TJX Cos. has increased estimates of its costs dealing with a computer data breach to around $20 million, in addition to $5 million it had previously spent, and said it still cannot predict what its final cost will be.

In a securities filing describing its earnings results for the three months ended April 28, the company said it took an after-tax charge of about $12 million, or 3 cents per share, for costs to “investigate and contain the intrusion, enhance computer security and systems, and communicate with customers, as well as technical, legal, and other fees.”

According to the Boston Globe, the computer breach may become a long-running issue for the company. TJX said it “does not yet have enough information” to predict future costs in areas such as payments it may owe to credit card companies and banks and for various legal costs.

The scale of the TJX breach makes it the largest on record and has led to much criticism from banks that face millions of dollars to replaced compromised accounts. TJX is currently facing many lawsuits, including one by the Massachusetts Bankers Association, over these costs, plus investigations by regulators, including the Federal Trade Commission. Technology analysts project that the total cost to TJX may exceed $1 billion, including reduced revenue from lost business.

Two months ago, retailer TJX, owner and operator of 2,500 stores in the United States, revealed that hackers who accessed the company’s customer information stole data from at least 45.7 million credit and debit cards. According to the Associated Press, at the time, the company said that about three-quarters of those cards had either expired at the time of the theft, or data from their magnetic strips had been hidden — stored as asterisks rather than numbers.

However, TJX says that it still knows little about the full scope of the breach. The hacker or hackers accessed TJX’s encryption software and may have been able to unscramble the information. “There is a lot of information we don’t know, and may never be able to know, which is why this investigation has been so laborious,” TJX spokeswoman Sherry Lang says.

Here is a recap of the investigation to date:
• The company’s computer systems were first breached in July 2005 by a hacker or hackers who accessed information from customer transactions dating to January 2003. TJX was unaware of the breach until about three months ago.
• Information from 45.7 million cards was stolen from transactions beginning in January 2003 and ending Nov. 23 of that year. The company did not provide estimates of the number of cards from which information was stolen for transactions occurring from Nov. 24, 2003 to June 28, 2004.
• The intruder may have had access to the decryption tool for the encryption software utilized by TJX.
• Police charged six people in Florida last week with using credit card numbers that investigators believe were stolen from a TJX database to buy about $1 million in merchandise with gift cards.
The filing gives the first detailed account of the breach initially disclosed TJX, the owner of T.J. Maxx, Marshall’s and other stores in North America and the United Kingdom.