Karsten Nohl and Sylvain Munaut demonstrated their eavesdropping toolkit at the Chaos Computer Club Congress (CCC) in Berlin.
The work builds on earlier research that has found holes in many parts of the most widely used mobile technology.
The pair spent a year putting together the parts of the eavesdropping toolkit.
"Now there's a path from your telephone number to me finding you and listening to your calls," Mr Nohl told BBC News. "The whole way."
He said many of the pieces in the eavesdropping toolkit already existed thanks to work by other security researchers but there was one part the pair had to create themselves.
"The one piece that completed the chain was the ability to record data off the air," he said.
In a demonstration at the CCC, the pair took attendees through all the steps that led from locating a particular phone to seizing its unique ID, then leap-frogging from that to getting hold of data swapped between a handset and a base station as calls are made and texts sent.
Key to grabbing the data from the air were cheap Motorola phones which can have their onboard software swapped for an open source alternative.
"We used the cheap Motorola telephones because a description of their firmware leaked to the internet," he said.
This led to the creation of open source alternative firmware that, he said, has its "filters" removed so it could see all the data being broadcast by a base station.
The eavesdropping work builds on earlier work to list GSM encryption keys This allows attackers to home in on the data they need to eavesdrop, said Mr Nohl. The encryption system that scrambles this data can be defeated using a huge list of encryption keys, called a rainbow table, that Mr Nohl generated in a separate research project.
"Any GSM call is fair game," he said.
GSM is the name of the technology used on the vast majority of mobile phone networks around the world. The GSMA, which represents operators and phone makers, estimates that there are more than five billion GSM mobiles in use around the world.
The GSMA has not responded to requests for comment about the research.
Playing around Simeon Coney, a spokesman for mobile security firm Adaptive Mobile, said the work looked fairly thorough.
"Especially interesting is how the attack is aimed at a specific target phone, which could lead to malicious interest of high value targets," he added.
"This isn't an attack that is today readily repeatable yet by the anyone unfamiliar with the underlying technology," he said. "However, it does illustrate the manners in which the mobile phone system could be compromised in a focussed attack in less protected markets."
Mr Nohl said that before now commercial equipment that could spy on calls cost upwards of £35,000. The kit demonstrated at the Berlin event cost far less than that, he said. For instance, the Motorola phones used to grab data cost only 10 euros (£9) each.
Despite showing off the entire eavesdropping kit, there were no plans to release all of it for others to use, said Mr Nohl.
However, recreating the missing parts would not be difficult for a tech savvy amateur, he added.
"I expect people to do it for the fun of doing it."
Mr Nohl said the motivation for carrying out the research was to create awareness around the problem and perhaps prompt operators to improve security.
A few simple steps could make it much harder for eavesdroppers, he said.
"Raising their awareness is the most likely outcome, but the technical changes would be better."
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