## CryptoDB

### Christian Schaffner

#### Affiliation: QuSoft and University of Amsterdam

#### Publications

**Year**

**Venue**

**Title**

2019

CRYPTO

Quantum Indistinguishability of Random Sponges
Abstract

In this work we show that the sponge construction can be used to construct quantum-secure pseudorandom functions. As our main result we prove that random sponges are quantum indistinguishable from random functions. In this setting the adversary is given superposition access to the input-output behavior of the construction but not to the internal function. Our proofs hold under the assumption that the internal function is a random function or permutation. We then use this result to obtain a quantum-security version of a result by Andreeva, Daemen, Mennink, and Van Assche (FSE’15) which shows that a sponge that uses a secure PRP or PRF as internal function is a secure PRF. This result also proves that the recent attacks against CBC-MAC in the quantum-access model by Kaplan, Leurent, Leverrier, and Naya-Plasencia (Crypto’16) and Santoli, and Schaffner (QIC’16) can be prevented by introducing a state with a non-trivial inner part.The proof of our main result is derived by analyzing the joint distribution of any q input-output pairs. Our method analyzes the statistical behavior of the considered construction in great detail. The used techniques might prove useful in future analysis of different cryptographic primitives considering quantum adversaries. Using Zhandry’s PRF/PRP switching lemma we then obtain that quantum indistinguishability also holds if the internal block function is a random permutation.

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.

2010

EPRINT

Random Oracles in a Quantum World
Abstract

Once quantum computers reach maturity most of todays traditional cryptographic schemes based on RSA or discrete logarithms become vulnerable to quantum-based attacks. Hence, schemes which are more likely to resist quantum attacks like lattice-based systems or code-based primitives have recently gained significant attention. Interestingly, a vast number of such schemes also deploy random oracles, which have mainly be analyzed in the classical setting.
Here we revisit the random oracle model in cryptography in light of quantum attackers. We show that there are protocols using quantum-immune primitives and random oracles, such that the protocols are secure in the classical world, but insecure if a quantum attacker can access the random oracle via quantum states. We discuss that most of the proof techniques related to the random oracle model in the classical case cannot be transferred immediately to the quantum case. Yet, we show that quantum random oracles can nonetheless be used to show for example that the basic Bellare-Rogaway encryption scheme is quantum-immune against plaintext attacks (assuming quantum-immune primitives).

2008

TCC

2007

EPRINT

Randomness Extraction via Delta-Biased Masking in the Presence of a Quantum Attacker
Abstract

Randomness extraction is of fundamental importance for information-theoretic cryptography. It allows to transform a raw key about which an attacker has some limited knowledge into a fully secure random key, on which the attacker has essentially no information.
We show a new randomness-extraction technique which works also in case where the attacker has quantum information on the raw key. Randomness extraction is done by XORing a so-called delta-biased mask to the raw key. Up to date, only very few techniques are known to work against a quantum attacker, much in contrast to the classical (non-quantum) setting, which is much better understood and for which a vast amount of different techniques for randomness extraction are known.
We show two applications of the new result. We first show how to encrypt a long message with a short key, information-theoretically secure against a quantum attacker, provided that the attacker has enough quantum uncertainty on the message. This generalizes the concept of entropically-secure encryption to the case of a quantum attacker.
As a second application, we show how the new randomness-extraction technique allows to do error-correction without leaking partial information to a quantum attacker. Such a technique is useful in settings where the raw key may contain errors, since standard error-correction techniques may provide the attacker with information on, say, a secret key that was used to obtain the raw key.

2007

EPRINT

Secure Identification and QKD in the Bounded-Quantum-Storage Model
Abstract

We consider the problem of secure identification: user U proves to server S that he knows an agreed (possibly low-entropy) password w, while giving away as little information on w as possible, namely the adversary can exclude at most one possible password for each execution of the scheme. We propose a solution in the bounded-quantum-storage model, where U and S may exchange qubits, and a dishonest party is assumed to have limited quantum memory. No other restriction is posed upon the adversary.
An improved version of the proposed identification scheme is also secure against a man-in-the-middle attack, but requires U and S to additionally share a high-entropy key k. However, security is still guaranteed if one party loses k to the attacker but notices the loss. In both versions of the scheme, the honest participants need no quantum memory, and noise and imperfect quantum sources can be tolerated. The schemes compose sequentially, and w and k can securely be re-used.
A small modification to the identification scheme results in a quantum-key-distribution (QKD) scheme, secure in the bounded-quantum-storage model, with the same re-usability properties of the keys, and without assuming authenticated channels. This is in sharp contrast to known QKD schemes (with unbounded adversary) without authenticated channels, where authentication keys must be updated, and unsuccessful executions can cause the parties to run out of keys.

2007

EPRINT

A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
Abstract

We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings.
Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded-quantum-storage model according to new strong security definitions.
As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model).
Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.

2006

EPRINT

Information-Theoretic Conditions for Two-Party Secure Function Evaluation
Abstract

The standard security definition of unconditional secure function evaluation, which is based on the ideal/real model paradigm, has the disadvantage of being overly complicated to work with in practice. On the other hand, simpler ad-hoc definitions tailored to special scenarios have often been flawed. Motivated by this unsatisfactory situation, we give an information-theoretic security definition of secure function evaluation which is very simple yet provably equivalent to the standard, simulation-based definitions.

2005

EPRINT

Cryptography In the Bounded Quantum-Storage Model
Abstract

We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's {\em quantum}memory is of bounded size. We show that oblivious transfer and bit
commitment can be implemented in this model using protocols where honest parties need no quantum memory, whereas an adversarial player needs quantum memory of size at least $n/2$ in order to break the protocol, where $n$ is the number of qubits transmitted. This is in sharp contrast to the classical bounded-memory model, where we can only tolerate adversaries with memory of size quadratic in honest players' memory size. Our protocols are efficient, non-interactive and can be implemented using today's technology. On the technical side, a new entropic uncertainty relation involving min-entropy is established.

2005

EPRINT

Oblivious Transfer and Linear Functions
Abstract

We study unconditionally secure 1-out-of-2 Oblivious Transfer (1-2 OT). We first point out that a standard security requirement for 1-2 OT of bits, namely that the receiver only learns one of the bits sent, holds if and only if the receiver has no information on the XOR of the two bits. We then generalize this to 1-2 OT of strings and show that the security can be characterized in terms of binary linear functions. More precisely, we show that the receiver learns only one of the two strings sent if and only if he has no information on the result of
applying any binary linear function (which non-trivially depends on both inputs) to the two strings.
We then argue that this result not only gives new insight into the nature of 1-2 OT, but it in particular provides a very powerful tool for analyzing 1-2 OT protocols. We demonstrate this by showing that with our characterization at hand, the reduceability of 1-2 OT (of strings) to a wide range of weaker primitives follows by a very simple argument. This is in sharp contrast to previous literature, where reductions of 1-2 OT to weaker flavors have rather complicated and sometimes even incorrect proofs.

#### Program Committees

- Eurocrypt 2019
- PKC 2018
- Crypto 2017
- Eurocrypt 2015
- Crypto 2013

#### Coauthors

- Gorjan Alagic (1)
- Dan Boneh (1)
- Harry Buhrman (1)
- Nishanth Chandran (1)
- Claude Crépeau (2)
- Jan Czajkowski (1)
- Özgür Dagdelen (2)
- Ivan Damgård (8)
- Jelle Don (1)
- Yfke Dulek (2)
- Serge Fehr (13)
- Marc Fischlin (2)
- Tommaso Gagliardoni (2)
- Ran Gelles (1)
- Vipul Goyal (1)
- Andreas Hülsing (3)
- Eike Kiltz (1)
- Anja Lehmann (2)
- Carolin Lunemann (1)
- Vadim Lyubashevsky (1)
- Christian Majenz (1)
- Rafail Ostrovsky (1)
- Renato Renner (2)
- Louis Salvail (9)
- George Savvides (2)
- Miroslava Sotáková (1)
- Florian Speelman (2)
- Jürg Wullschleger (2)
- Mark Zhandry (1)