Last July, after virtually every adult in India was connected to the world’s biggest biometric identity database, one of the government officials behind it issued a challenge. R.S. Sharma, who oversees the country’s telecom regulatory agency, publicly disclosed his personal ID number in the system and taunted skeptics and potential hackers. “Show me one concrete example where you can do any harm to me!” he tweeted.

Opponents of the system swarmed, looking to show the dangers of having too much information amassed in one place....