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THE CODEBREAKERS by David Kahn. 1,164 pages. Macmillan. $14.95.

In his letters to Cicero, Julius Caesar employed a cipher in which each character was replaced by one standing three places down the alphabet—thus D stood for a, E for b, F for c, etc. Mary Queen of Scots wrote conspiratory messages in cipher; when intercepted and interpreted by England's first great cryptanalyst, Thomas Phelippes, they helped bring Mary to the chopping block. In the U.S., Benedict Arnold employed several codes, including one that was keyed to Volume I of the fifth Oxford edition of Blackstone's Commentaries.

Such are some of the nuggets from the cryptologic trove amassed by David Kahn, past president of the American Cryptogram Association. His huge volume shows how the science of cryptology has influenced the course of nations and the fate of rulers and rogues, soldiers and statesmen, poets and pirates. The speed with which the Navy switched codes following the Pueblo crisis is only the latest public indication of cryptology's continuing importance.

Since the purpose of codes is secrecy, there probably cannot ever be a "definitive" book on the subject. Still, Kahn, an ex-reporter, has produced an astonishingly thorough study. He deals not only with the codebreakers but also with the codemakers and nearly everyone of any consequence who has ever used codes—or seriously thought about them. As he guides the reader through the difficulties of steganography (invisible ink, microdots), monalphabetics (simple, one-alphabet systems, such as the one described in the box, next page), and polyalphabetics (many alphabets used in the same cipher message), Kahn keeps his subject lively and even dramatic. He describes, for example, how cryptology helped get the U.S. into one world war— and helped shorten another.

The Purple Code. The World War I episode concerns the notorious telegram sent by the German Foreign Minister, Arthur Zimmermann, to his envoy in Mexico; in code it stated Germany's intention of opening unlimited submarine warfare against the U.S. and offered various bribes to get Mexico's support. Decoded by British cryptanalysts, the telegram provided President Wilson with telling evidence to support the U.S. declaration of war on Germany.

As for World War II, almost everyone knows that the U.S. broke Japan's highest level "Purple Code" before Pearl Harbor. But precious few realize what the breakthrough entailed. The code was based on a rotor system—mazes of wires connecting two or more alphabetic rotors that change ciphers at every punch of a keyboard. The use of two rotors permits 676 different cipher positions; five rotors provide 11,881,376 codes.

The solution of the Purple Code fell to the U.S. Army Signal Corps' chief cryptologist, William Friedman, whom Kahn calls the world's greatest code expert. Friedman and his superb team had a head start. For example, they had already solved lower-level codes, and were familiar with common Japanese forms, such as "I have the honor to inform Your Excellency." As Kahn says, "these constituted virtual cribs."