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arXiv · 2610.18799

$\mathsf{EFI}\Leftrightarrow\mathsf{1PRS}$

Rishabh Batra
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Abstract

A series of recent works has established EFI pairs as the "minimal" assumption for quantum cryptography. Recently, Cavalar et al. [CCC+26] showed that EFI pairs are equivalent to non-uniform expanding single-copy pseudorandom state generators (1PRS), and obtained a non-uniform meta-complexity characterization of EFI pairs. We remove the non-uniformity in their construction and prove that EFI pairs are equivalent to expanding 1PRS. As a corollary, we obtain the first uniform meta-complexity characterization of EFI pairs. Together with the equivalence of statistically verifiable one-way state generators and commitments proved by Batra and Jain [BJ24], this gives a quantum analogue of the classical equivalence between one-way functions, commitments, and pseudorandom generators.

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Rishabh Batra. 2026-10-13. $\mathsf{EFI}\Leftrightarrow\mathsf{1PRS}$. https://arxiv.org/abs/2610.18799

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