Some security experts disagreed. While the disclosure does not by itself threaten the security of voice data, one analyst said companies and governmental organizations should take the same steps to ensure the security of their wireless conversations as they do with antivirus software for computer files.

“Organizations must now take this threat seriously and assume that within six months their organizations will be at risk unless they have adequate measures in place to secure their mobile phone calls,” said Stan Schatt, a vice president for health care and security at the technology market researcher ABI Research in New York.

Mr. Nohl, who has a doctorate in computer engineering from the University of Virginia, is a widely consulted encryption expert who waged a similar campaign this year that prodded the DECT Forum, a standards group based in Bern, to upgrade the security algorithm for 800 million cordless home phones.

Mr. Nohl has now set his sights on G.S.M., whose second-generation digital technology is still the most widely used wireless-communications standard in the world. About 3.5 billion of the world’s 4.3 billion wireless connections use G.S.M.; it is used by about 299 million consumers in North America.

In August, at a hackers’ forum in Amsterdam, Mr. Nohl challenged other computer hackers to help him crack the G.S.M. code. He said about 24 people, some members of the Chaos Computer Club, which is based in Berlin, worked independently to generate the necessary volume of random combinations until they reproduced the G.S.M. algorithm’s code book — a vast log of binary codes that could theoretically be used to decipher G.S.M. phone calls.

During an interview, Mr. Nohl said he took precautions to remain within legal boundaries, emphasizing that his efforts to crack the G.S.M. algorithm were purely academic, kept within the public domain, and that the information was not used to decipher a digital call.

“We are not recommending people use this information to break the law,” Mr. Nohl said. “What we are doing is trying to goad the world’s wireless operators to use better security.”

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Mr. Nohl said the algorithm’s code book was available on the Internet through services like BitTorrent, which some people use to download vast quantities of data like films and music. He declined to provide a Web link to the code book, for fear of the legal implications, but said its location had spread by word of mouth.

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The G.S.M. algorithm, technically known as the A5/1 privacy algorithm, is a binary code — which is made exclusively of 0’s and 1’s — that has kept digital phone conversations private since the G.S.M. standard was adopted in 1988.

But the A5/1 algorithm is a 64-bit binary code, the modern standard at the time it was developed, but simpler than the 128-bit codes used today to encrypt calls on third-generation networks. The new codes have twice as many 0’s and 1’s.

In 2007, the G.S.M. Association developed a 128-bit successor to the A5/1, called the A5/3 encryption algorithm, but most network operators have not yet invested to make the security upgrade.

The encryption key itself does not enable surveillance of mobile calls, which must still be overheard and identified from the digital stream of thousands of calls transmitted through a single cellphone station.

The undertaking is complex because a digital call typically hops among up to 60 different broadcast frequencies during a single conversation, as the mobile network operator maximizes the use of its available bandwidth.

In a statement, the G.S.M. Association said efforts to crack the algorithm were more complex than critics have asserted, and that operators, by simply modifying the existing algorithm, could thwart any unintended surveillance.

The group said that hackers intent on illegal eavesdropping would need a radio receiver system and signal processing software to process raw radio data, much of which is copyrighted.

But Mr. Nohl, during a presentation Sunday to attendees at the Berlin conference, said the hardware and software needed for digital surveillance were available free as an open-source product in which the coding is available for individuals to tailor to their needs.

Simon Bransfield-Garth, the chief executive of Cellcrypt, a company based in London that sells software, said Mr. Nohl’s efforts could put sophisticated mobile interception technology — limited to governments and intelligence agencies — within the reach of “any reasonable well-funded criminal organization.”

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“This will reduce the time to break a G.S.M call from weeks to hours,” Mr. Bransfield-Garth said during an interview. “We expect as this further develops it will be reduced to minutes.”