Abstract: This disclosure relates to protocols and systems for generating random bit strings by amplifying weak bit strings using certified quantum random bit strings generated by measuring a quantum state of entangled photons. Some disclosed systems include a quantum apparatus comprising one or more quantum systems configured to generate entangled photons and measure their quantum state. Certain disclosed systems include one or more security tests, wherein at least one security test evaluates the quantum nature of the measurements using a Bell inequality. A randomness extractor can amplify the randomness of weak random strings using random strings certified by the security tests. The generated random bit strings may be used as cryptographic keys.