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.”

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.

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.