Statements

Status	Statement	Tags
	Constant-round Luby–Rackoff, quantum Open for every round count: whether some constant number of Luby-Rackoff rounds with random round functions is indistinguishable from a random invertible permutation against quantum queries in both directions. Four rounds are refuted by a known quantum attack, and the source reports that the published proof of the weaker forward-only four-round claim is flawed. 6 open	otherequivalenceresearch-opennew-idea (ai)
	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
	Four-party NIKE, quadratic, Maurer’s model Open. Achieved in Shoup’s generic group model by the source paper (Construction 9, Theorem 10); in Maurer’s model the paper’s own O(n^2) attack sets a ceiling that a construction would meet exactly, and nothing is known about reaching it. 5 open	ggmseparationresearch-opennew-idea (ai)
	Quadratic attack on 3-NIKE, Shoup’s model Open in Shoup’s model. Settled by the source paper in Maurer’s model for every K at least 3, including imperfect correctness; its own three-party Shoup construction achieves only an n^1.5 gap, so the truth for three parties lies somewhere between n^1.5 and n^2. 5 open	ggmlower-boundresearch-opennew-idea (ai)
	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)
	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)
	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
	Split-source decomposition Open for a query budget of two or more: whether a random oracle decomposes into bit-fixing mixtures when the advice is produced by two sources that never communicate. Proved and tight at q = 0, and proved at q = 1 under an extra hypothesis. 4 open	romtight-boundresearch-opennew-idea (ai)
	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)
	CRS-free everlasting commitment from malicious PUFs Open: whether everlasting UC commitment is achievable in the fully malicious token model with no trusted setup. The source achieves it with a common reference string (its Theorem 31) and explicitly leaves removing the CRS as a question, noting that the usual equivocation techniques do not transfer to the everlasting setting. 6 open	otherassumptionresearch-opennew-idea (ai)
	6-round Feistel indifferentiability Whether 6-round Feistel is fully indifferentiable from a random permutation is open, bridging the proven r=5 attack and the proven r>=8 construction. 2 open	othertight-boundresearch-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)
	Groth16 optimality (pure GGM) Open: whether every sound, non-interactive, publicly verifiable pairing-based argument in the pure generic group model needs at least three group elements, matching Groth16. 2 open	ggmtight-boundresearch-opennew-idea (ai)
	Double-sided zero search Open: whether finding x with H(x\|\|0^n) = y\|\|0^n is hard for a quantum adversary with polynomially many queries to a random permutation H and its inverse. The source proves it only under its own compressed-permutation-oracle soundness conjecture, as a usage example. 6 open	otherlower-boundresearch-opennew-idea (ai)
	LHL extraction, public seed Proven, and the statement is now formalized in Lean with an AI match check: the public-seed bound holds with a concrete constant, but the proof itself is still only informal (PDF), unreviewed, and unformalized. 4 open	romtight-boundresearch-solvedadaptation (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 key agreement from GC-OWF Open for round complexity growing with the security parameter. Proved in full for two messages, which is public-key encryption; the constant-round extension is sketched in the paper’s appendix without a theorem, its security half deferred to the PKE proof. 5 open	otherseparationresearch-openadaptation (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
	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)
	OWFs are black-box helpful for CRHFs Open in both directions. Two relaxations — distributional and class-reduction helpfulness — are proved conditional on the Simon-oracle amplification conjecture; neither yields the universal auxiliary primitive the full statement needs. 5 open	otherseparationresearch-opennew-idea (ai)
	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)
	Simon-oracle amplification, strong version Open. The version without the collision finder is known only when the one-way function is itself a random oracle; with an arbitrary one-way function, with or without the collision finder, nothing is established. 5 open	otherlower-boundresearch-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)
	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)
	3-way collision, oblivious sequential curve Open: closing the factor-root-S gap between the proved oblivious lower bound and a matching table-and-hunt algorithm for finding a 3-way collision with an oblivious sequential branching program. 2 open	romtight-boundresearch-openadaptation (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)
	Compressed permutation oracle soundness Open: whether the compressed permutation oracle is indistinguishable from a random permutation with inverse access, against polynomially many quantum queries. The source defines the oracle and proves only a conditional converse; the statement itself is settled nowhere. 5 open	otherequivalenceresearch-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)
	Polynomial Compatibility Conjecture Open in the inverse-polynomial regime. Proved for exponentially small influences by the paper that introduced it, and false for influences at or above 1/(2d); everything between is what the quantum separations depend on. 5 open	qromassumptionresearch-opennew-idea (ai)
	Three moves from DL, ROM only Open: three moves, black-box in the group, ROM only, from DL alone. Three moves is achieved from DDH in the ROM and from DL in AGM+ROM; four moves is achieved from DL in the ROM. 5 open	romassumptionresearch-opennew-idea (ai)
	Tight \(k\)-collision time-space tradeoff The exact tight time-space tradeoff for k>=3 collisions under preprocessing is open; only the k=2 case has a matching upper and lower bound. 2 open	romtight-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)