Pseudo-Entanglement is Necessary for EFI Pairs

TL;DR

This paper demonstrates that EFI pairs imply the existence of pseudo-entanglement, establishing pseudo-entanglement as a minimal quantum resource necessary for foundational cryptographic primitives.

Contribution

It proves that EFI pairs imply pseudo-entanglement, positioning pseudo-entanglement as a new minimal assumption for cryptography based on quantum resources.

Findings

EFI pairs imply pseudo-entanglement

Pseudo-entanglement is necessary for key cryptographic primitives

Establishes a link between physical quantum phenomena and cryptography

Abstract

Regarding minimal assumptions, most of classical cryptography is known to depend on the existence of One-Way Functions (OWFs). However, recent evidence has shown that this is not the case when considering quantum resources. Besides the well known unconditional security of Quantum Key Distribution, it is now known that computational cryptography may be built on weaker primitives than OWFs, e.g., pseudo-random states [JLS18], one-way state generators [MY23], or EFI pairs of states [BCQ23]. We consider a new quantum resource, pseudo-entanglement, and show that the existence of EFI pairs, one of the current main candidates for the weakest computational assumption for cryptography (necessary for commitments, oblivious transfer, secure multi-party computation, computational zero-knowledge proofs), implies the existence of pseudo-entanglement, as defined by [ABF+24, ABV23] under some reasonable adaptations. We prove this by constructing a new family of pseudo-entangled quantum states given only EFI pairs. Our result has important implications for the field of computational cryptography. It shows that if pseudo-entanglement does not exist, then most of cryptography cannot exist either. Moreover, it establishes pseudo-entanglement as a new minimal assumption for most of computational cryptography, which may pave the way for the unification of other assumptions into a single primitive. Finally, pseudo-entanglement connects physical phenomena and efficient computation, thus, our result strengthens the connection between cryptography and the physical world.