Mozilla is throwing more muscle behind its fight against two measures that empower the federal government to take down Web sites that host pirated material even if the sites were unaware of the piracy.

Taking aim at the Senate’s Protect IP bill (PIPA), Mozilla is organizing a phone campaign encouraging people to persuade their lawmakers to revise the measure’s language.

Mozilla was part of a viral campaign earlier this month, called American Censorship Day, that organizers said sparked a million e-mails and 87,000 phone calls to Congress to protest the wording of the House’s Stop Online Piracy bill (SOPA). Now Mozilla is trying to tap into the same viral energy to fight the Senate proposal.

The nonprofit organization, which publishes the Firefox browser, is asking citizens to call Senate Majority Leader Harry Reid (D-Nev.) next Tuesday to protest the bill.

Mozilla says the anti-piracy and protection acts would grant the federal government to much power to take down sites such as YouTube or Tumblr for unknowingly hosting pirated material. But the company also says that the measures could threaten cybersecurity.

“Just like SOPA, this bill will create new cybersecurity risks and jeopardize the basic structure of the internet as we know it,” Mozilla wrote in a statement on its Web site.

Other critics say that the method to stop traffic to rogue sites proposed in the Senate bill could put bad information into the Web’s domain name structure and compromise cybersecurity.

Rep. Zoe Lofgren (D-Calif.), a House Judiciary Committee member, has expressed strong reservations to the House bill as written, citing concerns over free speech and censorship, among other issues. Earlier this month, she released a letter from Sandia National Laboratories director Leonard Napolitano, who said that the DNS filtering in the SOPA and PIPA proposals are “unlikely to be effective” and would hurt U.S. and global cybersecurity. Sandia National Laboratories, part of the U.S. Department of Energy, is operated by a division of Lockheed Martin called the Sandia Corp.

Napolitano said that provisions in the bills could hamper an initiative known as DNSSEC that aims to make it harder for bad actors to redirect traffic without a Web user’s knowledge by requiring more validation. The filtering proposed in the two bills — which would direct traffic away from any site with pirated content — would make it difficult for U.S. sites to comply with this protocol, Napolitano said.

Supporters of the measures, including the Motion Picture Association of America, have argued that DNS filtering does not pose a security risk and that DNSSEC can be adapted to fit the bill’s provisions.

PIPA is expected to go to a Senate vote later in the year or early 2012, a Senate staffer said. The bill passed the Senate Judiciary Committee, but Sen. Ron Wyden (D-Ore.) placed a hold on it and has vowed to filibuster the bill. Wyden expressed concerns that the measure as written would obstruct “a free and open Internet” and lead to abuses.

SOPA, which has 25 co-sponsors from both parties, is expected to go to markup around Dec. 15 but there is no firm schedule, according to a House Judiciary Committee staffer.

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SOPA goes for House debate Dec. 15