Young Cubans, eager to connect with the world,have built ingenious ways around the government’s controls. In the past two years, a black market data sharing system known as el paquete, or the packet, has enabled Cubans to gain access to a menu of news sites, television shows, movies and snapshots of websites that are bundled weekly and disseminated door to door through hard drives and memory sticks. They also have used wireless routers to create neighborhood networks that are not connected to the Internet but that enable users to chat and share media.

Earlier this year, the government, responding to popular pressure, established 35 wireless centers where Cubans can use smartphones and laptops to go online for about $2 an hour. Although that amounts to roughly 10 percent of the median monthly salary on the island, the centers have been mobbed. Norges Rodríguez, an engineer and prominent blogger in Havana, said that Cuban officials were wrestling with a quandary. “They are aware that for the economy to advance, the economy must be online,” he said in a phone interview. “But our society, by design, is like the one the Soviets had: a closed society.”

Within Cuba’s opaque power structure there is a split between hard-liners who are worried that broader Internet access could fuel dissent and more progressive leaders who see the embrace of technology as a matter of economic survival. Google, which has recently made it a priority to expand online access in some of the world’s least plugged-in societies, has invigorated that debate in recent months by offering to rapidly upgrade the island’s Internet infrastructure.