Paul said he agrees with the landmark Supreme Court case Griswold v. Connecticut, which first declared that the Constitution protects privacy and invalidated a state law banning access to contraceptives.
He also said that the right to privacy extends to personal records, even when they are under the control of a third party, like a website, bank or telecommunications provider.
Paul said that laws like the Patriot Act that give the government access to personal information when it is under the control of a company "erode" the Fourth Amendment.
But Paul argued that people have a right to privacy only from intrusion by the government, not private corporations.
"Some people say, 'Google has no right to this information.' Well, you make a contract with Google, and Google has the right to whatever you sign away as far as a contract," Paul said.
In recent years, the Federal Trade Commission (FTC) has cracked down on companies, including Google and Facebook, if they violate their own privacy policies.
Paul said companies should not be allowed to mislead their customers or violate their contracts, but he said he prefers class-action lawsuits to government enforcement.
"I worry about who's in charge of the FTC. Are they overly zealous people and busybodies getting involved? I don't necessarily like that approach," Paul said.
He said he doesn't think the government is competent enough to set standards for cybersecurity.
He argued that broad liability protections for companies that meet security standards might only encourage them to violate their contracts with their customers.
The only cybersecurity measure that Paul said he would support would be granting antitrust exceptions to allow companies to share information about cyber threats with each other.