Serge Fehr

Jelle Don, Serge Fehr, Christian Majenz et al.

Commit-and-open Sigma-protocols are a popular class of protocols for constructing non-interactive zero-knowledge arguments and digital-signature schemes via the Fiat-Shamir transformation. Instantiated with hash-based commitments, the resulting non-interactive schemes enjoy tight online-extractability in the random oracle model. Online extractability improves the tightness of security proofs for the resulting digital-signature schemes by avoiding lossy rewinding or forking-lemma based extraction. In this work, we prove tight online extractability in the quantum random oracle model (QROM), showing that the construction supports post-quantum security. First, we consider the default case where committing is done by element-wise hashing. In a second part, we extend our result to Merkle-tree based commitments. Our results yield a significant improvement of the provable post-quantum security of the digital-signature scheme Picnic. Our analysis makes use of a recent framework by Chung et al. [arXiv:2010.11658] for analysing quantum algorithms in the QROM using purely classical reasoning. Therefore, our results can to a large extent be understood and verified without prior knowledge of quantum information science.

Jelle Don, Serge Fehr, Christian Majenz et al.

We show the following generic result. Whenever a quantum query algorithm in the quantum random-oracle model outputs a classical value $t$ that is promised to be in some tight relation with $H(x)$ for some $x$, then $x$ can be efficiently extracted with almost certainty. The extraction is by means of a suitable simulation of the random oracle and works online, meaning that it is straightline, i.e., without rewinding, and on-the-fly, i.e., during the protocol execution and without disturbing it. The technical core of our result is a new commutator bound that bounds the operator norm of the commutator of the unitary operator that describes the evolution of the compressed oracle (which is used to simulate the random oracle above) and of the measurement that extracts $x$. We show two applications of our generic online extractability result. We show tight online extractability of commit-and-open $Σ$-protocols in the quantum setting, and we offer the first non-asymptotic post-quantum security proof of the textbook Fujisaki-Okamoto transformation, i.e, without adjustments to facilitate the proof.

Kai-Min Chung, Serge Fehr, Yu-Hsuan Huang et al.

We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends to the parallel-query QROM, where in each query-round the considered algorithm may make several queries to the QROM in parallel. This variant of the QROM allows for a more fine-grained query-complexity analysis. Our main technical contribution is a framework that simplifies the use of (the parallel-query generalization of) the compressed oracle technique for proving query complexity results. With our framework in place, whenever applicable, it is possible to prove quantum query complexity lower bounds by means of purely classical reasoning. More than that, for typical examples the crucial classical observations that give rise to the classical bounds are sufficient to conclude the corresponding quantum bounds. We demonstrate this on a few examples, recovering known results (like the optimality of parallel Grover), but also obtaining new results (like the optimality of parallel BHT collision search). Our main target is the hardness of finding a $q$-chain with fewer than $q$ parallel queries, i.e., a sequence $x_0, x_1,\ldots, x_q$ with $x_i = H(x_{i-1})$ for all $1 \leq i \leq q$. The above problem of finding a hash chain is of fundamental importance in the context of proofs of sequential work. Indeed, as a concrete cryptographic application of our techniques, we prove that the "Simple Proofs of Sequential Work" proposed by Cohen and Pietrzak remains secure against quantum attacks. Such an analysis is not simply a matter of plugging in our new bound; the entire protocol needs to be analyzed in the light of a quantum attack. Thanks to our framework, this can now be done with purely classical reasoning.

Jelle Don, Serge Fehr, Christian Majenz

We revisit recent works by Don, Fehr, Majenz and Schaffner and by Liu and Zhandry on the security of the Fiat-Shamir transformation of $Σ$-protocols in the quantum random oracle model (QROM). Two natural questions that arise in this context are: (1) whether the results extend to the Fiat-Shamir transformation of multi-round interactive proofs, and (2) whether Don et al.'s $O(q^2)$ loss in security is optimal. Firstly, we answer question (1) in the affirmative. As a byproduct of solving a technical difficulty in proving this result, we slightly improve the result of Don et al., equipping it with a cleaner bound and an even simpler proof. We apply our result to digital signature schemes showing that it can be used to prove strong security for schemes like MQDSS in the QROM. As another application we prove QROM-security of a non-interactive OR proof by Liu, Wei and Wong. As for question (2), we show via a Grover-search based attack that Don et al.'s quadratic security loss for the Fiat-Shamir transformation of $Σ$-protocols is optimal up to a small constant factor. This extends to our new multi-round result, proving it tight up to a factor that depends on the number of rounds only, i.e. is constant for any constant-round interactive proof.

Jelle Don, Serge Fehr, Christian Majenz et al.

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called sigma-protocol, into a non-interactive proof in the random-oracle model. We study this transformation in the setting of a quantum adversary that in particular may query the random oracle in quantum superposition. Our main result is a generic reduction that transforms any quantum dishonest prover attacking the Fiat-Shamir transformation in the quantum random-oracle model into a similarly successful quantum dishonest prover attacking the underlying sigma-protocol (in the standard model). Applied to the standard soundness and proof-of-knowledge definitions, our reduction implies that both these security properties, in both the computational and the statistical variant, are preserved under the Fiat-Shamir transformation even when allowing quantum attacks. Our result improves and completes the partial results that have been known so far, but it also proves wrong certain claims made in the literature. In the context of post-quantum secure signature schemes, our results imply that for any sigma-protocol that is a proof-of-knowledge against quantum dishonest provers (and that satisfies some additional natural properties), the corresponding Fiat-Shamir signature scheme is secure in the quantum random-oracle model. For example, we can conclude that the non-optimized version of Fish, which is the bare Fiat-Shamir variant of the NIST candidate Picnic, is secure in the quantum random-oracle model.

Thomas Attema, Emiliano Mancini, Gabriele Spini et al.

Background: Clinical decision support systems (CDSS) are a category of health information technologies that can assist clinicians to choose optimal treatments. These support systems are based on clinical trials and expert knowledge; however, the amount of data available to these systems is limited. For this reason, CDSSs could be significantly improved by using the knowledge obtained by treating patients. This knowledge is mainly contained in patient records, whose usage is restricted due to privacy and confidentiality constraints. Methods: A treatment effectiveness measure, containing valuable information for treatment prescription, was defined and a method to extract this measure from patient records was developed. This method uses an advanced cryptographic technology, known as secure Multiparty Computation (henceforth referred to as MPC), to preserve the privacy of the patient records and the confidentiality of the clinicians' decisions. Results: Our solution enables to compute the effectiveness measure of a treatment based on patient records, while preserving privacy. Moreover, clinicians are not burdened with the computational and communication costs introduced by the privacy-preserving techniques that are used. Our system is able to compute the effectiveness of 100 treatments for a specific patient in less than 24 minutes, querying a database containing 20,000 patient records. Conclusion: This paper presents a novel and efficient clinical decision support system, that harnesses the potential and insights acquired from treatment data, while preserving the privacy of patient records and the confidentiality of clinician decisions.

Frédéric Dupuis, Serge Fehr, Philippe Lamontagne et al.

We prove a general relation between adaptive and non-adaptive strategies in the quantum setting, i.e., between strategies where the adversary can or cannot adaptively base its action on some auxiliary quantum side information. Our relation holds in a very general setting, and is applicable as long as we can control the bit-size of the side information, or, more generally, its "information content". Since adaptivity is notoriously difficult to handle in the analysis of (quantum) cryptographic protocols, this gives us a very powerful tool: as long as we have enough control over the side information, it is sufficient to restrict ourselves to non-adaptive attacks. We demonstrate the usefulness of this methodology with two examples. The first is a quantum bit commitment scheme based on 1-bit cut-and-choose. Since bit commitment implies oblivious transfer (in the quantum setting), and oblivious transfer is universal for two-party computation, this implies the universality of 1-bit cut-and-choose, and thus solves the main open problem of [FKSZZ13]. The second example is a quantum bit commitment scheme proposed in 1993 by Brassard et al. It was originally suggested as an unconditionally secure scheme, back when this was thought to be possible. We partly restore the scheme by proving it secure in (a variant of) the bounded quantum storage model. In both examples, the fact that the adversary holds quantum side information obstructs a direct analysis of the scheme, and we circumvent it by analyzing a non-adaptive version, which can be done by means of known techniques, and applying our main result.