Construction of scalable pseudorandom unitaries

Construct scalable pseudorandom unitaries that decouple the output length from the security parameter, extending the scalable pseudorandom-state and pseudorandom-function-like-state constructions described in the paper.

Background

The paper studies the role of coherent oracle access in constructing quantum cryptographic primitives, especially pseudorandom states (PRSs) with superlogarithmic output length. Its oracle separation shows that logarithmic-length pseudorandom function-like states can exist while longer PRSs do not, emphasizing that quantum-primitive length extension is substantially more difficult than classical length extension.

In a footnote discussing an orthogonal research direction, the paper notes that scalable PRS and PRFS constructions have been proposed to decouple primitive length from the security parameter, but that the corresponding construction for scalable pseudorandom unitaries remains unresolved. A solution would provide a scalable PRU construction with analogous length-security-parameter decoupling.