A Modular Framework for Quantum-Proof Randomness Extractors

A quantum-proof extractor is a function that is used to extract randomness from any weakly random source X in the presence of prior quantum information about X . It is known that some constructions are quantum-proof, such as Trevisan’s construction. However, these extractors are generally restrictive for applications on the one-bit output construction and the weak design. Here, we give a modular framework to combine multi-bit output extractors (not only one-bit) with pseudorandom transform, and show that it is sound in the presence of quantum side information. Then combined with the theory of operator spaces, we improve previous theoretical proofs, and discuss the security of two-bit output extractor by giving a tighter bound for it.