How, in a time of deep cynicism, does a friend of the president become attorney general and satisfy the public that integrity governs the administration of justice?

That question finds no good answer. But there are better ways to deal with the problem than having semi-public slanging matches about Frank Sinatra.

The friend in question, of course, is William French Smith, the prominent Los Angeles lawyer who is Ronald Reagan's choice to be attorney general. Smith served Reagan as his lawyer for years, and handled most of his financial dealings. He was a leading adviser during the presidential campaign and when Reagan served as governor of California. In the nature of things, Smith is partial to Reagan.

Otherwise, his credentials are in good order. Many people feel, as I do after two long sessions with him during the past few months, that he is careful, responsive, open-minded, with a penetrating intellent and a clear sense of priorities. Colleagues and clients commend his professional expertise. Many assert that among persons close to Reagan, Smith has the strongest feel for quality. Other volunteer the view that his integrity is beyond question.

But, naturaly, that's not nearly good enough. The spirit of the times features skepticism and dobut and successful persons, especially in the government. Many of us in the press and television confuse suspicion with insight. Trivial gossip tends to take precedence over serious thought.

Particularly when it comes to the office of the attorney general. By its very nature, the Justice Department deals with the powers of darkness. Decesion to prosecute or not are tricky and easy to criticize. The recent record, moreover, supports a certain wariness.

Two of the past seven attorneys general (John Mitchell and Richard Kleindienst) were associated with the massive fix of Watergate. A third (Elliot Richardson) was fired for standing up to the White House. A fourth (Griffin Bell) acknowledged on leaving the Justice Department that if it hadn't been for the looks of the thing he would have compromised on a major antitrust case. A fifth (Benjamin Civiletti) didn't come clean with White House officials about a conversation he had with the president concerning the case of Billy Carter.

So the beginning of wisdom for an attorney general lies in the recognition that he is guilty until proven innocent. Character assassination goes with the job, as does the questioning of integrity and the impugning of motives. Nor is it only those of us in the press who itch to find fault. For keener are the self-promoting professional prosecutors in the department who tend to regard every president as a crook and every attorney general as his partner in crime.

Even before taking office, Smith had a taste of the bitter reality. A small fact -- that he attended a birthday party for Frank Sinatra -- was worked up into a suspicion of peddling influence. Smith denounced the stories as "scurrilous." But that only fanned the flames.

What all this means is that the attorney general has to go out of his way every day to demonstrate integrity. It is important to stay clear -- even in casual social encounters -- of persons of doubtful reputations. It is a good idea to avoid participation -- and anounce it publicly -- in cases where there is even the tenuous possibility of a conflict of interest.

Even more essential is the choice of associates. The attorney general needs to have as his main subordinates persons of different political background, high professional expertise and spotless integrity. They should make, on their own, decisions in cases that touch the president and his familiars. It would be particularly helpful if Smith could retain in high posts at least some of those who served in the Carter administration.

Having to advertise one's honesty in that way is awkward, even demeaning. The public business gets done less efficiently. But the central point is that the office of the attorney general, and the Justice Department itself, are surrounded by a nimbus of corrosive skepticism. Dispelling suspicion and building an atmosphere of trust tops the agenda at the Justice Department. Only after evident efforts to that end have been made can truth began to vindicate itself against slander.