Apple responded in court Thursday to an order it hack an iPhone linked to the San Bernardino, California, terrorist attack, calling the FBI's demand unconstitutional, illegal and dangerous.

"No court has ever authorized what the government now seeks, no law supports such unlimited and sweeping use of the judicial process, and the constitution forbids it," lawyers for Apple wrote in a 36-page motion filed in federal district court in California.

A federal judge last week ordered Apple to help the FBI crack the encryption on the iPhone used by Syed Rizwan Farook, who along with his wife killed 14 people in the December 2 shooting spree.

Apple chief executive Tim Cook refused the order in an open letter published on Apple's website, setting off a public debate about the competing demands of privacy and security.

Cook said forcing Apple to write software to override protections that erase data after too many failed password attempts would effectively create a "back door" to the iPhone.

He said that once created, such an opening could be exploited by anyone from criminal organizations to repressive regimes to the US government.

US authorities have said they are only asking Apple to hack the single iPhone, and that Apple could destroy the software once it has been used.

"The government says 'just this once' and 'just this phone.' But the government knows these statements are not true," Apple said.

Earlier this week a judge in New York unsealed documents detailing a dozen more pending cases in which authorities sought to compel Apple to hack encryption on other devices.

New York prosecutor Cyrus Vance Jr told a television interviewer he wanted the power to access data on encrypted devices in every criminal case, according to the motion.

"This is not a case about one isolated iPhone," Apple's motion read. "Rather, this case is about the Department of Justice and the FBI seeking through the courts a dangerous power that Congress and the American people have withheld."

It pointed that amid a recent public debate over laws defining tech companies' obligations to law enforcement, US legislators had stopped short of requiring software developers to equip data security systems with back doors for government access.

Technology company chiefs including Facebook, Google and WhatsApp have declared their support for Apple in the case, as have fugitive cyberspying whistleblower Edward Snowden and prominent civil liberties groups.

A recent opinion poll showed 51 per cent of Americans sided with the FBI.

In the motion, Apple argued that forcing it to undermine its own security product violated its constitutional rights and those of its users.

Apple said that compelling it to "create a crippled and insecure product" would only send criminals in search of other encryption methods, while leaving the public exposed to data theft and spying.

In an affidavit attached to the motion, Apple user privacy manager Erik Neuenschwander explained the steps involved in hacking the iPhone in the way the FBI has demanded.

Neuenschwander said it would take a team of Apple engineers weeks to write a new version of the software, incorporating elements that Apple has never included in its operating systems such as the ability to enter passwords digitally rather than manually.

He said safely deploying the software would require the installation of a separate secure, isolated physical facility at Apple to keep it from being copied or leaked.

But Neuenschwander said the government's suggestion that once deployed, the software could be destroyed, was "fundamentally flawed."

"The virtual world is not like the physical world. When you destroy something in the physical world, the effort required to recreate it is roughly equivalent to the effort required to create it in the first place," he said.

"When you create something in the virtual world, the process of creating an exact and perfect copy is as easy as a computer key stroke."

Even if the code were somehow completely erased, he said, the process to create it would persist in engineers' knowledge, and so the government-ordered software "would not be truly destroyed."

A hearing in the case is scheduled for March 22.

Related stories

Apple, FBI headed for showdown over San Bernardino encryption

Google, WhatsApp back Apple in encryption fight with FBI

FBI opens iPhone without Apple's help

Apple and FBI to face off in court

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