arXiv subjects

Christian Majenz

Publications and source records attributed to Christian Majenz.

At least 37 records · Page 2Linked to original sources

arXiv2021

Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives. We develop a quantum game-playing proof framework by generalizing two recently developed proof techniques. First, we describe how Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy sampling of a class of non-uniform function distributions. Second, we observe how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied to compressed oracles, providing a quantum counterpart to the fundamental lemma of game-playing. Subsequently, we use our game-playing framework to prove quantum indifferentiability of the sponge construction, assuming a random internal function.

quant-ph↗

arXiv2021

A Guide for New Program Committee Members at Theoretical Computer Science Conferences

In theoretical computer science, conferences play an important role in the scientific process. The decisions whether to accept or reject articles is taken by the program committee (PC) members. Serving on a PC for the first time can be a daunting experience. This guide will help new program-committee members to understand how the system works, and provide useful tips and guidelines. It discusses every phase of the paper-selection process, and the tasks associated to it.

cs.GL↗

arXiv2021

Non-malleability for quantum public-key encryption

Non-malleability is an important security property for public-key encryption (PKE). Its significance is due to the fundamental unachievability of integrity and authenticity guarantees in this setting, rendering it the strongest integrity-like property achievable using only PKE, without digital signatures. In this work, we generalize this notion to the setting of quantum public-key encryption. Overcoming the notorious "recording barrier" known from generalizing other integrity-like security notions to quantum encryption, we generalize one of the equivalent classical definitions, comparison-based non-malleability, and show how it can be fulfilled. In addition, we explore one-time non-malleability notions for symmetric-key encryption from the literature by defining plaintext and ciphertext variants and by characterizing their relation.

quant-ph↗

arXiv2020

Tight adaptive reprogramming in the QROM

The random oracle model (ROM) enjoys widespread popularity, mostly because it tends to allow for tight and conceptually simple proofs where provable security in the standard model is elusive or costly. While being the adequate replacement of the ROM in the post-quantum security setting, the quantum-accessible random oracle model (QROM) has thus far failed to provide these advantages in many settings. In this work, we focus on adaptive reprogrammability, a feature of the ROM enabling tight and simple proofs in many settings. We show that the straightforward quantum-accessible generalization of adaptive reprogramming is feasible by proving a bound on the adversarial advantage in distinguishing whether a random oracle has been reprogrammed or not. We show that our bound is tight by providing a matching attack. We go on to demonstrate that our technique recovers the mentioned advantages of the ROM in three QROM applications: 1) We give a tighter proof of security of the message compression routine as used by XMSS. 2) We show that the standard ROM proof of chosen-message security for Fiat-Shamir signatures can be lifted to the QROM, straightforwardly, achieving a tighter reduction than previously known. 3) We give the first QROM proof of security against fault injection and nonce attacks for the hedged Fiat-Shamir transform.

quant-ph↗

arXiv2020

Weak approximate unitary designs and applications to quantum encryption

Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm. Math. Phys. 2009), we prove that sampling $d^t\mathrm{poly}(t,\log d, 1/ε)$ unitaries from an exact $t$-design provides with positive probability an $ε$-approximate $t$-design, if the error is measured in one-to-one norm distance of the corresponding $t$-twirling channels. As an application, we give a partially derandomized construction of a quantum encryption scheme that has roughly the same key size and security as the quantum one-time pad, but possesses the additional property of being non-malleable against adversaries without quantum side information.

quant-ph↗

arXiv2020

Security of the Fiat-Shamir Transformation in the Quantum Random-Oracle Model

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.

cs.CR↗

arXiv2020

Secure Multi-party Quantum Computation with a Dishonest Majority

The cryptographic task of secure multi-party (classical) computation has received a lot of attention in the last decades. Even in the extreme case where a computation is performed between $k$ mutually distrustful players, and security is required even for the single honest player if all other players are colluding adversaries, secure protocols are known. For quantum computation, on the other hand, protocols allowing arbitrary dishonest majority have only been proven for $k=2$. In this work, we generalize the approach taken by Dupuis, Nielsen and Salvail (CRYPTO 2012) in the two-party setting to devise a secure, efficient protocol for multi-party quantum computation for any number of players $k$, and prove security against up to $k-1$ colluding adversaries. The quantum round complexity of the protocol for computing a quantum circuit of $\{\mathsf{CNOT, T}\}$ depth $d$ is $O(k \cdot (d + \log n))$, where $n$ is the security parameter. To achieve efficiency, we develop a novel public verification protocol for the Clifford authentication code, and a testing protocol for magic-state inputs, both using classical multi-party computation.

quant-ph↗

arXiv2019

Asymptotic performance of port-based teleportation

Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number $N$ of ports, the error of the optimal protocol is proportional to the inverse square of $N$. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur-Weyl distribution by Johansson, which might be of independent interest.

quant-ph↗

arXiv2019

Efficient simulation of random states and random unitaries

We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that $t$-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs. In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error. These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects.

quant-ph↗

arXiv2018

Disentanglement Cost of Quantum States

We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman, PRA 72, 032317 (2005)] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically transform the state to a locally recoverable version of the state.

quant-ph↗

arXiv2018

Constraints on Multipartite Quantum Entropies

The von Neumann entropy plays a vital role in quantum information theory. The von Neumann entropy determines, e.g., the capacities of quantum channels. Also, entropies of composite quantum systems are important for future quantum networks, and their characterization is related to the quantum marginal problem. Furthermore, they play a role in quantum thermodynamics. In this thesis the set of quantum entropies of multipartite quantum systems is studied. The problem of its characterization is not new -- however, progress has been sparse, indicating that the problem might be hard and that new methods might be needed. Here, a variety of different and complementary approaches are taken. First, I look at global properties. It is known that the von Neumann entropy region -- just like its classical counterpart -- forms a convex cone. I describe the symmetries of this cone and highlight geometric similarities and differences to the classical entropy cone. In a different approach, I utilize the local geometric properties of extremal rays of a cone. I show that quantum states whose entropy lies on such an extremal ray of the quantum entropy cone have a very simple structure. As the set of all quantum states is very complicated, I look at a simple subset called stabilizer states. I improve on previously known results by showing that under a technical condition on the local dimension, entropies of stabilizer states respect an additional class of information inequalities that is valid for random variables from linear codes. In a last approach I find a representation-theoretic formulation of the classical marginal problem simplifying the comparison with its quantum mechanical counterpart. This novel correspondence yields a simplified formulation of the group characterization of classical entropies (IEEE Trans. Inf. Theory, 48(7):1992-1995, 2002) in purely combinatorial terms.

quant-ph↗

arXiv2018

Entropy in Quantum Information Theory -- Communication and Cryptography

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves differently. A long-standing open question is, whether there are quantum analogues of unconstrained non-Shannon type inequalities. Here, a new constrained non-von-Neumann type inequality is proven, a step towards a conjectured unconstrained inequality by Linden and Winter. *IID quantum state merging can be optimally achieved using the decoupling technique. The one-shot results by Berta et al. and Anshu at al., however, had to bring in additional mathematical machinery. We introduce a natural generalized decoupling paradigm, catalytic decoupling, that can reproduce the aforementioned results when used analogously to the application of standard decoupling in the asymptotic case. *Port based teleportation, a variant of standard quantum teleportation protocol, cannot be implemented perfectly. We prove several lower bounds on the necessary number of output ports N to achieve port based teleportation for given error and input dimension, showing that N diverges uniformly in the dimension of the teleported quantum system, for vanishing error. As a byproduct, a new lower bound for the size of the program register for an approximate universal programmable quantum processor is derived. *In the last part, we give a new definition for information-theoretic quantum non-malleability, strengthening the previous definition by Ambainis et al. We show that quantum non-malleability implies secrecy, analogous to quantum authentication. Furthermore, non-malleable encryption schemes can be used as a primitive to build authenticating encryption schemes. We also show that the strong notion of authentication recently proposed by Garg et al. can be fulfilled using 2-designs.

quant-ph↗

arXiv2018

Unforgeable Quantum Encryption

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

quant-ph↗

arXiv2018

Deconstruction and conditional erasure of quantum correlations

We define the deconstruction cost of a tripartite quantum state on systems $ABE$ as the minimum rate of noise needed to apply to the $AE$ systems, such that there is negligible disturbance to the marginal state on the $BE$ systems, while the system $A$ of the resulting state is locally recoverable from the $E$ system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems $ABE$ is equal to its conditional quantum mutual information (CQMI) $I(A;B|E)$, thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems $AE$ in order to decouple system $A$ from systems $BE$, while causing negligible disturbance to the marginal state of systems $BE$. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI $I(A;B|E)$. State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction/conditional erasure if Alice has available the best possible system $E$ to help in the deconstruction/conditional erasure task.

quant-ph↗

arXiv2018

Conditional Decoupling of Quantum Information

Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Physical Review A 72, 032317 (2005)] showed that the quantum mutual information $I(A;B)$ quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems $AB$. Here, we investigate correlations in tripartite systems $ABE$. In particular, we are interested in the minimal rate of noise needed to apply to the systems $AE$ in order to erase the correlations between $A$ and $B$ given the information in system $E$, in such a way that there is only negligible disturbance on the marginal $BE$. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states $ABE$. Our main result is that both are equal to the conditional quantum mutual information $I(A;B|E)$ -- establishing it as an operational measure for tripartite quantum correlations.

quant-ph↗

arXiv2017

Quantum non-malleability and authentication

In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. Ambainis, Bouda and Winter gave a definition of non-malleability for the encryption of quantum data. In this work, we show that this definition is too weak, as it allows adversaries to "inject" plaintexts of their choice into the ciphertext. We give a new definition of quantum non-malleability which resolves this problem. Our definition is expressed in terms of entropic quantities, considers stronger adversaries, and does not assume secrecy. Rather, we prove that quantum non-malleability implies secrecy; this is in stark contrast to the classical setting, where the two properties are completely independent. For unitary schemes, our notion of non-malleability is equivalent to encryption with a two-design (and hence also to the definition of Ambainis et al.). Our techniques also yield new results regarding the closely-related task of quantum authentication. We show that "total authentication" (a notion recently proposed by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant improvement over the eight-design construction of Garg et al. We also show that, under a mild adaptation of the rejection procedure, both total authentication and our notion of non-malleability yield quantum authentication as defined by Dupuis, Nielsen and Salvail.

quant-ph↗

arXiv2016

Catalytic Decoupling of Quantum Information

The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of catalytic decoupling, that is, decoupling in the presence of an uncorrelated ancilla system. This removes a restriction on the standard notion of decoupling, which becomes important for structureless resources, and yields a tight characterization in terms of the max-mutual information. Catalytic decoupling naturally unifies various tasks like the erasure of correlations and quantum state merging, and leads to a resource theory of decoupling.

quant-ph↗

arXiv2014

Information-Theoretic Implications of Quantum Causal Structures

The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional dependencies. In this work, we describe a general algorithm for computing information-theoretic constraints on the correlations that can arise from a given interaction pattern, where we allow for classical as well as quantum variables. We apply the general technique to two relevant cases: First, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among a larger number of parties.

quant-ph↗