Lower Bound

Status	Statement	Tags
	Planted-Subgraph Character Sum The source derives the formula governing low-degree detection of a planted subgraph, observes the character sum in it should be small for most graphs, and says it leaves the rigorous study of the question to future work. No bound is proved and none is stated as a target. 5 open	Average Case Hardness Planted Subgraph Problemslower-boundadaptation (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	Generic Group Model Non Interactive Key Exchangeggmlower-bound
	Two-block sponge attack, quadratic advice Open: whether the multi-instance two-block sponge attack of advantage (S^2T4/C²⁾S lifts to an auxiliary-input attack of advantage S^2T4/C^2, matching the best proved security bound. Settled in the multi-instance model; no partial result in the auxiliary-input model. 7 open	Collision Finding Collision Resistant Hashing Time Space Tradeoffspromlower-boundadaptation (ai)
	AVPs Are Lengthy Posed as Hypothesis 1.2 and offered both as a working hypothesis and as an ambitious target. Theorem 1.3 proves it implies super-polynomial lower bounds on sd-PIR, general secret sharing and fully-decomposable randomized encodings – for none of which a super-linear lower bound is currently known. The source adapts counting-based arguments to the model but does not reach the best-known bound for any primitive. 4 open	Garbled Circuits Private Information Retrieval Proof Size Lower Bounds Randomized Encodingslower-boundbarrier (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	Coin Tossinglower-bound
	CSAT with Small Space and Preprocessing Conjecture 1.2 of the source, a parameterized family rather than a single claim. Corollary 1.3 turns each parameter setting into a limitation on succinct IOPs. The source attaches decreasing confidence as the class T grows, calling the largest setting only (arguably) unlikely to be false rather than confidently believed. 4 open	Interactive Oracle Proofs Proof Size Lower Bounds Space Bounded Computation Time Space Tradeoffslower-boundbarrier (ai)
	Classical presampling, quantum queries Open, and provably hard to prove: the source’s Theorem 4 shows it implies a central open problem in quantum computing. No refutation has been attempted either, and the source takes no position on which way it goes – it states the conjecture in order to show that the classical technique cannot simply be transplanted. 6 open	Presampling Quantum Query Complexity Quantum Random Oracle Model Random Oracle Modelqromlower-boundbarrier (ai)
	Distance from Lines Modulo a Prime Numbered Conjecture 5.37 of the source, described there as a natural but apparently new number-theoretic conjecture whose study may be of independent interest. Nothing is proved about it; the source notes a deterministic variant might be easier to prove and is still useful. 5 open	Oblivious Linear Evaluation Oblivious Transferlower-bound
	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	Block Ciphers Mirror Theory Pseudorandom Permutationslower-bound
	Double-sided zero search Resolved, unconditionally. Carolan (Compressed Permutation Oracles, ePrint 2025/1734, STOC 2026) proves this exact statement – his Problem 3, p. 72, naming it ‘the double-sided zero search problem, due to Unruh’ – as a corollary (Corollary 7.6) of a general predicate-search lower bound (Theorem 7.5) proved directly from his own compressed permutation oracle’s soundness (Theorem 5.19). Unlike Unruh’s own derivation, this proof does not route through Unruh’s CPO-soundness conjecture (c/0036) at all, so it holds regardless of that conjecture’s status.	Compressed Oracle Quantum Query Complexityotherlower-boundresearch-solved
	RBE needs Ω(log n) updates Refuted. Mahmoody and Qi, Online Mergers and Applications to Registration-Based Encryption and Accumulators (ITC 2023), construct an RBE scheme with O(log n / log log n) decryption updates and poly(kappa, log n) public parameters – strictly below the Omega(log n) this statement conjectured – via a fully online merger structure, matching the known lower bound exactly. The paper states this explicitly resolves the open question. 4 open	Registration Based Encryptionlower-boundresearch-solvedadaptation (ai)
	EA-Code Distance over Rings Theorem 3.10 of the source proves the distance bound over F_2 only. Over a ring of size q its proof technique forces the rate to satisfy R much less than 1/ln q, which the source states it believes is an artefact of the argument, supported by small-parameter weight-distribution experiments over F_17 and Z_16. 5 open	Code Based Cryptography Dual Distance Learning Parity With Noise Pseudorandom Correlation Functionslower-boundadaptation (ai)
	iO Overhead, Single-Output The first of the source’s named main open problems. Its main theorem gives an Omega(s/log s) additive overhead lower bound for iO on multi-output circuits under NP not in BPP – an assumption that is minimal, since a zero-overhead scheme exists if NP is in BPP. The single-output case is not covered, and the source says why: its route runs through NP-hardness of Multi-MCSP. 4 open	Black Box Separations Minimum Circuit Size Problem One Way Functionslower-boundbarrier (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	Black Box Separations Collision Resistant Hashing One Way Functionsotherlower-bound
	Quasi-Abelian GV, Growing Group Named as a conjecture by the source, which says the development is out of reach of the article. It is what makes the choice of group free in the QA-SD line: resistance to every linear test, for any abelian G, reduces to it. Partially advanced in 2026 by concrete non-asymptotic bounds for particular groups, which restate the general question as open. 5 open	Code Based Cryptography Dual Distance Pseudorandom Correlation Functions Syndrome Decodinglower-boundadaptation (ai)
	RBR Soundness Amplification Known in the special case of r-round protocols whose standard and round-by-round soundness errors are maximally separated, eps_RBR about eps^{1/r}; open in general, including the eps^{2/r} regime the source’s own protocol occupies. 4 open	Fiat Shamir Parallel Repetitionlower-bound
	Binary dual-distance bound is the worst case Open, and asserted rather than asked – the source writes that it expects the inequality, gives an intuition covering one of the two competing effects, records that all prior work assumes it, and proves nothing. A probe at small parameters is consistent with it; the parameters the source’s own construction uses are out of computational reach, which is why the source does not check it either. 7 open	Average Case Hardness Dual Distance Learning Parity With Noiselower-boundadaptation (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	Block Ciphers Pseudorandom Permutationslower-bound
	MDSD Linear-Test Bias The source proves a non-tight reduction from standard decisional syndrome decoding and separately conjectures that the DOOM algorithm is the best attack; the linear-test bias is the one quantity it states it cannot bound. 5 open	Learning Parity With Noise Shuffle Model Syndrome Decodinglower-bound
	RBE update bound, key-dependent schedules Resolved. Wei Qi, Tight Lower Bound on Witness Update Frequency in Additive Positive Accumulators (IACR Communications in Cryptology, 2026), generalizes the Mahmoody-Qi-Rahimi lower-bound framework to schedules that may depend on the sampled public keys themselves, via a new combinatorial structure (the falling-step sequence), and proves the same asymptotic bound holds. The paper states this explicitly resolves the open problem left in the source paper. 5 open	Registration Based Encryptionlower-boundresearch-solvedadaptation (ai)