The pizza delivery giant told affected French and Belgian clients Friday that it had been hacked into and that "some passwords" had been taken, giving those behind the attack access to data such as phone numbers and addresses, though not to bank details.
That same day, a hacking group called Rex Mundi tweeted on an account that has since been deleted that it had given the US chain until 1800 GMT Monday to pay EUR 30,000 in exchange for not publishing the data.
But a spokesperson for Domino's Pizza told AFP Tuesday the US group had not paid the money, refusing "to yield to blackmail from any form of criminal organisation". It is not yet known whether the hackers have published the data.
According to Gerome Billois, an expert at IT consultants Solucom, Rex Mundi is not an unknown group of hackers.
"Already in 2012, they attacked and tried to extort (French cable operator) Numericable, as well as a bank in (the south-eastern city of) Nice whose customer data they then published on the Internet," he said.
"But it's quite rare that these cases go public."
Loic Guezo, a strategic director at IT security company Trend Micro, said it was the first time to his knowledge that hackers had gone public with their ransom demands, adding that this new development was "terrifying".
"It's the law of the jungle, we're in the Wild West and consumers are publicly taken hostage," he said.
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