Tight Bound

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
	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
	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
	Quantum two-block MD collisions Open, in both directions and with no partial result: whether the best known quantum preprocessing attack, of advantage ST^2/N + T^3/N, is optimal for two-block Merkle-Damgård collisions. The source reports that no matching quantum bounds are known at any block length. 7 open	Collision Finding Collision Resistant Hashing Quantum Query Complexity Quantum Random Oracle Model Time Space Tradeoffsqromtight-bound
	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)
	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
	One Haar State Looks Like Many Stated in the source’s Open Problems section as a conjecture it believes true, with the note that it could neither prove it nor find it proved or even formalised anywhere. The source proves a strictly weaker pointwise domination bound, its Lemma 2, sufficient for its own applications and silent about total variation distance. 5 open	Pseudorandom Quantum States Quantum Cryptography Quantum Informationothertight-boundadaptation (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)
	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
	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	Multi Source Extractors Random Oracle Model Randomness Extractionromtight-bound
	r-round DLOG tradeoff Open for every intermediate r: the r = 1 endpoint is the source’s own theorem and r = T is Corrigan-Gibbs–Kogan, with nothing proved in between. The source conjectures the interpolating formula and says a matching attack exists at every r, so the missing half is the lower bound. 6 open	Adaptivity Discrete Logarithm Generic Group Model Time Space Tradeoffsggmtight-bound
	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	Feistel Networks Indifferentiability Pseudorandom Permutationsothertight-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)
	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. 6 open	Leftover Hash Lemma Random Oracle Model Randomness Extractionromtight-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	Search Treestight-bound
	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
	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)
	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
	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	Collision Finding Random Oracle Model Time Space Tradeoffsromtight-boundadaptation (ai)
	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
	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
	Non-adaptive DDH bound Open, and asserted rather than asked: the source proves 1/2 + O~(T^2/N + sqrt(ST/N)), states twice that it conjectures this is not tight for DDH, and names 1/2 + O~(T^2/N + ST/N) as the right answer. The same theorem’s square-DDH bound is sharp, with a matching attack, which is what makes the DDH case a question rather than a suspicion. 6 open	Adaptivity Discrete Logarithm Generic Group Model Time Space Tradeoffsggmtight-boundadaptation (ai)
	STB conjecture (Merkle-Damgård) Open for non-constant B in the regime ST^2 > 2^n, where the best published security bound and the best published attack are a factor of up to S apart; settled at B=1, B=2, every constant B, B~T, and every 2<B<T with ST^2 <= 2^n. 6 open	Collision Finding Collision Resistant Hashing Random Oracle Model Time Space Tradeoffsromtight-boundbarrier (ai)
	STB conjecture (sponge) Open for every B >= 2 except B ~ T: at B=2 in the regime ST^3 > C, and at B >= 3 with a gap of about T/B. The source asks for a proof or a refutation and takes no position. 7 open	Collision Finding Collision Resistant Hashing Time Space Tradeoffspromtight-boundbarrier (ai)
	Single-session lattice Chevallier-Mames tightness Open: whether the one-session lattice translation of the Chevallier-Mames signature has a tight SUF-CMA reduction to search Module-LWE, or whether the paper’s two-fold parallel repetition (which doubles signature size and signing time) is inherent to a tight proof of this shape. 4 open	Learning With Errors Signature Schemes Tight Reductionsromtight-bound
	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	Collision Finding Random Oracle Model Time Space Tradeoffsromtight-bound