The government is using the Social Security Administration's giant computer system to track down more than 500,000 young men who haven't registered for the draft. Their names eventually will be turned over to the Justice Department for possible criminal prosecution.

The Social Security files contain the names of virtually everyone born from 1960 to 1963, the group required to register for the draft. By matching the list of those who registered against the SSA's larger list of males in that age group, the government hopes to learn who hasn't signed up.

Although few people are aware of it, the use of the Social Security computers to nab non-registrants is actually no secret. It was made permissible by a House rider to the Defense Department authorization bill signed into law last Dec. 1. Moreover, a recorded phone message warns callers to Selective Service here that a computer match using Social Security data will be used to track down those who don't register.

Social Security records, which contain the names of everyone who has ever had a card, are already helping to trace illegal aliens and locate fathers who flee child-support obligations.

Nevertheless, the use of the agency's vast computer files in draft registration cases is strongly opposed by the American Civil Liberties Union, which has brought a federal court suit on one aspect of the practice; an initial ACLU court victory helped spur the congressional action last year.

David Landau, legislative counsel at ACLU's national office here, said that the widespread use of Social Security records for law enforcement has disturbing implications.

"When people give information to the Social Security Administration it is for a single purpose, the benefit system, and it is implicit that it is confidential and is not going to be used for other purposes," he said. "Then the government turns around and uses it for other purposes. That violates the purpose of the 1974 Privacy Act, saying that one U.S. agency can't disclose information in its files to another without the subject's consent."

Landau said that Congress has sometimes authorized use of Social Security data for other purposes, but he said the draft-registration provision is "the broadest exemption so far."

Public officials don't see it that way. Joan Lamb, public affairs director for Selective Service, said men who don't register throw a heavier burden on those who do in case the draft is reinstated, and this is simply a way of locating them.

In any event, in a big computer run last week Social Security said it pulled out the names, addresses and Social Security numbers of about 9 million men aged 18 to 22. In the next week, according to Lamb, SSA will turn the names over to Selective Service, which, in turn, will match them electronically against its own list of people who have already registered.

The names that aren't on that list will be compared with the names of those already serving in the armed forces and the Coast Guard and thus not required to register. What is left, according to Lamb, should be the names of the estimated 527,000 men who have not registered.

These names will be cross-checked with the Internal Revenue Service electronic files to get their latest home addresses. Then letters will be sent asking them to register. If they don't respond, the names will be sent to the Justice Department. So far, only 225 names have been sent to Justice; no one has been prosecuted yet.