“You have to ask yourself, ‘To what end?’ ” he said.

Before he was arrested in November 1995, Mr. Sarraff worked in the cryptology section of Cuba’s Directorate of Intelligence and was an expert on the codes used by Cuban spies in the United States to communicate with Havana. According to members of his family, he had studied journalism at the University of Havana and had the rank of first lieutenant at the intelligence directorate.

It is not clear when Mr. Sarraff, now 51, began working for the C.I.A. Chris Simmons, who was the chief of a Cuban counterintelligence unit for the Defense Intelligence Agency from 1996 to 2004, said that he worked with another man — José Cohen, one of Mr. Sarraff’s childhood friends — to pass encryption information to the C.I.A. that led to the arrest of a number of Cuban agents operating in the United States.

Mr. Simmons said that Cuba’s spy service regularly communicated with its agents in America using encrypted messages sent over shortwave radio. After Mr. Sarraff helped the United States crack the codes, he said, the F.B.I. was able to arrest Cuban spies years after Mr. Sarraff was discovered and put in prison in Cuba.

“When Roly was providing information, he was giving us insights about where there were weaknesses in the Cuban encryption system,” Mr. Simmons said.

Cuban authorities arrested Mr. Sarraff in November 1995 and put him on trial for espionage, revealing state secrets and other acts against state security. According to one senior American official, the Cuban government learned of his plans to defect when he was on assignment in a third country and recalled him to Cuba and put him in jail.

According to members of Mr. Sarraff’s family, he went to work one day in 1995 and never came home. Cuban officials told the family for more than a week that Mr. Sarraff was on a job in the country’s interior and would be back soon.