War by Computer Virus : TRAPDOOR by Bernard J. O’Keefe (Houghton Mifflin: $17.95; 324 pp.)

You’ve heard the one about the guy who wired together all the computers in the country. His first question to this monster computer: “Is there a god?” Its answer: “There is now.”

A god-computer of that sort may be the most interesting character in Bernard J. O’Keefe’s “Trapdoor,” a first novel whose author calls it, in an epilogue, a “parable to point out the complexity of modern technology and to demonstrate how one error, one misjudgment, or one act of sabotage could lead to actions that would annihilate civilization.”

The trapdoor of the title is not stage business but mathematics. If I want to bar your path to my computer, I need only make access depend on your coming up with an incalculably large number. Of course, no number is literally incalculable, but an intruder would need more than a quadrillion years on the fastest computer in existence, O’Keefe says, to analyze the product of two 60-digit prime numbers (numbers not divisible by any number but themselves and the number 1). Blocked by such Brobdingnagian arithmetic, the intruder will drop through a figurative trapdoor, and your computer will be secure.

But wait a minute. Who made the computer? What if she switches one of the 60-digit prime numbers on you? Now you can’t get in either!

That is what happens in this novel. A Lebanese computer whiz from Stanford who happens also to be a PLO sympathizer has had a role in the construction of “Permissive Action Links,” release control devices on U.S. nuclear weapons that entail the use of two large primes. One prime remains in the custody of the President. The other is in the bombs themselves. Unless both are known, the bombs cannot be exploded. The United States, O’Keefe explains, needs such devices more than the Soviet Union does because so many of our weapons are on foreign soil. We have greater reason to fear the theft of a warhead than the Kremlin does, and we want to be able to render a stolen warhead useless.

What the beautiful saboteuse does is turn this very safeguard against us. By satellite transmission, the Pentagon changes the bomb-release number-pairs every three months. At one of these change points, the virus that June Malik has implanted in the Pentagon computer rejects the Pentagon’s number and transmits her own number instead. Only she knows this number, and she has delayed the action of her virus long enough for her to flee to Lebanon. The result: America no longer knows the code necessary to launch its own weapons. The nation is defenseless.

Here is where the computer god becomes a major actor. (Deus ex machina was never like this!) A quadrillion years on the fastest computer in existence is only a trillion years on one thousand of the fastest computers in existence, right? A trillion years is only a billion years on another thousand of the fastest computers in existence, and so forth. How many computers can be mobilized for the “parallel processing” that alone can prevent America from being rendered, at a stroke, helpless before its great enemy?

All the great university computers are mobilized, all the insurance computers, all the Wall Street computers. “Not a chance,” I hear a hacker cry: “The number is still too big.” Perhaps, but by a twist in the plot, the saboteuse, who has had a change of heart, manages to reveal--from the camp in Southern Lebanon where she is being held hostage--two of the three-digit primes she used to build up her giant prime. Later, on closed-circuit television from the camp, she will mime three zeros: one with her mouth, two with her thumbs and index fingers. The American code-crackers catch on: All three-digit primes have zero as the middle digit; she has just told them that she used only three-digit primes. With this clue, the hackers begin to close in.

Her former co-conspirators, now her captors, are so confident that they have disarmed the entire American nuclear arsenal that they have brought a stolen American bomb to their camp in Lebanon. The President can see it on the television screen. They dare him to set the bomb off. If it goes off, they die. If it fails to go off, the Soviet Union will demand the immediate surrender of American sovereignty. Everything depends on whether the hackers of the country, working as one giant hacking team with all the hardware in the nation at their disposal, can get the number in time.

Can it all happen as O’Keefe has written it? Not quite, as he points out in his epilogue. “Permissive Action Links” involving virtually incalculable numbers are not in place on all American warheads. Those without this safeguard are more than enough to provide a deterrent even if the others are disabled.

But this is cold comfort. O’Keefe, who has previously written to chilling effect on nuclear terrorism (see his “Nuclear Hostages” (Houghton Mifflin)), believes that nuclear attack by either the United States or the Soviet Union is unlikely. Far more likely is the theft of a nuclear weapon--one of those whose availability, as just noted, makes the “Trapdoor” scenario for now only a scenario--and its detonation on, say, a pleasure boat on the Potomac River.

Our capital would be gone, were that to happen, but who did it? Do we strike back at the Soviet Union, unleashing the same horror on many other cities in the United States? What if the Soviet Union didn’t do it? What if it was a suicide squad from the Ayatollah Khomeini, determined to provoke the Great Satans into destroying each other? But then again, how can we know? What if it was the Soviet Union after all, anticipating just this kind of self-deterrence on the part of a nation literally wondering what hit it.

O’Keefe, though a “Star Wars” skeptic, is no dove. He worked with Enrico Fermi and J. Robert Oppenheimer on the Manhattan Project, which produced the Hiroshima and Nagasaki bombs. If a third mission had been ordered, O’Keefe was scheduled to fly it. EG&G;, the Fortune 500 company he heads, has, according to his publisher, “conducted all nuclear weapons tests for the U.S. government for the last forty years” and “is the operating contractor for the Kennedy Space Center.” The man knows whereof he warns.

O’Keefe is also, be it said, more engineer than novelist. His novel is overcrowded with fictionalized incidents from his long and colorful career, including some of scanty relevance to his central parable. He has given his saboteuse, ultimately his heroine, a pair of traffic-stopping breasts, which distract the reader no less than they do the male engineers in the novel every time they bob up. Further, though O’Keefe is clear enough in his essential technical explanations, the mathematics and nuclear strategy involved in his book are inherently so difficult and so unfamiliar that repeated exposition (which could easily have been fed into the narrative as word about the sabotage spread through Washington) would have served his parabolic purposes better than supernumerary shootouts, chase scenes and opera bouffe voluptuosity.

A parable ought to sacrifice everything to economy, and here O’Keefe seems to have faltered. Still, this criticism registered, there remains a lean and gripping parable hiding inside his only slightly overweight thriller. For all its novelistic faults, I can’t imagine a timelier read or a better Christmas gift for anyone serious about computers or math.

And that, of course, is just the beginning. If the computers that control our nuclear weapons can be disabled, what about the computers that control our nuclear power plants? What about the computers that control our vote-counting and our stock transactions? O’Keefe alludes to these and other computer-related vulnerabilities in his epilogue. Chernobyl was a warning. The near “meltdown” of the Stock Market in October, 1987, was a warning. The Challenger disaster, KAL 007 and the Iranian airliner shootdown were all warnings. How many warnings do we need? O’Keefe asks.

And that’s what we should be asking too.