Cryptographers have moved closer to their goal of eavesdropping on cellphone conversations after cracking the secret code used to prevent the interception of radio signals as they travel between handsets and mobile operators’ base stations.

The code is designed to prevent the interception of phone calls by forcing mobile phones and base stations to rapidly change radio frequencies over a spectrum of 80 channels. Without knowing the precise sequence, would-be eavesdroppers can assemble only tiny fragments of a conversation.

At a hacker conference in Berlin that runs through Wednesday, the cryptographers said they’ve cracked the algorithm that determines the random channel hopping and have devised a practical means to capture entire calls using equipment that costs about $4,000. At the heart of the crack is open-source software for computer-controlled radios that makes the frequency changes at precisely the same time, and in the same order, that the cellphone and base station do.

“We now know this is possible,” said Karsten Nohl, a 28-year-old cryptographer and one of the members of an open-source project out to prove that GSM, the technical standard used by about 80 percent of the mobile market, can’t be counted on to keep calls private. The attack “is practical, and there are real vulnerabilities that people are exploiting.”

A spokeswoman for the GSM Association, which represents 800 operators in 219 countries, said officials hadn’t yet seen the research.

“GSM networks use encryption technology to make it difficult for criminals to intercept and eavesdrop on calls,” she wrote in an email. “Reports of an imminent GSM eavesdropping capability are common.”

The channel-hopping crack comes as the collective is completing the compilation of a rainbow table that allows them to decrypt calls as they happen. The table works because GSM encryption uses A5/1, a decades-old algorithm with known weaknesses. The table – a 2-terabyte list of known results that allows cryptographers to deduce the unique key that encrypts a given conversation – was developed by volunteers around the globe using giant clusters of computers and gaming consoles.

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