Outline and contributions of this thesis Sample Clauses

Outline and contributions of this thesis. Section 1.2
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Outline and contributions of this thesis. In this dissertation, we will introduce new techniques that facilitate security reductions in the quantum random-oracle model. We present them alongside a number of applications, obtaining rigorous relations between the security of post-quantum cryptosystems and the hardness of certain computational prob- lems. The main chapters are based on the following papers: [DFMS19] Xxxxx Xxx, Xxxxx Xxxx, Xxxxxxxxx Xxxxxx, and Xxxxxxxxx Xxxxxxxxx. “Security of the Fiat-Shamir Transformation in the Quantum Random-Oracle Model”. In:Advances in Cryptology – CRYPTO 2019. Ed. by Xxxxxxxxx Xxxxxxxxx and Xxxxxxx Xxxxxxxxxx. Cham: Springer International Publishing, 2019, pp. 356–383. [DFM20] Xxxxx Xxx, Xxxxx Xxxx, and Xxxxxxxxx Xxxxxx. “The Measure-and- Reprogram Technique 2.0: Multi-round Fiat-Shamir and More”. In:Advances in Cryptology – CRYPTO 2020. Ed. by Xxxxxxx Xxx- xxxxxxx and Xxxxxx Xxxxxxxxxx. Cham: Springer International Publishing, 2020, pp. 602–631. [DFMS22a] Xxxxx Xxx, Xxxxx Xxxx, Xxxxxxxxx Xxxxxx, and Xxxxxxxxx Xxxxxxxxx. “Online-Extractability in the Quantum Random-Oracle Model”. In:Advances in Cryptology – EUROCRYPT 2022. Ed. by Xxx Xxxxxxxxx and Xxxxxx Xxxxxxxxxxx. Cham: Springer Interna- tional Publishing, 2022, pp. 677–706. [DFMS22b] Xxxxx Xxx, Xxxxx Xxxx, Xxxxxxxxx Xxxxxx, and Xxxxxxxxx Xxxxxxxxx. “Efficient NIZKs and Signatures from Commit-and-Open Proto- cols in the QROM”. In:Advances in Cryptology – CRYPTO 2022. Ed. by Xxxxxxxx Xxxxx and Xxxxxx Xxxxxxxxx. Cham: Springer Nature Switzerland, 2022, pp. 729–757. In the course of his PhD, the author has additionally co-authored the fol- lowing papers, which are not included in this thesis: [DFH22] Xxxxx Xxx, Xxxxx Xxxx, and Xx-Xxxxx Xxxxx. “Adaptive Versus Static Multi-oracle Algorithms, and Quantum Security of a Split- Key PRF”. In:Theory of Cryptography. Ed. by Xxxx Xxxxx and Xxxxx Xxxxxxxxxxxxxx. Cham: Springer Nature Switzerland, 2022, pp. 33–51.isbn: 978-3-031-22318-1.
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Outline and contributions of this thesis hash based commitment that we model as a random oracle – at least in the classical case,online extraction[Fis05] is possible. ‘Online’ in this case means straight-line (no rewinding) and on-the-fly (during protocol execution and with- out disturbing it). Rewinding often causes a reduction loss (because we need the adversary to succeed twice) and evidently a disturbance in the adversary’s state causes a loss as well. If possible, online extraction is thus the preferred option. A Building upon the compressed oracle framework [Zha19a], in this chapter we introduce a statistically indistinguishable simulator for a quantum random oracle, with both a query and an extraction interface. We show the following generic result: Consider an arbitrary quantum query algorithm in the QROM, which announces during its execution some classical valuetthat is supposed to be equal tof(x, H(x))for somex. Here,fis an arbitraryfixed function, subject to that it must tietsufficiently toxandH(x), e.g., there must not be too many y’s withf(x, y) =t; a canonical example is the functionf(x, y) =yso thatt is supposed to bet=H(x). In general, it is helpful to think oft=f(x, H(x)) A ∅ A as a commitment tox. We then show thatxcan be efficiently online-extracted with almost certainty, by queryingtto the extraction interface of our simulator, obtaining a ‘guess’ˆx. Whenever outputsxwithf(x, H(x)) =tat some later point,ˆx=xholds except with negligible probability, whileˆx= (some special symbol) indicates that will not be able to output such anx. At the core of our result is a new commutator bound, that quantifies the potential disturbance caused by swapping an extraction measurement of the compressed oracle with a random-oracle query from the adversary. If the above relation is tight enough, the disturbance is negligible, and we can thus freely add extraction queries by inserting them at the end of the adverary’s run and then swapping them up to any point aftertwas put on the table. Thus, under the right circumstances, online extraction is possible in the QROM as well. As a not unimportant side-effect, the abstraction of our simulator, with its extraction interface and properties formulated in classical terms, cryptog- raphers with no background in quantum information theory can argue about such examples as the above (in the QROM!) using only classical reasoning. Ourfirst main application is to so-called ‘commit-and-open protocols’. C&O protocols form a subclass ofΣ-protocols, were thefirst m...
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Outline and contributions of this thesis and-reprogram technique, inflicting a(2q+1) 2 multiplicative loss for the success probability of the reduction. Xxxxx Xxxxxxxxx was thefirst to aim for online extractability of the Fiat- Shamir transformation in the QROM for this class of protocols. Indeed, the Fiat-Shamir transformation of C&OΣ-protocols are known to be online ex- tractable in the classical ROM (see e.g. discussion in [Fis05]). In afirst at- tempt [Cha19], Xxxxxxxxx tried to lift the argument to the quantum setting by means of Xxxxxxx’x compressed-oracle technique [Zha19a], which offers a pow- erful approach for re-establishing ROM results in the QROM, that has been successful in many instances. Unfortunately, thisfirst attempt contained a sub- tleflaw, which turned out to be unfixable, and despite changing the technical approach, the latest version [Cha21] of this work still contains a gap in the proof, which is put as an assumption. || The situation is complicated because the adversary queries the random or- acle to determine both itsfirst messagey=H(m)(consisting of a set of hash- based commitments) and the corresponding challenge (computed asH(x y)), and may use these queries to search for a suitable commitment-challenge pair that allows it to pass verification without actually knowing the witness. To tackle the problem, we build upon and slightly extend the [CFHL21] framework for the compressed oracle. [CFHL21] introduced the notion of ‘quan- tum transition capacity’ of two ‘database properties’P,P ′, a measure of how much more likely we are tofind the recorded queries of the compressed ora- cle to satisfy a propertyP ′ after each query by the adversary, if the database started inP. Wefirst extend the framework by proving a revised version of the main theorem that bounds a quantum transition capacity in terms of the considered properties. In our security reduction we then define a database prop- erty of exactly the case described above, where the queries to the oracle allow the adversary tofind a commitment-challenge pair that help him forge a proof without knowing a witness. We are then able to show that quantum transition capacity from the empty to this special database is small, i.e. for a bounded query algorithm the described situation can be achieved only with negligible probability. Our security reduction is tight: Whenever a prover outputs a valid proof, the online-extractor succeeds, except with a small probability accounting for collision and preimage attacks on the involved...
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