Random Oracle Model
Statements set in the classical (non-quantum) random oracle model.
| Status | Statement | Tags |
|---|---|---|
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Subexponential-query PCF from sparse LPN Open in both directions, and the source paper poses it as a question rather than conjecturing an answer; the affirmative direction is this page’s reading. The one follow-up construction from sparse LPN inherits the same superpolynomial ceiling and says so. 6 open |
Learning Parity With NoisePseudorandom Correlation FunctionsRandom Oracle Modelromassumption | |
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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 NoisePseudorandom Correlation FunctionsRandom Oracle Modelassumption | |
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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 |
PresamplingQuantum Query ComplexityQuantum Random Oracle ModelRandom Oracle Modelqromlower-boundbarrier (ai) | |
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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 ExtractorsRandom Oracle ModelRandomness Extractionromtight-bound | |
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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 LemmaRandom Oracle ModelRandomness Extractionromtight-boundresearch-solvedadaptation (ai) | |
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Computationally unique VDFs in the ROM Resolved. Guan, Riazanov and Yuan, Breaking Verifiable Delay Functions in the Random Oracle Model (ePrint 2024/766, CRYPTO 2025), prove that no VDF in the parallel ROM can have completeness and computational uniqueness and be sigma-sequential for sigma a fixed polynomial in the security parameter and the Setup/Verify query counts – their Theorem 5.1, which in fact covers general (not just perfect) completeness error, strictly more than this conjecture asked for. The proof is human-authored and published; it has not yet been independently re-derived by this site or formalized in Lean. 3 open |
Black Box SeparationsRandom Oracle ModelVerifiable Delay Functionsromimpossibilityresearch-solved | |
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Salt Length vs. Call Count Fully open in both directions: no construction with \(O(\lambda)\)-length, message-independent salts and \(O(1)\) Merkle-Damgård calls is known, and no proof that none can exist, nor any trade-off between the two, has been given either. 4 open |
IndifferentiabilityRandom Oracle Modelromcharacterization | |
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Short-Salt MD Combiner Security Open in both directions: the source’s Theorem 3.1 proves security only when salts exceed the message by at least the security parameter, and reports neither an attack nor a security proof once the salts shrink to a constant number of blocks. 4 open |
IndifferentiabilityRandom Oracle Modelromcharacterizationadaptation (ai) | |
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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 FindingRandom Oracle ModelTime Space Tradeoffsromtight-boundadaptation (ai) | |
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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 FindingCollision Resistant HashingRandom Oracle ModelTime Space Tradeoffsromtight-boundbarrier (ai) | |
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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 |
Blind SignaturesRandom Oracle ModelSignature SchemesTight Reductionsromassumption | |
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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 FindingRandom Oracle ModelTime Space Tradeoffsromtight-bound |
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