A privacy advocacy group has filed a formal legal complaint with the US Federal Trade Commission, asking the agency to begin an investigation "into Google’s in-store tracking algorithm to determine whether it adequately protects the privacy of millions of American consumers."

In the Monday filing, the Electronic Privacy Information Center (EPIC) said it is concerned with Google’s new Store Sales Management program, which debuted in May. The system allows the company to extend its online tracking capabilities into the physical world. The idea is to combine credit card and other financial data acquired from data brokers to create a singular profile as a way to illustrate to companies what goods and services are being searched for online, which result in actual in-person sales.

Because the algorithm that Google uses is secret, EPIC says, there is no way to determine how well Google’s claimed anonymization feature—to mask names, credit card numbers, location, and other potentially private data—actually works. While Google has been cagey about exactly how it does this, the company has previously revealed that the technique is based on CryptDB.

"The foundational algorithm on which the Google algorithm is based has known security flaws," the complaint states. "In 2015, researchers were able to hack into a CryptDB protected database of healthcare records and access over 50 percent (sometimes 100 percent) of sensitive patient data at an individual level." (Ars covered the 2015 research into CryptDB at the time that it came out.)

Worse still, it seems practically impossible for consumers to do anything about this potential tracking in EPIC's view.

"Consumers cannot easily avoid Google’s tracking of their in-store purchase behavior," EPIC argues. "As described above, there appears to be no mechanism by which Google users can opt out of purchase tracking other than by disabling location tracking entirely. It is not clear to users, however, that the way to avoid tracking of purchases is by disabling location tracking."

It is possible to opt out of this tracking. Google users can simply go to the My Activity Page, click on Activity Controls, and uncheck "Web and Web Activity."

But that’s not enough, EPIC says, noting that "there does not appear to be a way to prevent Google from matching user data to credit card transaction data held by a third party."

Google did not immediately respond to Ars’ request for comment.

UPDATE Tuesday 12:04pm ET: Suzanne Blackburn, a Google spokeswoman, sent Ars a corporate statement on Monday late afternoon.