Mr. Carter’s careful appeal was part of a campaign last week by government officials trying to undo the damage of Mr. Snowden’s revelations. While Mr. Carter got a respectful hearing, Jeh Johnson, the secretary of Homeland Security, and a group of other government officials ran into a buzz saw of skepticism at the world’s largest conference of computer security professionals, just 30 miles to the north.

Those officials argued for some kind of technical compromise to allow greater security of electronic communications while enabling the F.B.I. and intelligence agencies to decode the emails and track the web activities of suspected terrorists or criminals. Yet many among the computer security professionals at the conference argued that no such compromise was possible, saying that such a system would give Russians and Chinese a pathway in, too, and that Washington might abuse such a portal.

Not long after Mr. Johnson declared that “encryption is making it harder for your government to find criminal activity and potential terrorist activity,” large numbers of entrepreneurs and engineers crammed into the first of several seminars, called “Post-Snowden Cryptography.” There, they took notes as the world’s best code makers mocked the Obama administration’s drive for a “technical compromise” that would ensure the government some continued access.

Ronald Rivest, one of the inventors of a commonly used encryption algorithm, took on the arguments by Mr. Johnson and other senior officials, including John P. Carlin, the head of the Justice Department’s national security division, that the best minds in Silicon Valley could find a way to ensure legal government access while still assuring users that communications and data stored in their iPhones and the cloud are safe.

“There are lots of problems with these ideas,” Mr. Rivest said. “We live in a global information system now, and it’s not going to be just the U.S. government that wants a key. It’s going to be the U.K., it’s going to be Germany, it’s going to be Israel, it’s going to be China, it’s going to be Iran, etc.”