Florian John Curchod

Achieving computational advantage using NISQ devices on practically useful problems is a long standing challenge. We report two papers that experimentally demonstrate a concrete application, namely certified randomness generation, which could be useful for multi-party cryptographic protocols and improving imperfect physical sources of randomness. Both papers involve substantial theoretical contributions to the protocol. We devise a realistic protocol that maximizes practical hardness. The verifier first asks the server to prepare a quantum state using a random circuit and then sends a random measurement basis right before the result must be received. This is repeated for many rounds. We show complexity theoretic evidence for entropy generation and provide improved entropy bounds against adversaries with oracle access to the random circuits. We also construct an end-to-end application of randomness amplification of imperfect sources into nearly perfect randomness, notably achieving everlasting security which uplifts computational security to information theoretic security.

Randomness extractors are an essential component in numerous applications, for example, for privacy amplification in quantum key distribution and randomness extraction in random number generation. Despite their importance, selecting, optimising and implementing the appropriate extractor and parameters requires significant expertise and time investment. We present Cryptomite, a publicly available software library that provides a variety of two-source, seeded, and deterministic randomness extractor implementations with state-of-the-art performance. The software is efficient, numerically precise and capable of handling input sizes up to $10^{12}$, allowing for use even in resource intensive protocols, e.g. device-independent ones. Alongside the software, we provide theoretical contributions that include improvements and generalisations to existing extractors, new extractor constructions and parameter calculation in a variety of useful security models. To showcase the library, we empirically compare the properties of the output of several random number generators and the effect of different randomness extraction methods on it, using intense statistical testing.