Form: impossibility

Statements with form: impossibility. This page only exists because at least one statement currently uses this value – if you add a statement with a new form value not listed under Problems, copy this page as the starting point for its facet page (see CONTRIBUTING.md).

Status	Statement	Tags
	Fully quantum time-lock puzzles Open in the fully quantum case. Settled by the source paper when the generator is classical and the solver quantum, and when the generator is quantum and the solver classical under perfect completeness; a classical-query attack on the remaining cell would prove a simulation conjecture. 5 open	qromimpossibilityresearch-opennew-idea (ai)
	CAQB key agreement, imperfect completeness Open. Settled for perfect completeness by the source paper’s Theorem 3.1; the argument’s final step uses perfect completeness in a way that no known weakening survives, and the paper’s Simulation-Conjecture barrier does not cover this party structure. 5 open	qromimpossibilityresearch-opennew-idea (ai)
	No 2-element split NILPs Open: whether a 2-element split NILP can be statistically sound against affine provers for any hard relation generator, the information-theoretic core of whether Groth16’s 3-element proof size is optimal. 2 open	standardimpossibilityresearch-opennew-idea (ai)
	OWFs are black-box useless for key agreement Open in the general case, which the paper names as the central open problem left by its work. Settled for three restricted protocol classes: constant-query perfect, constant-round constant-query imperfect, and Merkle-type. 6 open	otherimpossibilityresearch-opennew-idea (ai)
	No round-optimal pairing-free blind signature Open for a polynomial query budget. The impossibility is proved when User_2 and Verify together make O(log lambda) random-oracle queries, including when oracle outputs contain group elements; the superpolynomial message space hypothesis is retained. 5 open	ggmimpossibilityresearch-openadaptation (ai)
	Computationally unique VDFs in the ROM Open under computational uniqueness, which is the notion the definition of a VDF actually requires. Settled for perfect uniqueness with perfect completeness, and settled in the tight regime even with no uniqueness assumption at all. 5 open	romimpossibilityresearch-opennew-idea (ai)