While working on a project at the University College, Dublin (UCD) Archives, Tom Mahon came upon hundreds of IRA (Irish Republican Army) documents from the 1920s containing enciphered messages. The search for someone to help him read these messages led to the American Cryptogram Association’s  James J. Gillogly.
Gillogly is well known to those in the field of cryptology for his 1999 decipherments of the first three parts of the text on James Sanborn’s sculpture Kryptos , located inside CIA headquarters. (It turns out that CIA employee David Stein had solved these portions the year before, but his results were classified and therefore unknown to Gillogly! The final part of this ciphertext remains an open problem.) He has demonstrated his skills by solving other ciphers, including one from 15th century England and another by a Cambridge don .
Following Mahon’s introduction, Gillogly provides a 28 page description of how he cracked the IRA ciphers, making extensive use of computer programs of his own creation. The ciphers were almost exclusively of the transposition variety. An (incomplete) list of keys was found, but it was enciphered as well! — this time using a variant of the Vigenère cipher. Gillogly knew none of this in advance. He was looking at ciphers in unknown systems. Other difficulties included typos and illegible characters in the ciphertexts. I greatly enjoyed these 28 pages. Tales of decipherment, be they on lost scripts (Egyptian Hieroglyphs, Linear B) , important military systems (Enigma, Purple) , or hidden messages in old books (Trithemius)  are among my favorites in the literature of cryptology. Gillogly’s explanations are clear and give great insight into how codebreaking works in the real world — as opposed to the sometimes artificial textbook examples!
The remainder of the book details the new facets of IRA history revealed by the decipherments. These include IRA spying in Britain and America on behalf of the USSR in exchange for badly needed funding. Some context is provided, but for someone who has very little previous knowledge of the IRA, it might be too little. A very nice feature is 27 figures showing original ciphertexts along with their decipherments. Also, all material recovered by Gillogly is placed in a distinct font when it is quoted. For those of you wishing you had the first chance to crack these ciphers, Figure 7 shows a message that remains unsolved — good luck!
Any mathematician with an interest in the IRA is strongly encouraged to seek out this work. For those who are only interested in the cryptologic side, Gillogly’s 28 pages will have to be weighed against the cost of the entire book.
 American Cryptogram Association, http://www.cryptogram.org/
 Budiansky, Stephen, Battle Of Wits: The Complete Story of Codebreaking in World War II, The Free Press, New York, 2000. There are hundreds of books/papers on these systems, but this is a good place to start.
 Gillogly, James J. and Larry Harnisch Cryptograms from the Crypt, Cryptologia, October 1996, Volume XX, Number 4.
 Gordon, Cyrus H., Forgotten Scripts, Revised and enlarged edition, 1998, Basic Books, Inc., New York. This is a great introduction to the topic aimed at a general audience.
 Markoff, John, "CIA's Artistic Enigma Reveals All but Final Clues," June 16, 1999, New York Times.
 Reeds, J. A., Solved: The Ciphers in Book III of Trithemius's Steganographia, Cryptologia, October, 1998, Volume XXII, Number 4.
Craig Bauer is the editor-in-chief of Cryptologia
, a quarterly journal devoted to all aspects of cryptology (mathematical, historical, & pedagogical). James J. Gillogly serves on Cryptologia
’s editorial board.