One of the wildest stories of World War II is hidden behind a curious and disappointing new exhibit in the Smithsonian's National Museum of American History.

The story, only recently declassified, is of the "Magic" and "Ultra" teams who cracked the Axis codes. Their work made it possible for the crippled American fleet to turn the tide in the Pacific War at Midway, and for Churchill often to see Hitler's top-secret messages before der Fuhrer did.

The cryptologists didn't win the war, but they shortened it by years and saved countless lives. The tale is full of spies and suspense, blood and boldness, esoteric science and eccentric scientists, and moments when the fates of nations were shaped by exhausted or half-mad men and women hunched over weird machines.

But you wouldn't guess any of the above from the Smithsonian's new cipher exhibit. It manages to be dull -- and cryptic -- even though it includes what is said to be the first public display of German and Japanese "Enigma" encoders and a rare photo of "the Bombe," a British machine that swallowed Enigma's baffling jumbles of letters and spit out enemy plots and plans in plaintext.

A museum is expected to be informative and accurate. This exhibit, dealing with a subject of profound importance in modern history, is mystifying and misleading. It does not tell us what we need to know, and some of what it does say is wrong.

Those who already know the story -- or the parts of it that have been told -- will be glad at last to be able to see some of the hardware. But other museumgoers who ferret out the exhibit, tucked away behind dreary ranks of early computers, will come away all unaware of the blood, toil, tears and sweat involved. The display tells virtually nothing of how and by whom he work was done or its effect on the war; it is about as gripping as the history of the typewriter.

The Bombe, ticking away in a shabby hut at Bletchley Park outside London, was so vital that many lives were sacrificed to keep the Axis unaware their codes had been broken (but not, whatever you may have read, the lives of the citizens of Coventry).

The security lid stayed on for 30 years after V-J Day, so that all histories of the war have been skewed by official lies and omissions. Historians have begun to reexamine every campaign and leading commander in light of the influence of the intercepts.

Meanwhile many of the quiet heroes of the code war, some broken in body and spirit, have gone to their graves with little more recognition than a handshake and a whispered "Well done." The Smithsonian exhibit names none of them.

Alfred Dilwyn Knox, the early scientific leader of the Ultra team, "was the prototype of the absent-minded intellectual," said David Kahn, author of The Codebreakers . "Day after day he would try to leave his office through the closet." And day after day, as he lay dying from throat cancer, "Dilly" Knox continued to slave away on the codes, coming up with a breakthrough that saved perhaps six precious months.

No less eccentric, but even more brilliant, was Alan Turing, who chained his tea mug to a radiator and buried the family treasure in a woods where he never could find it again. An overstrained genius equally enraptured by far-our math and fairy tales, Turing killed himself by biting a poisoned apple.

The excruciating effort that led to so many breakdowns among those who broke down the enemy ciphers can be appreciated when one considers that the relays and cogs of an Enigma machine could spin out as many as $1,000,000,000,000,000,000,000,000, different codes. American William Friedman, working almost alone on the Japanese version, broke it with pencil and paper. It also broke him; he spent 3 1/2 months in a psychiatric ward.

Friedman, thought by many to be the greatest cryptologist of all time, also developed the "Sigaba" machine that kept U.S. signals secure throughout the war, but is given no credit in the exhibit. And the U.S. Army M209 cipher machine shown next to it was invented in Sweden, but by not saying so the Smithsonian implies it also is one of ours.

It is only since lilacs last in dooryard bloomed that the National Security Agency declassified the devices in the exhibit, even though computers have taken over big-league cryptology since 1945. Enigma and the Bombe (which was not a computer but an adaptation of a theoretical device known as "Turing's Universal Machine") are quaint and primitive by comparison.

"First developed in Poland . . . [the Bombe] was perfected by the English," the exhibit says. Not so, said cryptologist C. A. Deavours in the July 1980 issue of the respected journal Cryptologia : "Gordon Welchman and Alan Turing are the architects of the bombe's design. . . No cryptanalytic debt is owed to the Poles since it is clear that the British bombes were not technological descendants of the Polish bomba . . ."

And the builders were British , not "the English." The Smithsonian should know the difference.

The exhibit text card goes on to say that "The U.S. Army and U.S. Navy then built a number of these machines and used them to break German Enigma messages." Although U.S. and other Allied experts joined the Ultra project, the handling of German codes was first to last a British show. American commanders from Ike on down got their Ultra from British Special Liaison Units.

Only a single example of an intercepted Ultra message is included, an innocuous signal from Grand Admiral Doenitz announcing that he had been named Hitler's successor. Surely NSA, which lent the materials, could have supplied one of the Fuehrer's "hold at all costs" orders, the intercept that led to the aerial assassination of the Japanese admiral who planned Pearl Harbor, or a plea from the beleaguered Rommel in North Africa.

A Smithsonian curator conceded that the exhibit "doesn't have much pizazz, but we jumped at the chance to show these machines for the first time, and didn't have much money or space to work with. We hope to install a much more exciting one soon."

Yet only about a third of the available space has been devoted to Magic and Ultra; by using it all the museum could have at least have given visitors some idea of what the bloody business was all about, and credit to those whose brains helped win the war.

The exhibit's de-emphasis of the Ultra and Magic stories is so striking one is led to wonder whether it has something to do with the fact that the British effort was so much more efficient and effective than ours.

CIPHER MACHINES -- At the National Museum of American History