Model: standard

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

Status	Statement	Tags
	Best-first search trees Open, with no bound of any kind proved for the best-first algorithm on any class of query distributions. Exact optimality is already refuted by the paper’s own exhaustive search, so only the approximation ratio remains, and a workload on which greedy is off by an unbounded factor would settle it. 5 open	standardtight-boundresearch-opennew-idea (ai)
	Dream DPT for a moderately hard function Open: whether there exists a function family, and a standard fine-grained hardness hypothesis (the paper suggests NSETH as an example), for which solving t independent instances requires resources within a subexponentially small factor of solving them one at a time, with no loss in the exponent. The source reduces its permissionless consensus protocol to exactly this statement and leaves it unconstructed. 5 open	standardassumptionresearch-opennew-idea (ai)IOG
	Optimal martingale gap finders Open for small mu. Settled when mu is bounded away from zero, where the Cleve-Impagliazzo gap finder already gives the conjectured product; for general mu the known bound is a factor mu short and the paper states it does not know the answer. 5 open	standardlower-boundresearch-opennew-idea (ai)
	Partial-PKI consensus up to one-half resilience Open: whether consensus is achievable at every resilience gamma < 1/2 in the paper’s permissionless common-random-string setting, by some protocol using any means of bootstrapping party identities. The source proves resilience up to 1/4(1-3*epsilon) via a specific protocol and proves 1/4 is tight only for the restricted class of protocols that sign everything they send and verify everything they receive; the gap to the classical 1/2 ceiling is open for arbitrary protocols. 5 open	standardtight-boundresearch-opennew-idea (ai)IOG
	Erasing real-or-random vs Boneh–Zhandry Open: whether erasing real-or-random security implies Boneh-Zhandry security. The reverse non-implication is proved only in the quantum random oracle model, and this direction is one of six non-implications the source paper conjectures and does not prove. 5 open	standardseparationresearch-opennew-idea (ai)
	Generalized mirror theory The fully generalized Mirror Theory bound for arbitrary cycle-consistent multi-graphs up to the information-theoretic limit is open; current techniques only reach component size O(N^{1/4}). 2 open	standardlower-boundresearch-opennew-idea (ai)
	Level-optimal beyond disjunctions Open beyond disjunctive queries, and the authors state it as a conjecture without naming the broader class – identifying one is part of the problem. Proved for every distribution supported on disjunctions, where the log n factor is also shown necessary. Wide open for conjunctive queries, where the paper’s proof technique demonstrably fails. 5 open	standardtight-boundresearch-opennew-idea (ai)
	Logarithmic independence implies PRP Open at independence order log n. The same implication is refuted at order 4 and at every constant order by an explicit construction; the logarithmic-order form is untouched, and no unconditional proof of it can be expected. 5 open	standardcharacterizationresearch-opennew-idea (ai)
	RBE needs Ω(log n) updates Open. The number of updates for fixed-update-time schemes with polylogarithmic public parameters is known to lie between Omega(log n / log log n) and O(log n); this statement picks the upper endpoint, and the paper’s own tool is proved tight, so it cannot decide the question. 5 open	standardlower-boundresearch-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)
	One erasing challenge vs many embedding learns Open: whether a single erasing two-ciphertext challenge query, with classical learning queries, implies security against polynomially many embedding-model superposition learning queries. One of six non-implications the source paper conjectures, and on its own account the one that would close the most remaining cells. 5 open	standardseparationresearch-opennew-idea (ai)
	Standard real-or-random vs embedding two-ciphertext Open: whether one standard-oracle real-or-random challenge query implies one embedding-model two-ciphertext challenge query, with classical learning queries on both sides. Both notions are singleton classes in the source’s classification, and this is one of six non-implications it conjectures. 5 open	standardseparationresearch-opennew-idea (ai)
	Threshold one-shot decryption without extractability Open: whether threshold one-shot decryption (for every corruption threshold f < 1/2) follows from one-shot signatures and an ordinary, non-extractable witness encryption scheme. The one known construction needs the witness-encryption extractor to run its security reduction, and the source paper leaves open whether extractability can be weakened or dropped altogether. 5 open	standardassumptionresearch-opennew-idea (ai)IOG
	OWF minimality, non-black-box reductions Open when the classical security implication is not witnessed by a black-box reduction between the two games. Settled affirmatively whenever it is, for uniform and non-uniform quantum adversaries alike, with the implementation reduction left arbitrary. 5 open	standardequivalenceresearch-opennew-idea (ai)
	PKE from constant-noise planted k-XOR Open: whether public-key encryption can be based on the hardness of planted k-XOR with a linear number of equations and a constant noise rate, as a single assumption. The survey poses it as one of two closing open questions and does not return to it; every combinatorial scheme it surveys needs sub-constant noise.	standardseparationresearch-openbarrier (ai)
	Ring-LWE error parity Open: whether recovering the Ring-LWE error modulo two is as hard as recovering the error itself. The easy direction is trivial; the source states it has no formal reduction for this one and relies on two heuristics instead, one of which changes the error distribution. 6 open	standardequivalenceresearch-opennew-idea (ai)
	Certifying no small non-expanding set Open: whether the non-existence of a small non-expanding set in a random unbalanced bipartite graph admits a nondeterministic certificate that is sound and complete on average, at the parameters the ABW cryptosystem uses. The survey poses it as one of two closing open questions, takes no position, and does not return to it.	standardseparationresearch-opennew-idea (ai)
	Censoring can only hurt Open. The censored side is proved at essentially optimal round count with matching lower bounds; what is missing is the transfer of any such bound to uncensored AES at the same round count. 5 open	standardlower-boundresearch-opennew-idea (ai)
	RBE update bound, key-dependent schedules Open exactly when the update schedule may depend on the sampled public keys, which is the standard on-demand completeness notion. Proved when the schedule is any fixed function of registration times (Theorem 4.1) or of the registered identity names and the CRS (Theorem 4.12). 5 open	standardlower-boundresearch-openadaptation (ai)