Encrypted smartphones and messaging apps that prevent even the companies that make them from decrypting their data are unreasonably hindering criminal investigations, and the situation is worsening, say law enforcement officials. A new report from the Center for Strategic and International Studies, a prominent bipartisan policy think tank, helps quantify the scale and complexity of the issue.

Apple helped catalyze a surge in popularity of devices with strong encryption when it redesigned iOS in 2014 so that it is impossible even for the company itself to break. That led to last year’s showdown with the FBI, and has helped to reignite the decades-old policy debate over encryption. Meanwhile, the popularity of encrypted messaging apps, including foreign products, is also growing rapidly, further complicating the issue for policymakers.

According to the report, some 13 percent of all mobile devices around the world now run iOS, and 95 percent of those run a version that Apple cannot access. In the U.S., 47 percent of all mobile devices work this way. During a recent discussion marking the release of the new report, the FBI’s general counsel, James A. Baker, said that between October and December 2016, the FBI was unable to access the data on 1,245 of the 2,870 devices it seized.

The authors of the new report estimate that 1.5 billion people in the world use messaging apps, including Apple’s iMessage and WhatsApp, with end-to-end encryption, which prevents third parties, including service providers, from being able to read messages. About 18 percent of the world’s total communications traffic is now inaccessible to law enforcement, they say.

Because the marketplace for encryption is global, a national law that restricts it or gives the government special access to encrypted data will not eliminate the obstacles the technology raises for law enforcement. People will simply switch to foreign products like Line and Viber, popular messaging apps made in Japan and Cyprus, respectively. People could also develop their own apps; the code that implements end-to-end encryption in WhatsApp, Facebook Messenger, and Signal is open source.