Özgür Dagdelen

Random oracles in a quantum world

The interest in post-quantum cryptography -- classical systems that remain secure in the presence of a quantum adversary -- has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum state. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore postquantum secure. We conclude with a rich set of open problems in this area.

Authenticated Key Exchange from Ideal Lattices

In this paper, we present a practical and provably secure two-pass authenticated key exchange protocol over ideal lattices, which is conceptually simple and has similarities to the Diffie-Hellman based protocols such as HMQV (CRYPTO 2005) and OAKE (CCS 2013). Our method does not involve other cryptographic primitives—in particular, it does not use signatures—which simplifies the protocol and enables us to base the security directly on the hardness of the ring learning with errors problem. The security is proven in the Bellare-Rogaway model with weak perfect forward secrecy in the random oracle model. We also give a one-pass variant of our two-pass protocol, which might be appealing in specific applications. Several concrete choices of parameters are provided, and a proof-of-concept implementation shows that our protocols are indeed practical.

Domain-Specific pseudonymous signatures for the german identity card

The restricted identification protocol for the new German identity card basically provides a method to use pseudonyms such that they can be linked by individual service providers, but not across different service providers (even not malicious ones). The protocol can be augmented to allow also for signatures under the pseudonyms. In this paper, we thus view --and define-- this idea more abstractly as a new cryptographic signature primitive with some form of anonymity, and use the term domain-specific pseudonymous signatures. We then analyze the restricted identification solutions in terms of the formal security requirements.

The PACE|AA Protocol for Machine Readable Travel Documents, and Its Security

We discuss an efficient combination of the cryptographic protocols adopted by the International Civil Aviation Organization (ICAO) for securing the communication of machine readable travel documents and readers. Roughly, in the original protocol the parties first run the Password-Authenticated Connection Establishment (PACE) protocol to establish a shared key and then the reader (optionally) invokes the Active Authentication (AA) protocol to verify the passport’s validity. Here we show that by carefully re-using some of the secret data of the PACE protocol for the AA protocol one can save one exponentiation on the passports’s side. We call this the PACE|AA protocol. We then formally prove that this more efficient combination not only preserves the desirable security properties of the two individual protocols but also increases privacy by preventing misuse of the challenge in the Active Authentication protocol. We finally discuss a solution which allows deniable authentication in the sense that the interaction cannot be used as a proof towards third parties.

Parallel enumeration of shortest lattice vectors

Lattice basis reduction is the problem of finding short vectors in lattices. The security of lattice based cryptosystems is based on the hardness of lattice reduction. Furthermore, lattice reduction is used to attack well-known cryptosystems like RSA. One of the algorithms used in lattice reduction is the enumeration algorithm (ENUM), that provably finds a shortest vector of a lattice. We present a parallel version of the lattice enumeration algorithm. Using multi-core CPU systems with up to 16 cores, our implementation gains a speed-up of up to factor 14. Compared to the currently best public implementation, our parallel algorithm saves more than 90% of runtime.

Security analysis of the extended access control protocol for machine readable travel documents

We analyze the Extended Access Control (EAC) protocol for authenticated key agreement, recently proposed by the German Federal Office for Information Security (BSI) for the deployment in machine readable travel documents. We show that EAC is secure in the Bellare-Rogaway model under the gap Diffie-Hellman (GDH) problem, and assuming random oracles. Furthermore, we discuss that the protocol achieves some of the properties guaranteed by the extended CK security model of LaMacchia, Lauter and Mityagin (ProvSec 2008).

The Fiat–Shamir Transformation in a Quantum World

The Fiat-Shamir transformation is a famous technique to turn identification schemes into signature schemes. The derived scheme is provably secure in the random-oracle model against classical adversaries. Still, the technique has also been suggested to be used in connection with quantum-immune identification schemes, in order to get quantum-immune signature schemes. However, a recent paper by Boneh et al. (Asiacrypt 2011) has raised the issue that results in the random-oracle model may not be immediately applicable to quantum adversaries, because such adversaries should be allowed to query the random oracle in superposition. It has been unclear if the Fiat-Shamir technique is still secure in this quantum oracle model (QROM).

Revisiting TESLA in the Quantum Random Oracle Model

We study a scheme of Bai and Galbraith (CT-RSA’14), also known as TESLA. TESLA was thought to have a tight security reduction from the learning with errors problem (LWE) in the random oracle model (ROM). Moreover, a variant using chameleon hash functions was lifted to the quantum random oracle model (QROM). However, both reductions were later found to be flawed and hence it remained unresolved until now whether TESLA can be proven to be tightly secure in the (Q)ROM.

Extended security arguments for signature schemes

The well-known forking lemma by Pointcheval and Stern has been used to prove the security of the so-called generic signature schemes. These signature schemes are obtained via the Fiat-Shamir transform from three-pass identification schemes. A number of five-pass identification protocols have been proposed in the last few years. Extending the forking lemma and the Fiat-Shamir transform would allow to obtain new signature schemes since, unfortunately, these newly proposed schemes fall outside the original framework. In this paper, we provide an extension of the forking lemma in order to assess the security of what we call n-generic signature schemes. These include signature schemes that are derived from certain (2n+1)-pass identification schemes. We thus obtain a generic methodology for proving the security of a number of signature schemes derived from recently published five-pass identification protocols, and potentially for (2n+1)-pass identification schemes to come.

Tuning GaussSieve for Speed

The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of lattice-based cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and Voulgaris presented a heuristic member of the sieving family, known as GaussSieve, demonstrating it to be comparable to enumeration methods in practice. With contemporary lattice-based cryptographic proposals relying largely on the hardness of solving the shortest and closest vector problems in ideal lattices, examining possible improvements to sieving algorithms becomes highly pertinent since, at present, only sieving algorithms have been successfully adapted to solve such instances more efficiently than in the random lattice case. In this paper, we propose a number of heuristic improvements to GaussSieve, which can also be applied to other sieving algorithms for SVP.