Paper 2023/1741

Pseudorandom Isometries

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 $$-fold Haar isometry on $$. By fine-tuning $$, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of $$-secure pseudorandom isometries (PRI) for different interesting settings of $$. 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.