[Resource Topic] 2023/1741: Pseudorandom Isometries

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Pseudorandom Isometries

Authors: Prabhanjan Ananth, Aditya Gulati, Fatih Kaleoglu, Yao-Ting Lin


We introduce a new notion called {\cal 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 {\cal Q}, for any polynomial q, should be computationally indistinguishable from the output of a q-fold Haar isometry on \rho.

By fine-tuning {\cal 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 {\cal Q}-secure pseudorandom isometries (PRI) for different interesting settings of {\cal Q}.

We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments.

ePrint: https://eprint.iacr.org/2023/1741

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