Existence of classical one-way functions

Determine whether classical one-way functions exist in computational complexity; specifically, establish whether there is a total function f: {0,1}* -> {0,1}* that is efficiently computable (e.g., in polynomial time) but cannot be inverted with non-negligible success probability by any probabilistic efficient algorithm.

Background

The paper recalls the standard notion of one-way functions in classical computational complexity: finite maps that are easy to compute but hard to invert, even probabilistically. This foundational assumption underpins modern cryptographic primitives, yet its validity remains unresolved.

The authors contrast this longstanding complexity-theoretic open problem with their focus on the computability-theoretic setting of real functions, where they construct collision-resistant one-way functions under Levin’s framework. Their results do not address the classical complexity question, which they acknowledge remains open.

References

Modern cryptographic primitives rely on their existence, an unproven hypothesis which remains a long-standing open problem.

— Collision-resistant hash-shuffles on the reals (2501.02604 - Barmpalias et al., 5 Jan 2025) in Section 1. Introduction