Scalable, quantum-accessible, and adaptive pseudorandom quantum state and pseudorandom function-like quantum state generators
This work advances the theoretical foundations of quantum cryptography by providing stronger security guarantees for PRFS, addressing a known gap in the literature.
The authors construct pseudorandom quantum states (PRS) and pseudorandom function-like quantum state (PRFS) generators that are scalable, quantum-accessible, and adaptive, achieving the first fully quantum-accessible PRFS under quantum-secure one-way functions.
We show new constructions for pseudorandom quantum states (PRS) and pseudorandom function-like quantum state (PRFS) generators satisfying scalability, which means the security parameter can be much larger than the number of qubits, quantum accessibility, which means the adversary can provide quantum input, and adaptivity, which means the adversary can query it adaptively. We present an isometric procedure to prepare quantum states that can be arbitrarily random (i.e., the trace distance from the Haar-random state can be arbitrarily small for the true random case, or the distinguishing advantage can be arbitrarily small for the pseudorandom case). This naturally gives the first construction for scalable, quantum-accessible, and adaptive PRFS assuming quantum-secure one-way functions. Compared to prior PRFS works, we use a stronger definition of quantum accessibility in which the adversary can be ancilla-assisted, i.e., the input state may not be pure and could be entangled with other quantum registers. Thus, our result also gives the first (fully) quantum-accessible PRFS. Our PRFS construction implies various primitives, including long-input PRFS, short-input PRFS, short-output PRFS, non-adaptive PRFS, and classically-accessible adaptive PRFS. This new construction may be helpful in simplifying the microcrypt zoo.