## CryptoDB

### Christian Majenz

#### Publications

**Year**

**Venue**

**Title**

2020

EUROCRYPT

Secure Multi-party Quantum Computation with a Dishonest Majority
📺
Abstract

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 {CNOT, T} depth d is O(k (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.

2020

EUROCRYPT

Efficient simulation of random states and random unitaries
📺
Abstract

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.

2020

EUROCRYPT

Quantum-access-secure message authentication via blind-unforgeability
📺
Abstract

Formulating and designing authentication of classical messages in the presence of adversaries with quantum query access has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of ``predicting an unqueried value'' when the adversary can query in quantum superposition.
We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability. This notion defines a function to be predictable if there exists an adversary who can use "partially blinded" oracle access to predict values in the blinded region. We support the proposal with a number of technical results. We begin by establishing that the notion coincides with EUF-CMA in the classical setting and go on to demonstrate that the notion is satisfied by a number of simple guiding examples, such as random functions and quantum-query-secure pseudorandom functions. We then show the suitability of blind unforgeability for supporting canonical constructions and reductions. We prove that the "hash-and-MAC" paradigm and the Lamport one-time digital signature scheme are indeed unforgeable according to the definition. In this setting, we additionally define and study a new variety of quantum-secure hash functions called Bernoulli-preserving.
Finally, we demonstrate that blind unforgeability is strictly stronger than a previous definition of Boneh and Zhandry [EUROCRYPT '13, CRYPTO '13] and resolve an open problem concerning this previous definition by constructing an explicit function family which is forgeable yet satisfies the definition.

2020

CRYPTO

The Measure-and-Reprogram Technique 2.0: Multi-Round Fiat-Shamir and More
📺
Abstract

We revisit recent works by Don, Fehr, Majenz and Schaffner and by Liu and Zhandry on the security of the Fiat-Shamir transformation of sigma-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 {\em 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 sigma-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.

2019

CRYPTO

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

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called
$$\Sigma {\text {-protocol}}$$
, 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
$$\Sigma {\text {-protocol}}$$
(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
$$\Sigma {\text {-protocol}}$$
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.

#### Coauthors

- Gorjan Alagic (4)
- Jelle Don (2)
- Yfke Dulek (1)
- Serge Fehr (2)
- Tommaso Gagliardoni (1)
- Alex B. Grilo (1)
- Stacey Jeffery (1)
- Alexander Russell (2)
- Christian Schaffner (2)
- Fang Song (1)