"We believe very strongly in end-to-end encryption and no back doors," Cook said in an interview with the Daily Telegraph during a visit to Britain that comes after plans for a new Investigatory Powers Bill were outlined this month.
The new bill, which has been heavily criticised by privacy campaigners, would not ban encryption altogether but would make it easier for Britain's security services to access encrypted communications.
"To protect people who use any products, you have to encrypt. You can just look around and see all the data breaches that are going on. These things are becoming more frequent," Cook said.
"Any back door is a back door for everyone. Everybody wants to crack down on terrorists. Everybody wants to be secure. The question is how. Opening a back door can have very dire consequences."
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Home Secretary Theresa May unveiled plans for a "world-leading oversight regime" on Internet communications, but the civil rights group Liberty called it a "breath-taking attack" on Britain's online security.
Campaigners have said the new legislative proposals could lead to the kind of blanket surveillance revealed by US whistleblower Edward Snowden.