## CryptoDB

### Tibor Jager

#### Affiliation: Paderborn University, de

#### Publications

**Year**

**Venue**

**Title**

2021

EUROCRYPT

Tightly-Secure Authenticated Key Exchange, Revisited
Abstract

We introduce new tightly-secure authenticated key exchange (AKE) protocols that are extremely efficient, yet have only a constant security loss and can be instantiated in the random oracle model both from the standard DDH assumption and a subgroup assumption over RSA groups. These protocols can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate a security loss with increased parameters and thus decreased computational efficiency.
We use the standard “Single-Bit-Guess” AKE security (with forward secrecy and state corruption) requiring all challenge keys to be simultaneously pseudo-random. In contrast, most previous papers on tightly secure AKE protocols (Bader et al., TCC 2015; Gjøsteen and Jager, CRYPTO 2018; Liu et al., ASIACRYPT 2020) concentrated on a non-standard “Multi-Bit-Guess” AKE security which is known not to compose tightly with symmetric primitives to build a secure communication channel.
Our key technical contribution is a new generic approach to construct tightly-secure AKE protocols based on non-committing key encapsulation mechanisms. The resulting DDH-based protocols are considerably more efficient than all previous constructions.

2021

PKC

Efficient Adaptively-Secure IB-KEMs and VRFs via Near-Collision Resistance
📺
Abstract

We construct more efficient cryptosystems with provable security against adaptive attacks, based on simple and natural hardness
assumptions in the standard model. Concretely, we describe:
– An adaptively-secure variant of the efficient, selectively-secure LWE-
based identity-based encryption (IBE) scheme of Agrawal, Boneh,
and Boyen (EUROCRYPT 2010). In comparison to the previously
most efficient such scheme by Yamada (CRYPTO 2017) we achieve
smaller lattice parameters and shorter public keys of size O(log \lambda),
where \lambda is the security parameter.
– Adaptively-secure variants of two efficient selectively-secure pairing-
based IBEs of Boneh and Boyen (EUROCRYPT 2004). One is based
on the DBDH assumption, has the same ciphertext size as the cor-
responding BB04 scheme, and achieves full adaptive security with
public parameters of size only O(log \lambda). The other is based on a q-
type assumption and has public key size O(\lambda), but a ciphertext is
only a single group element and the security reduction is quadrat-
ically tighter than the corresponding scheme by Jager and Kurek
(ASIACRYPT 2018).
– A very efficient adaptively-secure verifiable random function where
proofs, public keys, and secret keys have size O(log \lambda).
As a technical contribution we introduce blockwise partitioning, which
leverages the assumption that a cryptographic hash function is weak
near-collision resistant to prove full adaptive security of cryptosystems.

2021

PKC

Subversion-Resilient Public Key Encryption with Practical Watchdogs
📺
Abstract

Restoring the security of maliciously implemented cryptosystems has been widely considered challenging due to the fact that the subverted implementation could arbitrarily deviate from the official specification. Achieving security against adversaries that can arbitrarily subvert implementations seems to inherently require trusted component assumptions and/or architectural properties. At ASIACRYPT 2016, Russell et al. proposed a very useful model where a watchdog is used to test and approve individual components of implementation before or during deployment. Such a detection-based strategy has been shown very useful for designing a broad class of cryptographic schemes that are provable resilient to subversion.
We consider Russell et al.'s watchdog model from a practical perspective. We find that the asymptotic definitional framework, while permitting strong positive theoretical results, does not yet provide practical solutions, due to the fact that the running time of a watchdog is only bounded by an abstract polynomial. Hence, in the worst case, the running time of the watchdog might exceed the running time of the adversary, which seems not very practical. We adopt Russell et al.'s watchdog model to the concrete security setting. We design the first subversion-resilient public-key encryption scheme, which additionally allows for extremely efficient watchdogs with only linear running time.
At the core of our construction is a new variant of a combiner for key encapsulation mechanisms (KEMs) by Giacon et al. (PKC'18). We combine this construction with a new subversion-resilient randomness generator that also can be checked by a very efficient watchdog, even in constant time, which could be of independent interest for the design of other subversion-resilient cryptographic schemes with practical watchdogs. Our work thus shows how to apply Russell et al.'s watchdog model to design subversion-resilient cryptography with efficient and very practical watchdogs.

2021

PKC

More Efficient Digital Signatures with Tight Multi-User Security
📺
Abstract

We construct the currently most efficient signature schemes with tight multi-user security against adaptive corruptions. It is the first generic construction of such schemes, based on lossy identification schemes (Abdalla etal; JoC 2016), and the first to achieve strong existential unforgeability. It also has significantly more compact signatures than the previously most efficient construction by Gjosteen and Jager (CRYPTO 2018). When instantiated based on the decisional Diffie-Hellman assumption, a signature consists of only three exponents.
We propose a new variant of the generic construction of signatures from sequential OR-proofs by Abe, Ohkubo, and Suzuki (ASIACRYPT 2002) and Fischlin, Harasser, and Janson (EUROCRYPT 2020).
In comparison to Fischlin etal, who focus on constructing signatures in the non-programmable random oracle model (NPROM), we aim to achieve tight security against adaptive corruptions, maximize efficiency, and to directly achieve strong existential unforgeability (also in the NPROM).
This yields a slightly different construction and we use slightly different and additional properties of the lossy identification scheme.
Signatures with tight multi-user security against adaptive corruptions are a commonly-used standard building block for tightly-secure authenticated key exchange protocols. We also show how our construction improves the efficiency of all existing tightly-secure AKE protocols.

2019

EUROCRYPT

Session Resumption Protocols and Efficient Forward Security for TLS 1.3 0-RTT
📺
Abstract

The TLS 1.3 0-RTT mode enables a client reconnecting to a server to send encrypted application-layer data in “0-RTT” (“zero round-trip time”), without the need for a prior interactive handshake. This fundamentally requires the server to reconstruct the previous session’s encryption secrets upon receipt of the client’s first message. The standard techniques to achieve this are Session Caches or, alternatively, Session Tickets. The former provides forward security and resistance against replay attacks, but requires a large amount of server-side storage. The latter requires negligible storage, but provides no forward security and is known to be vulnerable to replay attacks.In this paper, we first formally define session resumption protocols as an abstract perspective on mechanisms like Session Caches and Session Tickets. We give a new generic construction that provably provides forward security and replay resilience, based on puncturable pseudorandom functions (PPRFs). This construction can immediately be used in TLS 1.3 0-RTT and deployed unilaterally by servers, without requiring any changes to clients or the protocol.We then describe two new constructions of PPRFs, which are particularly suitable for use for forward-secure and replay-resilient session resumption in TLS 1.3. The first construction is based on the strong RSA assumption. Compared to standard Session Caches, for “128-bit security” it reduces the required server storage by a factor of almost 20, when instantiated in a way such that key derivation and puncturing together are cheaper on average than one full exponentiation in an RSA group. Hence, a 1 GB Session Cache can be replaced with only about 51 MBs of storage, which significantly reduces the amount of secure memory required. For larger security parameters or in exchange for more expensive computations, even larger storage reductions are achieved. The second construction combines a standard binary tree PPRF with a new “domain extension” technique. For a reasonable choice of parameters, this reduces the required storage by a factor of up to 5 compared to a standard Session Cache. It employs only symmetric cryptography, is suitable for high-traffic scenarios, and can serve thousands of tickets per second.

2019

CRYPTO

Highly Efficient Key Exchange Protocols with Optimal Tightness
📺
Abstract

In this paper we give nearly-tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols, which are extremely simple and efficient. Unlike previous approaches, the combination of nearly-tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner.Our reductions have only a linear loss in the number of users, implying that our protocols are more efficient than the state of the art when instantiated with theoretically sound parameters. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions.

2019

JOFC

On Tight Security Proofs for Schnorr Signatures
Abstract

The Schnorr signature scheme is the most efficient signature scheme based on the discrete logarithm problem and a long line of research investigates the existence of a tight security reduction for this scheme in the random oracle model. Almost all recent works present lower tightness bounds and most recently Seurin EUROCRYPT 2012 showed that under certain assumptions the non -tight security proof for Schnorr signatures in the random oracle by Pointcheval and Stern EUROCRYPT’96 is essentially optimal. All previous works in this direction rule out tight reductions from the (one-more) discrete logarithm problem. In this paper, we introduce a new meta-reduction technique, which shows lower bounds for the large and very natural class of generic reductions. A generic reduction is independent of a particular representation of group elements. Most reductions in state-of-the-art security proofs have this property. It is desirable, because then the reduction applies generically to any concrete instantiation of the group. Our approach shows unconditionally that there is no tight generic reduction from any natural non-interactive computational problem $$\Pi $$ Π defined over algebraic groups to breaking Schnorr signatures, unless solving $$\Pi $$ Π is easy. In an additional application of the new meta-reduction technique, we also unconditionally rule out any (even non-tight) generic reduction from natural non-interactive computational problems defined over algebraic groups to breaking Schnorr signatures in the non-programmable random oracle model.

2018

EUROCRYPT

2018

CRYPTO

Practical and Tightly-Secure Digital Signatures and Authenticated Key Exchange
📺
Abstract

Tight security is increasingly gaining importance in real-world cryptography, as it allows to choose cryptographic parameters in a way that is supported by a security proof, without the need to sacrifice efficiency by compensating the security loss of a reduction with larger parameters. However, for many important cryptographic primitives, including digital signatures and authenticated key exchange (AKE), we are still lacking constructions that are suitable for real-world deployment.We construct the first truly practical signature scheme with tight security in a real-world multi-user setting with adaptive corruptions. The scheme is based on a new way of applying the Fiat-Shamir approach to construct tightly-secure signatures from certain identification schemes.Then we use this scheme as a building block to construct the first practical AKE protocol with tight security. It allows the establishment of a key within 1 RTT in a practical client-server setting, provides forward security, is simple and easy to implement, and thus very suitable for practical deployment. It is essentially the “signed Diffie-Hellman” protocol, but with an additional message, which is crucial to achieve tight security. This additional message is used to overcome a technical difficulty in constructing tightly-secure AKE protocols.For a theoretically-sound choice of parameters and a moderate number of users and sessions, our protocol has comparable computational efficiency to the simple signed Diffie-Hellman protocol with EC-DSA, while for large-scale settings our protocol has even better computational performance, at moderately increased communication complexity.

2018

ASIACRYPT

Short Digital Signatures and ID-KEMs via Truncation Collision Resistance
Abstract

Truncation collision resistance is a simple non-interactive complexity assumption that seems very plausible for standard cryptographic hash functions like SHA-3. We describe how this assumption can be leveraged to obtain standard-model constructions of public-key cryptosystems that previously seemed to require a programmable random oracle. This includes the first constructions of identity-based key encapsulation mechanisms (ID-KEMs) and digital signatures over bilinear groups with full adaptive security and without random oracles, where a ciphertext or signature consists of only a single element of a prime-order group. We also describe a generic construction of ID-KEMs with full adaptive security from a scheme with very weak security (“selective and non-adaptive chosen-ID security”), and a similar generic construction for digital signatures.

2018

ASIACRYPT

Simple and More Efficient PRFs with Tight Security from LWE and Matrix-DDH
Abstract

We construct efficient and tightly secure pseudorandom functions (PRFs) with only logarithmic security loss and short secret keys. This yields very simple and efficient variants of well-known constructions, including those of Naor-Reingold (FOCS 1997) and Lewko-Waters (ACM CCS 2009). Most importantly, in combination with the construction of Banerjee, Peikert and Rosen (EUROCRYPT 2012) we obtain the currently most efficient LWE-based PRF from a weak LWE-assumption with a much smaller modulus than the original construction. In comparison to the only previous construction with this property, which is due to Döttling and Schröder (CRYPTO 2015), we use a modulus of similar size, but only a single instance of the underlying PRF, instead of parallel instances, where is the security parameter. Like Döttling and Schröder, our security proof is only almost back-box, due to the fact that the number of queries made by the adversary and its advantage must be known a-priori.Technically, we introduce all-prefix universal hash functions (APUHFs), which are hash functions that are (almost-)universal, even if any prefix of the output is considered. We give simple and very efficient constructions of APUHFs, and show how they can be combined with the augmented cascade of Boneh et al. (ACM CCS 2010) to obtain our results. Along the way, we develop a new and more direct way to prove security of PRFs based on the augmented cascade.

2016

TCC

2015

EPRINT

2010

EPRINT

Simple and Efficient Public-Key Encryption from Computational Diffie-Hellman in the Standard Model
Abstract

This paper proposes practical chosen-ciphertext secure public-key encryption systems that are provably secure under the computational Diffie-Hellman assumption, in the standard model. Our schemes are conceptually simpler and more efficient than previous constructions.
We also show that in bilinear groups the size of the public-key can be shrunk from n to 2\sqrt{n} group elements, where n is the security parameter.

2010

PKC

2008

EPRINT

On Black-Box Ring Extraction and Integer Factorization
Abstract

The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete logarithms and solving the Diffie-Hellman problem and (ii) the in-existence of secure ring-homomorphic encryption schemes.
In the special case of a finite field, Boneh/Lipton and Maurer/Raub showed that there exist algorithms solving the black-box extraction problem in subexponential time. It is unknown whether there exist more efficient algorithms.
In this work we consider the black-box extraction problem over finite rings of characteristic $n$, where $n$ has at least two different prime factors. We provide a polynomial-time reduction from factoring $n$ to the black-box extraction problem for a large class of finite commutative unitary rings. Under the factoring assumption, this implies the in-existence of certain efficient generic reductions from computing discrete logarithms to the Diffie-Hellman problem on the one side, and might be an indicator that secure ring-homomorphic encryption schemes exist on the other side.

2008

EPRINT

The Generic Hardness of Subset Membership Problems under the Factoring Assumption
Abstract

We analyze a large class of subset membership problems related to integer factorization. We show that there is no algorithm solving these problems efficiently without exploiting properties of the given representation of ring elements, unless factoring integers is easy. Our results imply that problems with high relevance for a large number of cryptographic applications, such as the quadratic residuosity and the subgroup decision problems, are generically equivalent to factoring.

2008

EPRINT

Lower Bounds on Black-Box Ring Extraction
Abstract

The black-box ring extraction problem is the problem of extracting a secret ring element from a black-box by performing only the ring operations and testing for equality of elements. An efficient algorithm for the black-box ring extraction problem implies the equivalence of the discrete logarithm and the Diffie-Hellman problem. At the same time this implies the inexistence of secure ring-homomorphic encryption schemes.
It is unknown whether the known algorithms for the black-box ring extraction problem are optimal. In this paper we derive exponential-time lower complexity bounds for a large class of rings satisfying certain conditions. The existence of these bounds is surprising, having in mind that there are subexponential-time algorithms for certain rings which are very similar to the rings considered in this work. In addition, we introduce a novel technique to reduce the problem of factoring integers to the black-box ring extraction problem, extending previous work to a more general class of algorithms and obtaining a much tighter reduction.

#### Program Committees

- Crypto 2020
- PKC 2019
- PKC 2018
- PKC 2017
- Eurocrypt 2016
- PKC 2013

#### Coauthors

- Kristina Altmann (1)
- Nimrod Aviram (1)
- Christoph Bader (3)
- Pascal Bemmann (1)
- Florian Bergsma (2)
- Florian Böhl (2)
- Rongmao Chen (1)
- Katriel Cohn-Gordon (1)
- Cas Cremers (1)
- David Derler (1)
- Denis Diemert (1)
- Nils Fleischhacker (2)
- Kai Gellert (2)
- Kristian Gjøsteen (2)
- Felix Günther (1)
- Britta Hale (1)
- Kristiyan Haralambiev (2)
- Felix Heuer (1)
- Dennis Hofheinz (10)
- Håkon Jacobsen (1)
- Dakshita Khurana (1)
- Eike Kiltz (6)
- Edward Knapp (1)
- Jessica Koch (2)
- Florian Kohlar (3)
- Rafael Kurek (3)
- Sebastian Lauer (1)
- Yong Li (3)
- Lin Lyu (1)
- David Niehues (1)
- Jiaxin Pan (1)
- Doreen Riepel (1)
- Andy Rupp (4)
- Amit Sahai (1)
- Sven Schäge (7)
- Dominique Schröder (2)
- Jörg Schwenk (7)
- Jae Hong Seo (1)
- Victor Shoup (2)
- Daniel Slamanig (1)
- Martijn Stam (1)
- Ryan Stanley-Oakes (1)
- Christoph Striecks (3)
- Bogdan Warinschi (1)
- Brent Waters (1)
- Mark Zhandry (1)