The Kryptos Annex augments the Kryptos-related information already available on the web and represents my own investigation into Kryptos.

Part III of Kryptos is a novel transposition cipher based on the modulus operator. The mathematics of the design are simple, yet elegant. Despite the code having been broken over a decade ago, this cipher provides fertile ground for exercising one's analytical skills.

The modulus-based transposition can make the relationship between the input plain text and the output cipher text difficult to discern. This visual explanation demonstrates the transformation in a way in which this relationship can be readily seen.

While many different techniques for decoding part III of Kryptos were discovered, the actual paper-and-pencil technique, employing two completely filled grids, remained elusive. Starting with the algebraic equation for the transposition, I was able to synthesize a matching geometric interpretation. The interpretation was applied to part III and resulted in this demonstration of how two grids could be used for its encoding.

The words “illusion” and “underground” are misspelled as
“iqlusion” and “undergruund” in parts I and II of Kryptos.
These misspellings may be clues to the keys
(i.e. the number of columns in the encoding grids) of part III.
The locations of the misspellings
can be related
to the part III keys through the use of the
**Goldbach Conjecture**.

As it turns out, the misspelling of illusion was due to an encoding error.

The most interesting avenue for exploring Kryptos part III is to reverse engineer the end-user's manual. It would be more than just a demonstration of how to fill in the grids, as there are several important pitfalls to avoid when using this cipher. For example, the plain text just ends up being reversed when the number of columns in one grid matches the number of rows in the other. There are also instances where two grids generate the identical output as one single grid, which is extremely easy to crack. The susceptiblity of this cipher to one of the classical Incomplete Columnar transposition attacks also varies widely with the choice of keys. To counter this, additional key selection criteria may have been used. One such technique requires tweaking the length of the plain text to be a multiple of (1/2) n (n+1), where n is an odd number. In the specific case of Kryptos part III, the length is a multiple of 28 (n = 7). These and other questions make for an interesting diversion when the frustrations of working on part IV mount.

The cipher described in the article is a very clean and mathematically elegant cipher. It is based on parts I, II and III of Kryptos. Its output's characteristics bear a strong resemblance to those of other classical paper and pencil ciphers. I believe that in the past it has been stated that part IV is a combination of a transposition and a substitution cipher, yet I have not recently been able to locate the source. Should this be the case, then the described cipher may form the framework of the substitution portion of part IV (despite its not strictly being a substitution-only cipher). The cipher possesses nowhere near a high enough difficulty level to qualify it as the entire part IV cipher.

*The Cryptogram* is a publication of the
American Cryptogram Association.

Copyright © 2008-2009 Frank Corr. All rights reserved.