**Cryptography from Pseudorandom Quantum States**

*Prabhanjan Ananth and Luowen Qian and Henry Yuen*

**Abstract: **Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are efficiently-computable quantum states that are computationally indistinguishable from Haar-random states.
One-way functions imply the existence of pseudorandom states, but Kretschmer (TQC'20) recently constructed an oracle relative to which there are no one-way functions but pseudorandom states still exist.
Motivated by this, we study the intriguing possibility of basing interesting cryptographic tasks on pseudorandom states.

We construct, assuming the existence of pseudorandom state generators that map a $\lambda$-bit seed to a $\omega(\log\lambda)$-qubit state, (a) statistically binding and computationally hiding commitments and (b) pseudo one-time encryption schemes. A consequence of (a) is that pseudorandom states are sufficient to construct maliciously secure multiparty computation protocols in the dishonest majority setting.

Our constructions are derived via a new notion called {\em pseudorandom function-like states} (PRFS), a generalization of pseudorandom states that parallels the classical notion of pseudorandom functions. Beyond the above two applications, we believe our notion can effectively replace pseudorandom functions in many other cryptographic applications.

**Category / Keywords: **foundations / quantum cryptography

**Date: **received 18 Dec 2021, last revised 14 Mar 2022

**Contact author: **prabhanjan at cs ucsb edu, luowenq at bu edu, hyuen at cs columbia edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20220314:164825 (All versions of this report)

**Short URL: **ia.cr/2021/1663

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