In October 2017, a SWAT team descended on Jameson Lopp’s house in North Carolina. Someone — it still isn’t clear who — had called the police and falsely claimed that a shooter at the home had killed someone and taken a hostage. After the police left, Mr. Lopp received a call threatening more mayhem if he did not make a large ransom payment in Bitcoin.

To scare off future attackers, Mr. Lopp quickly posted a video on Twitter of himself firing off his AR-15 rifle. He also decided he was going to make it much harder for his enemies — and anyone else — to find him ever again.

Mr. Lopp, a self-described libertarian who works for a Bitcoin security company, had long been obsessed with the value of privacy, and he set out to learn how thoroughly a person can escape the all-seeing eyes of corporate America and the government. But he wanted to do it without giving up internet access and moving to a shack in the woods.

Many celebrities and wealthy people, wary of thieves, paparazzi and other predators, have tried to achieve Mr. Lopp’s vision of complete privacy. Few have succeeded.