On a Tuesday afternoon last month, engineers working for Sony Corp. were baffled when several servers running the company's PlayStation Network suddenly turned themselves off and then back on.

At the time, the unexpected rebooting seemed like an odd malfunction. The next day, however, the engineers found the first evidence that an intruder had penetrated Sony's systems, prompting the Japanese company to take what it calls "the almost unprecedented step" of shutting down the popular online gaming network.

Sony...