Need for Coherent Access in Constructing Quantum Cryptography
Oracle separation shows quantum-secure one-way functions can exist without long pseudorandom states, proving coherent oracle access is required for PRS constructions.
The authors construct quantum oracles relative to which quantum-secure one-way functions exist but pseudorandom states (PRSs) with superlogarithmic output length do not. The separation relies on classically accessible random oracles, and the impossibility extends to any classically accessible classical oracle. They further show logarithmic-length PRFSs exist relative to these oracles, proving fully black-box PRS length extension from logarithmic to superlogarithmic output must use coherent access to the underlying short PRS.
- Quantum-secure OWFs can coexist with absence of long pseudorandom states.
- Separation uses classically accessible oracles even for quantum algorithms.
- Logarithmic PRFSs exist where superlogarithmic PRSs do not.
- Black-box PRS length extension requires coherent quantum access.
From the original article
1 min read at arxiv.orgWe construct quantum oracles relative to which quantum-secure one-way functions (OWFs) exist but pseudorandom states (PRSs) with superlogarithmic output length do not. At first glance, this appears to contradict the known black-box constructions of PRS generators from quantum-secure OWFs.
By Minki Hhan · arxiv.org
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