Abstract
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.
Highlights
S ECRET, or private, randomness is essential for cryptography
When trying to implement quantum sources of randomness we find that creating perfect states and measurements is practically impossible
The main contribution of our work is a construction of a DI randomness amplification and privatization protocol that uses a single public SV-source to create secret and close to uniform randomness, with respect to all of the knowledge that the adversary has: Theorem 1 (Informal): Given any public SV-source with bias μ ∈ (0, 0.5) there exists a protocol, requiring a twocomponent device, such that: 1) (Soundness) For any device D used to implement the protocol such that Equation (1) holds, either the protocol aborts with overwhelming probability or an ε-close to uniform string K is produced
Summary
S ECRET, or private, randomness is essential for cryptography. The simplest example is that of the “one-time pad” – to create a ciphertext from the plaintext, the plaintext is masked using a truly random key. In this work we suggest a new quantum DI cryptographic protocol that uses a single public SV source as input and produces secret close to uniform randomness, even with respect to a quantum adversary. Realistic completeness is a requisite if one wishes to implement and use the cryptographic protocol in practice instead of merely considering the task of randomness amplification and privatization on the theoretical level. This crucial property was not achieved by previous works. By requiring a strong completeness statement, proving the security of the protocol becomes harder
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