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

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.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2610.18799 [quant-ph]

(or arXiv:2610.18799v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.18799 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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