After hackers breached the computer network of the U.C.L.A. medical center last summer, Janet Napolitano, president of the University of California, and her office moved to shore up security across the university system’s 10 campuses.

Under a program initiated by Ms. Napolitano, the former secretary of Homeland Security in the Obama administration, the university system began installing hardware and software in its data centers that would monitor patterns of digital traffic, like what websites are being visited by faculty and students, or telltale signs of cyber intruders. The program, which was begun with little notice or consultation, soon rankled a group of professors at one campus, Berkeley, which has a deep-seated ethos of academic freedom as the cradle of the free speech movement in the 1960s.

In recent days, the professors have begun speaking out publicly about the issue. “My primary concern is monitoring the private information of students and faculty in secret,” said Eric Brewer, a professor of computer science at U.C. Berkeley. “I’m sure there’s good intent. But I can’t see a good reason for doing it.”

The resistance from Mr. Brewer and other professors at Berkeley, which is now becoming a public debate with the university system’s administrators, raises the issue of how to define academic freedom in the age of online attacks. While some of the professors criticize the monitoring program as one that invades their privacy, the University of California has responded that “privacy perishes in the absence of security.”