Separating Pseudorandom Generators from Logarithmic Pseudorandom States
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915614606491648 |
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| author | Barhoush, Mohammed |
| author_facet | Barhoush, Mohammed |
| contents | 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 with tamper-resilient keys, 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.
This does not directly separate PRG from some of the applications of SPRS since these applications involve, as a first step, a non-black-box construction of a notion termed bot-PRGs. To address this, we present another unitary separation showing that PRG are also separated from bot-PRGs. Thus, we obtain separation from digital signatures and quantum public-key encryption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separating Pseudorandom Generators from Logarithmic Pseudorandom States Barhoush, Mohammed Cryptography and Security 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 with tamper-resilient keys, 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. This does not directly separate PRG from some of the applications of SPRS since these applications involve, as a first step, a non-black-box construction of a notion termed bot-PRGs. To address this, we present another unitary separation showing that PRG are also separated from bot-PRGs. Thus, we obtain separation from digital signatures and quantum public-key encryption. |
| title | Separating Pseudorandom Generators from Logarithmic Pseudorandom States |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2510.20131 |