ALBANY -- The federal blitz on legislative corruption that has snared dozens of New York lawmakers hinges largely on a complex law that is being applied to the political world, where the line between routine politics and corrupt acts can become blurred.

The federal law is known as "theft of honest services," which until recently was so broad that the U.S. Supreme Court struck down part of it. The ruling created a major hurdle for prosecutors. To get a conviction on the charge they now also must prove bribery, extortion and other crimes were committed, authorities said. Prosecutions can drag on for years.

Former Assembly Speaker Sheldon Silver was indicted Thursday for allegedly collecting $3.8 million in kickbacks and bribes. Silver, who remains in the Assembly, has pleaded not guilty, and a trial is still months away.

The federal case against former Senate Majority Leader Joseph Bruno began as early as 2007 and didn't conclude until his second trial ended in acquittal last year.

State Sen. John Sampson (D-Brooklyn) faces a corruption trial this year following his May 2013 arrest. Charges include obstruction of justice and witness tampering.

Former State Sen. Malcolm Smith (D-Queens) was convicted this month of bribery and extortion for a 2013 scheme after his first trial ended in a mistrial.

One former legislative staffer who saw the federal scrutiny firsthand in one corruption case said federal agents "looked at everything -- every memo and piece of paper that passed through the office."

"They literally went through anything that he ever did on a personal level and legislatively," recalled the former staffer.

Hard proof of bribery or other crime wasn't required of federal corruption cases under the honest services law until 2010.

That's when the U.S. Supreme Court struck down part of the honest services law as being overly broad, making a violation of it a crime on its own. The decision was prompted by the case of Jeffrey Skilling, the former CEO of Enron, who was accused in part of misrepresenting the earnings of the energy company, which eventually collapsed.

"Before the Skilling decision," said Albert W. Alschuler, professor emeritus at the University of Chicago Law School, "it was a matter of finding all the dirt on a politician you could and throwing it into a cauldron and saying, 'Ah ha! He deprived the public of his honest services.'"

But the Skilling decision ruled that specific bribes, kickbacks, extortion or other actions need to be proven to make the honest services law stick.

That's how the 2009 conviction of Bruno, the former state Senate majority leader, on a theft of honest services charge was overturned. In a second trial, under the revised statute requiring bribery to be proven, Bruno was acquitted.

Not only must prosecutors prove, for example, that a campaign contributor received some benefit from the politician, they must prove that was the intent from the beginning.

"It's not enough to say, 'This guy is one of my supporters and he's giving me cash and I'm going to do something from him,' " said Randall D. Eliason, a former federal prosecutor who once headed a public corruption unit and now lectures at George Washington University Law School. "That happens all the time."

Now, however, "it truly applies only to a bribe or kickback or so-called quid pro quo," said Robert Weisberg, a Stanford Law School professor and co-director of the Stanford Criminal Justice Center. "If you have very, very complex webs of alleged corruption with no monies or favors passing around through several parties, it is still possible, but harder to show there is a quid pro quo."

Unlike most criminal cases, public corruption investigations usually have no single victim who can identify a suspect, and few witnesses who aren't implicated in the scheme. As a result, they can go on for a year or more, as in Sampson's and Smith's cases, to nearly a decade, as happened with Bruno.

"They tend to be a lot more complicated and longer than a lot of cases," Alschuler said.

Add to that the nature of the political world, where special bonds are made over favors and alliances built over years behind closed doors, where millions of dollars are donated to campaigns and billions of dollars of taxpayers' money are spent.

"I think politicians definitely communicate in complicated networks," Weisberg said. "They involve indirect communication and -- I won't use the word money laundering in a technical sense -- but let's say they have interesting ways of moving money around," he said, referring to public budgets and discretionary spending.

From the outside, it can look simply like routine politics.

"If I bribe a politician, usually there is just the two of us there and neither of us wants it to come to light," said Eliason, who headed the Public Corruption/Government Fraud section in the District of Columbia from 1999 to 2001.

"The victim is the body politic -- the voters -- and they don't even know what happened," said Eliason. Such cases "are really challenging to prove . . . a lot of times it's sort of nods and winks behind closed doors. You have to trade on inferences and circumstantial evidence and the timing of events."

"One of the best ways and most common ways is to have one of the parties cooperating -- to get flipped," he said.

A co-conspirator who testifies against a public official can provide a narrative a jury needs to understand a complex scheme, but building such a case takes time, legal authorities agreed.

"With U.S. attorneys in these situations," Weisberg said, "if they are going for a big fish, they want a mega case before they announce. They probably have lots of lower-downs singing like canaries."

The complaint against Silver mentions clandestine recordings and an unidentified cooperating "co-conspirator."

At a news conference on the Silver complaint, U.S. Attorney Preet Bharara used charts to illustrate the flow of a $500,000 state grant for research to a physician, Robert N. Taub, an asbestos researcher, who referred patients with legal claims to the law firm Silver worked for, while Silver collected kickbacks for the referrals, according to the complaint. Taub resigned as director of a mesothelioma center at Columbia University after the charges against Silver became public.

The charges accuse Silver of depriving New Yorkers "of their "intangible right to Silver's honest services as an elected legislator and as the speaker."

Silver denies wrongdoing. His supporters say the actions he's accused of aren't illegal, because part-time legislators are allowed to hold outside jobs.

Alschuler said the criminal complaint against Silver doesn't identify specifically how, when or where Silver is accused of setting a clear deal to take official action to bring him millions in kickbacks. However, prosecutors will be expected to release more detail as the case heads to trial, Alschuler said.

"I would say that as for the complaint in the Silver case, a lot of it looks like an old-style, pre-Skilling honest services case," Alschuler said. "Even though it talks about bribery, it's very vague on just what the bribe is supposed to be and whether the bribe involves official acts."