so that
**P**and**C**are at the*zenith*—the top of the rings indicated by ▲. - Permute the rings according to the pattern indicated by the
colours. Note that
- one entry from each of the alphabets is moved to the bottom
of the rings, which is known as the
*nadir*(▼); - the yellow and green sections remain stationary relative to one another; and
- the red and pink sections are each offset by 1 relative to the yellow and green sections, but in opposite directions.

- one entry from each of the alphabets is moved to the bottom
of the rings, which is known as the

All subsequent symbols are enciphered in the same way, but now
starting from the permuted alphabets. *Deciphering* a text
follows exactly the same pattern—starting from the same
initial alphabet, locate the cipher-text symbol on the outer ring,
decode it to the plain-text symbol on the inner ring, and permute
the rings in the same manner as above.

In his book *Silent Years*, John F. Byrne devoted one chapter
to Chaocipher. After describing some of its history he
presented *4 challenges*, which he referred to
as *exhibits*. Each exhibit consisted of a plain text and its
encipherment. Byrne hoped to prove that his system was unbreakable,
even by "the believers in the wonderful capabilities of
electronic calculating machines". Byrne was correct in
believing that nobody would crack his ciphers, but he was playing a
somewhat *unfair game*. He never made the algorithm
underlying his system publicly known since he wanted to
commercialise it. This made it extremely difficult to even start
analysing the strength of the encryption scheme. Now, almost a
century after Byrne invented Chaocipher, the details of his system
are finally publicly known.

My approach to cracking Chaocipher will be described in a few articles, of which the first is complete.

*Cracking Exhibit 1*details the use of repetitions of plain-text and cipher-text symbols to crack the first exhibit, as well as a method for recovering the secret key used to initialise the cipher.*Cracking Exhibit 4*will explain how to use some statistical properties of Chaocipher texts to align plain and cipher texts, as well as revealing the solution to Byrne's fourth exhibit.- A final article will describe some attempts at cracking Exhibits 2 and 3, and explain how and why these attempts failed.