Paper 2022/1514

Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications

Prabhanjan Ananth, University of California, Santa Barbara
Aditya Gulati, University of California, Santa Barbara
Luowen Qian, Boston University
Henry Yuen, Columbia University

Pseudorandom quantum states (PRS) are efficiently constructible states that are computationally indistinguishable from being Haar-random, and have recently found cryptographic applications. We explore new definitions, new properties and applications of pseudorandom states, and present the following contributions: 1. New Definitions: We study variants of pseudorandom function-like state (PRFS) generators, introduced by Ananth, Qian, and Yuen (CRYPTO'22), where the pseudorandomness property holds even when the generator can be queried adaptively or in superposition. We show the feasibility of these variants assuming the existence of post-quantum one-way functions. 2. Classical Communication: We show that PRS generators with logarithmic output length imply commitment and encryption schemes with classical communication. Previous constructions of such schemes from PRS generators required quantum communication. 3. Simplified Proof: We give a simpler proof of the Brakerski-Shmueli (TCC'19) result that polynomially-many copies of uniform superposition states with random binary phases are indistinguishable from Haar-random states. 4. Necessity of Computational Assumptions: We also show that a secure PRS with output length logarithmic, or larger, in the key length necessarily requires computational assumptions.

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Publication info
A major revision of an IACR publication in TCC 2022
Quantum Cryptography
Contact author(s)
prabhanjan @ cs ucsb edu
adityagulati @ ucsb edu
luowenq @ bu edu
hyuen @ cs columbia edu
2023-06-09: revised
2022-11-02: received
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      author = {Prabhanjan Ananth and Aditya Gulati and Luowen Qian and Henry Yuen},
      title = {Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1514},
      year = {2022},
      note = {\url{}},
      url = {}
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