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Title:
Separating Pseudorandom Generators from Logarithmic Pseudorandom States
Authors: Mohammed Barhoush
Abstract:Pseudorandom generators (PRGs) are a foundational primitive in classical cryptography, underpinning a wide range of constructions. In the quantum setting, pseudorandom quantum states (PRSs) were proposed as a potentially weaker assumption that might serve as a substitute for PRGs in cryptographic applications. Two primary size regimes of PRSs have been studied: logarithmic-size and linear-size. Interestingly, logarithmic PRSs have led to powerful cryptographic applications, such as digital signatures and quantum public-key encryption, that have not been realized from their linear counterparts. However, PRGs have only been black-box separated from linear PRSs, leaving open the fundamental question of whether PRGs are also separated from logarithmic PRSs.
In this work, we resolve this open problem. We establish a quantum black-box separation between (quantum-evaluable) PRGs and PRSs of either size regime. Specifically, we construct a unitary quantum oracle with inverse access relative to which no black-box construction of PRG from (logarithmic or linear) PRS exists. As a direct corollary, we obtain separations between PRGs and several primitives implied by logarithmic PRSs, including digital signatures and quantum public-key encryption.
ePrint: https://eprint.iacr.org/2025/1994
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