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The hackers who attacked Target Corp and compromised up to 40 million credit cards and debit cards also managed to steal encrypted personal identification numbers (PINs), according to a senior payments executive familiar with the situation.

One major U.S. bank fears that the thieves would be able to crack the encryption code and make fraudulent withdrawals from consumer bank accounts, said the executive, who spoke on the condition of anonymity because the data breach is still under investigation.

The No. 3 U.S. retailer said last week that hackers stole data from as many as 40 million cards used at Target stores during the first three weeks of the holiday shopping season, making it the second-largest data breach in U.S. retail history.

While bank customers are typically not liable for losses because of fraudulent activity on their credit and debit cards, JPMorgan Chase & Co and Santander Bank said they have lowered limits on how much cash customers can take out of teller machines and spend at stores.

JPMorgan has said it was able to reduce inconvenience by giving customers new debit cards printed quickly at many of its branches, and by keeping branches open for extended hours.

Security experts said it is highly unusual for banks to reduce caps on withdrawals, and the move likely reflects worries that PINs have fallen into criminal hands, even if they are encrypted

The attack could end up costing hundreds of millions of dollars, but it is unclear so far who will bear the expense.