Cracking the Code – The Mathematics of Cryptanalysis Lesson 1 – Introduction In 1587, Mary, Queen of Scotts, was executed for treason against Elizabeth I, Queen of England, daughter of Henry VIII. Mary, a Catholic and a cousin of Elizabeth I, was considered the rightful queen of England by many English Catholics who deeply resented the repressive policies of Elizabeth’s government toward the Catholic Church. While imprisoned in London, Mary participated in a plot to have Elizabeth assassinated and to have herself crowned Queen of England. She communicated with her fellow conspirators by means of a cipher in which each letter of the plain text was replaced by a different symbol. (There were also symbols for certain code words, and some null symbols to confuse code-breakers.) What Mary did not realize was that the individual delivering the messages was a double agent, and that each message was taken to one of Europe’s most accomplished code-breakers and deciphered. Codes were used as early as the conflicts between Greece and Persia in the fifth century BC. The breaking of the German code “Enigma,” was a breakthrough for allied forces in World War II. Through the centuries in between, cryptanalysis evolved through a process of development of better codes, then development of better code-breaking strategies, then development of better codes to defeat the code-breaking strategies, then development of still better codes, etc. In this unit, we will study the mathematical properties of some simple ciphers and discover how to break them. We will study some historically important ciphers, and conclude with a study of the mathematics behind today’s state-of-the-art encryption systems. Decryption of ciphers is both an art and a science. Cryptographers at Bletchley Park, Britian’s center for the decryption of enemy messages during World War II, consisted of, in addition to mathematicians, linguists, a Museum curator, a chess champion, several bridge (card game!) experts and a number of cross word puzzle addicts. So take advantage of the abilities of everyone in your group, and tackle this cipher:Cypher #1 XJDPWQ HTES EPY RPYEWPXPY LYO L SFYOCPO ZQ ZFC QZWWZHPCD HTWW FYOPCELVP ESP OPWTGPCJ ZQ JZFC CZJLW APCDZY QCZX ESP SLYOD ZQ JZFC PYPXTPD QZC ESP OTDALENS ZQ ESP FDFCAPC QCZX ESP ZMPOTPYNP ZQ HSZX HP LCP MJ ESP PINZXXFYTNLETZY ZQ SPC XLOP QCPP ESPCP MP DTI YZMWP RPYEWPXPY LWW XJ ACTGLEP QCTPYOD HSZ QZC ESP KPLW ESPJ MPLC EZ ESP NLESZWTN NLFDP LYO JZFC XLUPDEJD DPCGTNP HTWW FYOPCELVP ESLE ECLRTNLW