Google will help advertisers track your spending in physical stores.

SAN FRANCISCO — Google will begin using data from billions of credit and debit card transactions — including card numbers, purchase amounts and time stamps — to solve the advertising juggernaut’s long-standing quest to prove that online ads prompt consumers to make purchases in brickand-mortar stores, the company said on Tuesday.

The advance, which enables Google to tell retailers how many sales they created through their digital ad campaigns, is a step toward what industry insiders have long described as the “holy grail” of digital advertising. If effective, the program could help persuade marketers to choose Google’s services over the TV advertising that still gobbles up the lion’s share of retailers’ ad budgets.

But Google’s latest move to tie people’s digital trails to their real world behaviors is also likely to renew concerns over whether technology giants and their affiliated companies know too much about people’s lives — and whether they disclose enough about how they collect and use that information.

Google collects massive amounts of personal data from smartphones and desktop computers, including location information from Google Maps and other apps, the search terms that people use in a Google search, and people’s Web browsing habits. All of that information is tied to the real identities of users when they log in to Google’s services.

Company executives say they are using complex, patent-pending mathematical formulas to protect the privacy of consumers when they match a Google user with a shopper who makes a purchase in a brick-and-mortar store. The mathematical formulas convert people’s names and other personal information into anonymous strings of numbers. The formulas make it impossible for Google to know the identity of the real-world shoppers, and for the retailers to know the identities of Google’s users, Google executives said. The companies know only that a match has been made.

In addition, Google does not get a detailed description of the individual transactions, just the amount spent.

“Through a mathematical property we can do double-blind matching between their data and our data,” said Jerry Dischler, vice president of product management for AdWords, in an interview. “Neither gets to the see the encrypted data that the other side brings.”

Dischler, who said the company had been working on the technology for years, described the modeling as a “revolutionary” step forward for both Google and advertisers.

But Google declined to share anything more than basic information about how the program worked.

Google would not say how merchants had obtained consent from consumers to pass along their credit card information. Tuesday’s initiative enables Google to use transaction data from a much wider swath of consumers than ever before.