International Association for Cryptologic Research

International Association
for Cryptologic Research


Pseudorandom Isometries

Prabhanjan Ananth , UCSB
Aditya Gulati , UCSB
Fatih Kaleoglu , UCSB
Yao-Ting Lin , UCSB
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Presentation: Slides
Conference: EUROCRYPT 2024
Abstract: We introduce a new notion called $\mathcal{Q}$-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an $n$-qubit state to an $(n+m)$-qubit state in an isometric manner. In terms of security, we require that the output of a $q$-fold PRI on $\rho$, for $ \rho \in \mathcal{Q}$, for any polynomial $q$, should be computationally indistinguishable from the output of a $q$-fold Haar isometry on $\rho$. By fine-tuning $\mathcal{Q}$, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of $\mathcal{Q}$-secure pseudorandom isometries (PRI) for different interesting settings of $\mathcal{Q}$. We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, MACs for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments.
  title={Pseudorandom Isometries},
  author={Prabhanjan Ananth and Aditya Gulati and Fatih Kaleoglu and Yao-Ting Lin},