## Trigram Disks and Cryptography

#### by Vincent deGuy

(Private email between the authors. Reprinted by permission.)

(Editor's note: The issues discussed here are in response to the emails of John Compton and Nancy Killia. deGuy is sometimes considered a "loose cannon" in the archeocomputing community, but his insights are often valuable and we have no qualms about printing his articles.)

Subject: Re: qching and john compton
From: Vincent deGuy
To: Martin Bulgerin

Your I Ching "odometer" is an interesting device, but you misunderstand its true purpose.

Here's a clue: Think of the old Enigma crypto machine the Germans used in WWII. It had multiple rotors (wheels with letters on the rim, and electrical contacts on the surface) and as you probably know, any combination of rotor settings constituted a unique code key. Keys were changed on a daily basis by setting the wheels to a new letter sequence in a code book. It took the great British mathematician Alan Turing to break the Enigma code, which arguably was the single greatest reason why the Allies beat Germany, and the machines Turing built to do it were the precursor of vacuum tube computers....

An Enigma machine could only hold 4 rotors at a time, allowing for 26^4=456,976 possible encryption keys. But rotors were removable, and there were 26! possible rotors (since there are 26*25*...1 ways to scramble the alphabet). The Nazis could pop one rotor out and insert another anytime they felt the urge to really baffle Allied code breakers.

An ancient Chinese "Enigma" would presumably use I Ching trigram discs of the sort Mr. Compton has discovered, drawing from that set of 8!=40,320 possible discs you mentioned. A single pair of rotors would represent a hexagram, so it would be very easy to distribute encryption keys using the I Ching. A 4-rotor device similar to the German model could be set into position simply using a single hexagram with moving lines. (Discs A & B set to upper & lower trigrams of the initial hexagram, discs C & D set to the resulting hexagram after lines move.)

A new key would literally be generated by casting yarrow stalks to divine a hexagram with moving lines.

Such a device would be fiendishly clever, but not beyond the mathematical or engineering ability of the ancient Chinese, who were famous for their secret codes. LTK wasn't just a programmer ... he was the world's first computational cryptographer. (Although similar work was undertaken by the early Celts at Stonehenge. As soon as I persuade the NSA to declassify my monograph on this subject, I'll be glad to share it with you.)

Clearly our mysterious Mr. Compton is an MI6 crypto-analyst-agent-archeologist, attempting to reconstruct the original I Ching Enigma machine in order to decode some Chinese text of an unknown nature. It's not a coincidence the US-China-North Korea nuclear talks are getting underway tomorrow. The CIA has asked the Brits for help deciphering secret communications intercepted from PRC field agents regarding weapons of mass destruction.

You (and Nancy) would do well to avoid this "Compton". He is undoubtedly ruthless and will stop at nothing to complete his mission.

- VdG