Boston ? A hacker or hackers stole data from at least 45.7 million credit and debit cards of shoppers at off-price retailers including T.J. Maxx and Marshalls in a case believed to be the largest such breach of consumer information.

For the first time since disclosing the theft more than two months ago, the parent company of nearly 2,500 discount stores put a number on how much card data was compromised – and it’s a number TJX Cos. acknowledges could go still higher.

Experts say TJX’s disclosures in a regulatory filing late Wednesday revealed security holes that persist at many firms entrusted with consumer data: failure to promptly delete data on customer transactions, and to guard secrets about how such data is protected through encryption.

“It’s not clear when information was deleted, it’s not clear who had access to what and it’s not clear whether the data kept in all these files was encrypted, so it’s very hard to know how big this was,” said Deepak Taneja, chief executive officer of Aveksa, a Waltham, Mass.-based firm that advises companies on information security.

The case has led banks to reissue cards to customers as a precaution against further fraud beyond cases detected as far away as Sweden and Hong Kong, according to the Massachusetts Bankers Association, which is tracking fraud reports linked to Framingham, Mass.-based TJX, parent company of stores across North America and the United Kingdom.

The only arrests believed tied to the case involve a gift card scam in which 10 people are suspected of buying data from the TJX hackers to purchase Wal-Mart gift cards in northern Florida.

Information from 45.7 million cards was stolen from transactions beginning in January 2003 and ending Nov. 23 of that year, TJX said in the filing with the Securities and Exchange Commission after business hours Wednesday. TJX did not estimate the number of cards from which information was stolen for transactions occurring from Nov. 24, 2003, to June 28, 2004.

TJX said about three-quarters of the 45.7 million cards had expired at the time of the theft or the stolen information didn’t include security code data from the cards’ magnetic stripes. Starting in September 2003, TJX began masking the codes by storing them in computers as asterisks rather than numbers, the company said.

The filing also said another 455,000 customers who returned merchandise without receipts had their data stolen, including driver’s license numbers.