Standard

Status	Statement	Tags
	192-Round AES Pairwise Independence Theorem 7 proves the bound for 192-round censored AES – real AES S-boxes and mixing layer, but a subset of the mixing layers removed. The source conjectures the same round count suffices for AES itself, and calls proving it an outstanding open problem. The best proved bound for actual AES is Liu, Tessaro and Vaikuntanathan’s, which needs more than 9000 rounds. 4 open	Block Ciphers Limited Independence Pseudorandom Permutations T Wise Independencetight-bound
	Balanced Root-n Preprocessing PIR The client-space-times-bandwidth product is settled up to n^{o(1)} by the source’s own matching bounds. What is open is whether client space, bandwidth and per-query server computation can all sit at O~(n^{1/2}) simultaneously; the best known point has client space and server computation O~(n^{2/3}). 4 open	Private Information Retrieval Time Space Tradeoffstight-bound
	CPA PKE, Quantumly Broken The first item in the source’s Open Problems section. It builds counterexamples for PRFs, CPA-secure symmetric-key encryption, MACs, signatures and CCA-2-secure public-key encryption, all classically secure under LWE via black-box reductions and all quantumly broken with two or three classical queries. CPA-secure public-key encryption is the case its technique cannot reach, and it says why. 4 open	Black Box Separations Learning With Errors Quantum Cryptographyseparation
	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)
	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	Search Treestight-bound
	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	Direct Product Theorems Fine Grained CryptographyassumptionIOG
	Perfectly Correct Statistical ARE Statistical security with statistical correctness is settled by the source for every finite function. Perfect correctness is known in the computational setting and, in the statistical setting, only in a relaxed Las Vegas form where the evaluator may declare failure. 4 open	Additive Randomized Encodings Shuffle Modelcharacterizationadaptation (ai)
	Two-scheme key cycle Open in both directions, and the source paper says why the existing separations miss it: the counterexamples fix both schemes, whereas here the second is chosen after the first. Two hypotheses left implicit in the printed statement have to be added before it is even non-vacuous. 7 open	Circular Security Fully Homomorphic Encryptionassumption
	Sources vs Randomness Blowup Conjecture 13 of the source. Its companion question – how many parties must be able to toss coins – is settled exactly by the same paper: t sources for deterministic functionalities, t+1 for randomized ones, even though the adversary may corrupt all of them. What the count costs is not settled. Both halves of the Theta are open. 5 open	Random Sources Randomness Complexitytight-bound
	Standard-model weak PCF from sparse LPN Open, posed by the source as its second open question with an obstruction it names explicitly; the affirmative direction is this page’s reading. An independent follow-up construction reports the same random oracle as inherent to the same recursion. 6 open	Learning Parity With Noise Pseudorandom Correlation Functions Random Oracle Modelassumption
	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)
	Efficient Parity-Tolerance Simulation Feasibility is settled: every circuit can be compiled into a t-parity-tolerant one. What is open is the simulator’s running time, which in the source’s construction is exponential in t; the source gives partial evidence, under LPN, that inefficient simulation may be inherent for a related relaxed notion. 4 open	Leakage Resilient Circuits Learning Parity With Noisecharacterization
	Optimal 2D LPHS Open, and asserted rather than asked: the source prints the algorithm, conjectures the error rate, reports experiments consistent with it, states it could not analyse it, and leaves settling it to future work. The matching lower bound is the source’s own theorem, so a proof would close the two-dimensional case exactly. 7 open	Distributed Discrete Logarithm Generic Group Model Locality Preserving Hashingtight-boundadaptation (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
	Planted k-OV Hardness Conjecture 10 of the source, and a newly proposed average-case assumption rather than a question the literature already asked. Its worst-case counterpart – that k-OV requires n^(k-o(1)) time – is a central conjecture of fine-grained complexity. The planting preserves the marginal distribution of any subset of fewer than k vectors, and the source gives a search-to-decision reduction. 5 open	Average Case Hardness Fine Grained Cryptography Orthogonal Vectors Planted Constraint Satisfactionassumption
	SZK Batch Verification Named by the source as the most pressing open question its work leaves. Its Theorem 1.1 gives the NISZK analogue: communication and CRS length poly(n, log k) for k up to 2⁽ⁿ0.01). A poly(n) dependence is unavoidable even at k = 1 under a sub-exponential hardness assumption, so log k is the aggressive part of the bound. The source also offers a weaker fallback target: any sub-linear dependence on k. 5 open	Batch Verification Direct Product Theorems Limited Independence Randomness Extractioncharacterization
	Sub-log Share Size for 2-out-of-n The information-theoretic share size is exactly log n and Shamir’s scheme matches it. The source proves a (1/5) log log n lower bound for the computational setting with public information, leaving a log n versus log log n gap, and proves that beating log n by any constant factor is equivalent to a concrete planted clique-and-independent-set problem. 4 open	Average Case Hardness Planted Subgraph Problems Threshold Secret Sharingtight-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)
	Almost k-Wise Locality Gap Settled up to a log n factor at word size 1 and at word size Omega(log^2 n) and above; the source gives no matching construction at all for intermediate word sizes, so the gap is recorded only where both a bound and a construction exist to compare. 4 open	Limited Independence Locally Computable Hashingtight-boundadaptation (ai)
	SBP Collision Resistance Posed as a displayed Open Question and called a central open challenge. The source gives an efficient online collision finder for small kappa and an overlap-gap-based online lower bound for a different, randomized activation – introduced precisely because the SBP’s own collision space resists a first-moment analysis. For very large kappa collisions become trivial. The middle window is reached by neither technique. 4 open	Average Case Hardness Collision Resistant Hashing Overlap Gap Property Planted Constraint Satisfactionseparation
	Sublinear-Time CGKA Refresh The source achieves worst-case sublinear communication with forward secrecy, but its refresh algorithms still run in time polynomial in the group size, and it leaves open, without committing to a specific target rate, whether sublinear-time refresh is achievable at all. 4 open	Broadcast Encryption Continuous Group Key Agreementcharacterization
	Conflict Checkable Codes Beyond Half-Singleton Theorem 1.8 proves k <= (n-d+2)/2 for codes that are both comparison-based and local-to-global consistent. Theorem 1.3 gives an almost-MDS conflict checkable code at k >= n-d+1-epsilon which bypasses that bound, but it is neither comparison-based nor known to be local-to-global consistent. The conjecture names comparison-basedness as the culprit. It already holds at d = n-1. 4 open	Code Based Cryptography Locally Testable Codes Threshold Secret Sharingseparationadaptation (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	Byzantine Agreementtight-boundIOG
	Constant-Overhead AMD Circuits Polylogarithmic overhead in \|C\| and lambda is achieved by Genkin, Ishai and Weiss; constant overhead is open. The source’s Theorem 43 shows that achieving it would – together with the source’s own constant-overhead OT protocol – settle the main open question on constant-overhead secure computation for general Boolean circuits. 4 open	Fault Tolerant Circuits Oblivious Transfercharacterization
	Degree-2 Statistical RE Question 1.6 of the harvested paper, attributed there to Ishai-Kushilevitz and Applebaum-Ishai-Kushilevitz and described as open for almost 20 years. Degree-3 statistical encodings exist for every finite function; negative results are known for perfectly private degree 2. The harvested paper adds a new consequence, its Proposition 1.7. 4 open	Arithmetic Cryptography Non Interactive Secure Computation Randomized Encodingscharacterizationbarrier (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
	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	Quantum Cryptography Quantum Encryption Notionsseparation
	Composability implies circular security Open with no partial result in either direction. The converse – circular security plus limited homomorphism gives full composability – is the source paper’s Theorem 6; this direction, which would make the two properties essentially equivalent, is conjectured there and nothing has been published towards it. 7 open	Circular Security Fully Homomorphic Encryptionequivalence
	Seeded Extractors Are Multi-Instance Posed by the source with both answers live. It proves the property for two code-based extractors via a hinting property it isolates; concurrent independent work of Dinur, Stemmer, Woodruff and Zhou proves it for universal hash functions by a different argument. No extractor is known to fail it and no general proof is known. 4 open	Incompressible Encryption Randomness Extractioncharacterization
	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
	DPP Field Size The small-field regime is settled: soundness Theta(1/sqrt q) is achieved and proved optimal. In the large-field regime the source achieves soundness eps for every prime p at least Omega~(S^9/eps6) and states in as many words that it believes the S-dependence is not tight. 4 open	Linear Pcps Snarkstight-boundadaptation (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	Search Treestight-bound
	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	Limited Independence Pseudorandom Permutationscharacterization
	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)
	NISC Overhead from a PRG The source poses this question and then answers the variant in which the pseudorandom generator is replaced by a random oracle, which leaves the question as posed unresolved. Each of the four relaxations – polylogarithmic overhead, correlated-abort security, extra rounds, or programmable OLE correlations – is already known. 4 open	Garbled Circuits Non Interactive Secure Computationcharacterizationadaptation (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)
	SK-DEPIR from One-Way Functions Stated by the source as its own conjecture and proved for two-round passive-server schemes. Its main theorem – that any crypto oracle can be stripped out of a SK-DEPIR and replaced by a one-way function – is stated conditionally on this, so the conjecture is the single remaining hypothesis between that compiler and a clean statement that no idealized generic primitive helps. 4 open	Black Box Separations One Way Functions Private Information Retrievalimpossibility
	No expanding weak quadratic PRGs Open: whether every family of quadratic Λ(n)-bounded polynomials at stretch m ≥ n^{1+ε} admits an efficient distinguisher from the same evaluations plus bounded independent noise; the paper proves only the i.i.d.-nice special case (Theorem 2) and reports, without proof, that no degree-two candidate survives its attacks experimentally. 3 open	Average Case Hardness Pseudorandom Generatorsimpossibility
	No Self-Reduction for LSN Conjecture 5.20 of the source. It proves no random self-reduction exists from an arbitrary worst-case QNCP instance into LSN, naming exchange symmetry between code and error as the obstruction, and proves the tableau-randomizing barrier conditionally on the scrambling gap being polynomially related to eps. It is explicit that this is not an impossibility for random self-reductions in general. 4 open	Average Case Hardness Learning Parity With Noise Quantum Information Stabilizer Codesimpossibilityadaptation (ai)
	No 2-element split NILPs A submitted construction gives a two-element split NILP for Boolean circuit satisfiability in the plain generic Type-III bilinear-group model; proof review and formalization remain open. 2 open	Generic Group Model Proof Size Lower Bounds Snarksimpossibilityresearch-solved
	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)
	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	Quantum Cryptography Quantum Encryption Notionsseparation
	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	Quantum Cryptography Quantum Encryption Notionsseparation
	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. 4 open	One Shot Signatures Witness EncryptionassumptionIOG
	Arithmetic Two-Server PIR Optimality O(n^{1/3}) is achieved by arithmetizing the classical two-server schemes. The source states that whether it can be improved – let alone brought to sub-polynomial – is unknown, and supplies a linear-algebraic characterization of exactly what an improvement would require. 5 open	Arithmetic Cryptography Private Information Retrievaltight-bound
	Perfect FASS at 3-out-of-5 Statistical and computational FASS are settled by the source and prior work. The perfect version is stated by the source to be open for every reconstruction threshold 3 <= t <= n-2, and open even for the weaker multi-dealer notion, with 3-out-of-5 the smallest open case. Con has settled the perfect case for gap threshold structures. 5 open	Anonymity Threshold Secret Sharingcharacterizationadaptation (ai)
	Polylog Shuffle PIR, Negligible Error Settled in three neighbouring corners: O(n^gamma) communication with inverse-polynomial error and polynomially many queries; polylogarithmic communication with n^{O(log n)} queries; and negligible error with O(n/log n) communication. The polylogarithmic-and-negligible corner with polynomially many queries is open, and is ruled out for inner-outer constructions with an additive inner layer by the source’s own Theorem 6.5. 5 open	Private Information Retrieval Shuffle Modelcharacterizationadaptation (ai)
	Blockwise-random quadratic recovery Open: whether there is a polynomial-time algorithm that provably recovers the planted input from m = n^{1+eps} published quadratics of the blockwise-random (Lin-Matt) form, sum of a random sparse (perfect-matching) part and an independent random dense part. The paper proves this for i.i.d.-nice polynomial distributions (Theorem 2) but the blockwise-random distribution is not nice, and reports only experimental recovery via a modified semidefinite program. 5 open	Average Case Hardness Pseudorandom Generatorsassumption
	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	Black Box Separations One Way Functions Quantum Cryptographyequivalence
	RS Proximity Gaps to Capacity Proved up to the Johnson/Guruswami-Sudan bound delta < 1 - sqrt(rho); conjectured up to capacity delta <= 1 - rho - eta. The source records that nothing known contradicts c1 = c2 = 2, and that in characteristic greater than the degree nothing known contradicts c1 = c2 = 1 – while those smaller exponents are provably ruled out in characteristic two. 5 open	Proximity Testing Reed Solomon Codes Snarkstight-boundbarrier (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.	Average Case Hardness Planted Constraint Satisfactionseparationbarrier (ai)
	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)
	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	Learning With Errorsequivalence
	RM Gap to Capacity for BEC Conjecture 14 of the source. That Reed-Muller codes achieve capacity for the BEC is a theorem of Kudekar et al.; the gap to capacity – a polynomial rate of convergence – is open. The source needs it to strengthen its refutation of the expansion-implies-hardness conjecture for noisy k-XOR from quasi-polynomially many constraints to polynomially many, and notes the question was raised explicitly in three prior works. 4 open	Average Case Hardness Code Based Cryptography Expander Graphs Reed Solomon Codestight-bound
	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
	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.	Average Case Hardness Expander Graphsseparation
	Signed rank-one reweighting below the square root Resolved, affirmatively and more strongly than asked: every Borel probability measure on the sphere admits a signed reweighting reaching an exact (not merely epsilon-close) nonzero rank-one second moment at entropy cost only O(log n) – below every n^delta, for every delta > 0, with the constant C(epsilon,delta) = 2/(e*delta) independent of epsilon. Proved by an AI-driven proof harness (conjecture-harness campaign c/0048) across six revision rounds, twenty independent blind adversarial referee passes over four audited rounds, and four independent triage rulings; the load-bearing chain (Lemmas 1-4, Theorem, Corollary, Corollary B) has never had an upheld finding against it. No human has reviewed the mathematics, and nothing here is formalized in Lean. A separate concurrent session forked the same campaign at round 3 and closed the same scope-commentary gap by a different (but mathematically equivalent) edit; both branches are recorded in the campaign ledger and the fork is not yet reconciled. 6 open	Log Rank Conjecture Sum Of Squaresassumptionresearch-solved
	SSS Implies Fiat-Shamir Friendly Conjecture 1.3 of the source. It is explicit that it does not prove it – ‘only conjecture it’ – and asks for the proof or refutation as an important open problem. It does prove that SSS implies straight-line soundness, hence post-quantum soundness, and that its own instantiation of Kilian’s protocol is SSS. 4 open	Commitment Schemes Fiat Shamir Snarkscharacterization
	Hold-Out Soundness, Dirty Coordinates The source’s distinguishing attack is unconditional and proved. Its decryption attack is heuristic, and this is the unproved step: completeness on clean coordinates is its Claim 6.2, while soundness on dirty ones is supported only by a heuristic dimension count and small-parameter experiments. 5 open	Code Based Cryptography Private Information Retrievalcharacterization
	Statistical Robust ARE The source asks whether all functions admit a statistically secure ARE, robust or non-robust, and strongly conjectures the answer is negative. The non-robust half was refuted: Bitansky, Erabelli, Garg and Ishai construct statistical AREs for all finite functions. The robust half is open, and is re-posed by that later work. 4 open	Additive Randomized Encodings Randomized Encodingscharacterization
	Best Separable State, constant completeness error Open: whether the paper’s 2^{Otilde(sqrt n)}-time algorithm for Best Separable State extends from perfect (and near-perfect, 1-1/n) completeness to any constant completeness error c < 1. The paper conjectures the affirmative and lists this first among its open questions; no partial result at any intermediate error is reported. 5 open	Quantum Information Sum Of Squaresassumption
	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
	Randomness Complexity of XOR The source proves an Omega(t^2) lower bound, matching Kushilevitz and Mansour’s non-explicit O(t^2 log(n/t)) upper bound up to a logarithmic factor, and up to a constant factor when t = Omega(n). It also gives an explicit protocol at O(t^2 log^2 n). It states it leaves the remaining polylogarithmic gaps open. 4 open	Limited Independence Randomness Complexitytight-bound
	Permuted Codes Conjecture A new hardness assumption, printed as Conjecture 3.1 of the source and stated in its most general form deliberately, as a target for cryptanalysis rather than as the minimum its applications need. Implied by the older permuted puzzles conjecture; statistically true for O(log n) samples over constant-size alphabets; false if any one of its three randomizations is dropped. 4 open	Code Based Cryptography Dual Distance Pseudorandom Codes Watermarkingassumptionbarrier (ai)
	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
	CHV Online Threshold Conjecture 1 of the source, its online threshold conjecture. The source gives an online algorithm achieving kappa = O(sqrt(alpha)/B) and an overlap-gap argument against stable algorithms; the conjecture pins the constant sqrt(pi/8) as the exact place where online algorithms stop. Separately it proves, under worst-case lattice hardness, that no polynomial-time algorithm solves CHV for kappa = O(1/(B n^(1/2+eps))). 4 open	Average Case Hardness Collision Resistant Hashing Locality Preserving Hashing Overlap Gap Propertytight-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)
	WP Threshold Share Size The 2-out-of-n case is settled: Beimel and Franklin give 1/n-weakly-private schemes with share size 2, against Theta(log n) for perfect privacy. The source states large thresholds are open and asks specifically about (n-1)-out-of-n at share size o(log n). 5 open	Threshold Secret Sharingcharacterizationadaptation (ai)
	XOR as a Weak 2-Immunizer The single unresolved cell in the source’s own table: XOR fails as a strong 2-immunizer under Alekhnovich, a bilinear pairing fails as a weak one under SXDH, a random oracle succeeds even with auxiliary input. The weak case for XOR is left open with a conjectured answer and a concrete route to it. 4 open	Backdoored Primitives Black Box Separations Pseudorandom Generatorsseparationadaptation (ai)
	AES t-Wise Independence, t > 2 Named by the source as the first of the two outstanding open problems that come of its work. It proves almost pairwise independence (t = 2) for multi-round AES with independent round keys, and an existential t-wise result for key-alternating ciphers with most permutations, but nothing for concrete AES beyond t = 2. Its Appendix B attacks 4-wise independence in the width-1 case with the same S-box. 4 open	Block Ciphers Limited Independence Pseudorandom Permutations T Wise Independencecharacterizationbarrier (ai)