By Michael Nienaber and Michael Roddy

BERLIN (Reuters) - The director of a new documentary outlining U.S. plans for an extensive cyber attack on Iran said on Wednesday he was angry and appalled by the rapidly growing trend towards secrecy in the U.S. government.

Veteran documentary maker Alex Gibney was speaking to reporters in Berlin, where his film "Zero Days" is being shown in competition for the Berlin International Film Festival's top Golden Bear prize.

The documentary says how the U.S.'s National Security Agency (NSA) developed a cyberwar program dubbed "Nitro Zeus" that it hoped would bring Iran to its knees in the event of hostilities.

"I am angry about the incredible amount of secrecy in the United States and how it has become a kind of obsession that is damaging our democracy," Gibney said at a post-screening news conference.

"I think, frankly, that the trend and the momentum towards greater and greater secrecy in the U.S. administration is appalling.

The documentary focuses on Stuxnet, a computer worm developed by the United States and Israel - but never acknowledged by either government - in order to attack Iran's nuclear program and sabotage centrifuges that were enriching uranium.

Through accounts of whistleblowers, analysts, journalists and secret service officials, the documentary shows how Stuxnet was the first known attack in which computer malware left the realm of cyberspace and caused physical destruction.

The film hints, based on accounts of several NSA insiders, that Stuxnet was just the tip of the iceberg.

"I mean you've been focusing on Stuxnet but that was just part of a much larger operation... Nitro Zeus, NZ," an actress says in the film, speaking for several NSA employees who were interviewed but whose identity was kept secret for source protection.

According to these accounts, the NSA spent "hundreds of millions, maybe billions" on Nitro Zeus to be prepared for the eventuality that Israel decided to attack Iran and the United States would be drawn into the conflict.

Details of the Nitro Zeus program were revealed in the New York Times on Wednesday.

The composite NSA source says that despite the deal agreed in July with Iran by the United States and its negotiating partners to curtail Iran's nuclear program, the Nitro Zeus capabilities remain "implanted" in Iran's servers and computers.

"We were everywhere inside Iran, still are," the actress speaking for the NSA sources says.

"I'm not going to tell you the operational capabilities of what we can do moving forward, or where, but the science fiction cyberwar scenario is here, that's Nitro Zeus."

The film suggests that Israel moved independently from its U.S. partners and changed the code of the initial Stuxnet virus in such a way that it spread all over the world with unforeseeable consequence, including allowing other governments to copy it.

Before its discovery in 2010, Stuxnet took advantage of previously unknown security holes in software from Microsoft Corp and Siemens AG to penetrate Iran's facilities without triggering security programs.

Gibney contends that Stuxnet opened forever the Pandora's Box of digital warfare, and that it had been used as an instrument of warfare against a country with which the United States was not at war.

He also says the United States could well be more vulnerable than other countries, taking into account that its economy and companies are the most Internet-connected in the world.

"And as we can see from this film and this subject, it's preventing a very important discussion about offensive cyber weapons which I think threaten us in a profound and existential way."

The film derives its title from the term used for previously unknown flaws in computer software that hackers and spy agencies can exploit to attack networks in order to damage infrastructure such as hospitals, transportation systems or power plants.

The U.S. distribution rights for "Zero Days" are owned by Magnolia Pictures which is planning to release it in theaters in late summer. Showtime owns the paid television rights.

(Reporting and writing by Michael Roddy and Michael Nienaber; Editing by Raissa Kasolowsky)