Randomness is an essential resource in computer science. In most applications perfect, and sometimes private, randomness is needed, while it is not even clear that such a resource exists. It is well known that the tools of classical computer science do not allow us to create perfect and secret randomness from a single weak public source. Quantum physics, on the other hand, allows for such a process, even in the most paranoid cryptographic sense termed "quantum device-independent cryptography". In this work we propose and prove the security of a new device-independent protocol that takes any single public Santha-Vazirani source as input and creates a secret close to uniform string in the presence of a quantum adversary. Our work is the first to achieve randomness amplification with all the following properties: (1) amplification and "privatization" of a public Santha-Vazirani source with arbitrary bias (2) the use of a device with only two components (compared to polynomial number of components) (3) non-vanishing extraction rate and (4) maximal noise tolerance. In particular, this implies that our protocol is the first protocol that can possibly be implemented with reachable parameters. We are able to achieve these by combining three new tools: a particular family of Bell inequalities, a proof technique to lower bound entropy in the device-independent setting, and a special framework for quantum-proof multi-source extractors.
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