International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Dennis Hofheinz

Publications

Year
Venue
Title
2022
TCC
The Price of Verifiability: Lower Bounds for Verifiable Random Functions
Verifiable random functions (VRFs) are a useful extension of pseudorandom functions for which it is possible to generate a proof that a certain image is indeed the correct function value (relative to a public verification key). Due to their strong soundness requirements on such proofs, VRFs are notoriously hard to construct, and existing constructions suffer either from complex proofs (for function images), or rely on complex and non-standard assumptions. In this work, we attempt to explain this phenomenon. We show that for a large class of pairing-based VRFs, it is not possible to obtain short proofs and a reduction to a simple assumption simultaneously. Since the class of "consecutively verifiable" VRFs we consider contains in particular the VRF of Lysyanskaya and that of Dodis-Yampolskiy, our results explain the large proof size, resp. the complex assumption of these VRFs.
2021
ASIACRYPT
Onion Routing with Replies 📺
Onion routing (OR) protocols are a crucial tool for providing anonymous internet communication. An OR protocol enables a user to anonymously send requests to a server. A fundamental problem of OR protocols is how to deal with replies: ideally, we would want the server to be able to send a reply back to the anonymous user without knowing or disclosing the user's identity. Existing OR protocols do allow for such replies, but do not provably protect the payload (i.e., message) of replies against manipulation. Kuhn et al. (IEEE S&P 2020) show that such manipulations can in fact be leveraged to break anonymity of the whole protocol. In this work, we close this gap and provide the first framework and protocols for OR with protected replies. We define security in the sense of an ideal functionality in the universal composability model, and provide corresponding (less complex) game-based security notions for the individual properties. We also provide two secure instantiations of our framework: one based on updatable encryption, and one based on succinct non-interactive arguments (SNARGs) to authenticate payloads both in requests and replies. In both cases, our central technical handle is an implicit authentication of the transmitted payload data, as opposed to an explicit, but insufficient authentication (with MACs) in previous solutions. Our results exhibit a new and surprising application of updatable encryption outside of long-term data storage.
2021
TCC
On the Impossibility of Purely Algebraic Signatures 📺
The existence of one-way functions implies secure digital sig- natures, but not public-key encryption (at least in a black-box setting). Somewhat surprisingly, though, efficient public-key encryption schemes appear to be much easier to construct from concrete algebraic assumptions (such as the factoring of Diffie-Hellman-like assumptions) than efficient digital signature schemes. In this work, we provide one reason for this apparent difficulty to construct efficient signature schemes. Specifically, we prove that a wide range of algebraic signature schemes (in which verification essentially checks a number of linear equations over a group) fall to conceptually surprisingly simple linear algebra attacks. In fact, we prove that in an algebraic signature scheme, sufficiently many signatures can be linearly combined to a signature of a fresh message. We present attacks both in known-order and hidden-order groups (although in hidden-order settings, we have to restrict our definition of algebraic signatures a little). More explicitly, we show: – the insecurity of all algebraic signature schemes in Maurer’s generic group model, as long as the signature schemes do not rely on other cryptographic assumptions, such as hash functions. – the insecurity of a natural class of signatures in hidden-order groups, where verification consists of linear equations over group elements. We believe that this highlights the crucial role of public verifiability in digital signature schemes. Namely, while public-key encryption schemes do not require any publicly verifiable structure on ciphertexts, it is exactly this structure on signatures that invites attacks like ours and makes it hard to construct efficient signatures.
2021
TCC
Towards Tight Adaptive Security of Non-Interactive Key Exchange 📺
We investigate the quality of security reductions for non-interactive key exchange (NIKE) schemes. Unlike for many other cryptographic building blocks (like public-key encryption, signatures, or zero-knowledge proofs), all known NIKE security reductions to date are non-tight, i.e., lose a factor of at least the number of users in the system. In that sense, NIKE forms a particularly elusive target for tight security reductions. The main technical obstacle in achieving tightly secure NIKE schemes are adaptive corruptions. Hence, in this work, we explore security notions and schemes that lie between selective security and fully adaptive security. Concretely: - We exhibit a tradeoff between key size and reduction loss. We show that a tighter reduction can be bought by larger public and secret NIKE keys. Concretely, we present a simple NIKE scheme with a reduction loss of O(N^2 log(\nu)/\nu^2), and public and secret keys of O(\nu) group elements, where N denotes the overall number of users in the system, and \nu is a freely adjustable scheme parameter. Our scheme achieves full adaptive security even against multiple "test queries" (i.e., adversarial challenges), but requires keys of size O(N) to achieve (almost) tight security under the matrix Diffie-Hellman assumption. Still, already this simple scheme circumvents existing lower bounds. - We show that this tradeoff is inherent. We contrast the security of our simple scheme with a lower bound for all NIKE schemes in which shared keys can be expressed as an ``inner product in the exponent''. This result covers the original Diffie-Hellman NIKE scheme, as well as a large class of its variants, and in particular our simple scheme. Our lower bound gives a tradeoff between the ``dimension'' of any such scheme (which directly corresponds to key sizes in existing schemes), and the reduction quality. For \nu = O(N), this shows our simple scheme and reduction optimal (up to a logarithmic factor). - We exhibit a tradeoff between security and key size for tight reductions. We show that it is possible to circumvent the inherent tradeoff above by relaxing the desired security notion. Concretely, we consider the natural notion of semi-adaptive security, where the adversary has to commit to a single test query after seeing all public keys. As a feasibility result, we bring forward the first scheme that enjoys compact public keys and tight semi-adaptive security under the conjunction of the matrix Diffie-Hellman and learning with errors assumptions. We believe that our results shed a new light on the role of adaptivity in NIKE security, and also illustrate the special role of NIKE when it comes to tight security reductions.
2020
JOFC
Multilinear Maps from Obfuscation
We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the $${\text {DDH}} $$ DDH assumption hold for them. Our first construction is symmetric and comes with a $$\kappa $$ κ -linear map $$\mathbf{e }: {{\mathbb {G}}}^\kappa \longrightarrow {\mathbb {G}}_T$$ e : G κ ⟶ G T for prime-order groups $${\mathbb {G}}$$ G and $${\mathbb {G}}_T$$ G T . To establish the hardness of the $$\kappa $$ κ -linear $${\text {DDH}} $$ DDH problem, we rely on the existence of a base group for which the $$\kappa $$ κ -strong $${\text {DDH}} $$ DDH assumption holds. Our second construction is for the asymmetric setting, where $$\mathbf{e }: {\mathbb {G}}_1 \times \cdots \times {\mathbb {G}}_{\kappa } \longrightarrow {\mathbb {G}}_T$$ e : G 1 × ⋯ × G κ ⟶ G T for a collection of $$\kappa +1$$ κ + 1 prime-order groups $${\mathbb {G}}_i$$ G i and $${\mathbb {G}}_T$$ G T , and relies only on the 1-strong $${\text {DDH}} $$ DDH assumption in its base group. In both constructions, the linearity $$\kappa $$ κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group $$\mathbb {Z}_N^{+}$$ Z N + . At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.
2020
EUROCRYPT
On Instantiating the Algebraic Group Model from Falsifiable Assumptions 📺
Thomas Agrikola Dennis Hofheinz Julia Kastner
We provide a standard-model implementation (of a relaxation) of the algebraic group model (AGM, [Fuchsbauer, Kiltz, Loss, CRYPTO 2018]). Specifically, we show that every algorithm that uses our group is algebraic, and hence "must know" a representation of its output group elements in terms of its input group elements. Here, "must know" means that a suitable extractor can extract such a representation efficiently. We stress that our implementation relies only on falsifiable assumptions in the standard model, and in particular does not use any knowledge assumptions. As a consequence, our group allows to transport a number of results obtained in the AGM into the standard model, under falsifiable assumptions. For instance, we show that in our group, several Diffie-Hellman-like assumptions (including computational Diffie-Hellman) are equivalent to the discrete logarithm assumption. Furthermore, we show that our group allows to prove the Schnorr signature scheme tightly secure in the random oracle model. Our construction relies on indistinguishability obfuscation, and hence should not be considered as a practical group itself. However, our results show that the AGM is a realistic computational model (since it can be instantiated in the standard model), and that results obtained in the AGM are also possible with standard-model groups.
2020
PKC
The Usefulness of Sparsifiable Inputs: How to Avoid Subexponential iO 📺
We consider the problem of removing subexponential reductions to indistinguishability obfuscation (iO) in the context of obfuscating probabilistic programs. Specifically, we show how to apply complexity absorption (Zhandry Crypto 2016) to the recent notion of probabilistic indistinguishability obfuscation (piO, Canetti et al. TCC 2015). As a result, we obtain a variant of piO which allows to obfuscate a large class of probabilistic programs, from polynomially secure indistinguishability obfuscation and extremely lossy functions. Particularly, our piO variant is able to obfuscate circuits with specific input domains regardless of the performed computation. We then revisit several (direct or indirect) applications of piO, and obtain – a fully homomorphic encryption scheme (without circular security assumptions), – a multi-key fully homomorphic encryption scheme with threshold decryption, – an encryption scheme secure under arbitrary key-dependent messages, – a spooky encryption scheme for all circuits, – a function secret sharing scheme with additive reconstruction for all circuits, all from polynomially secure iO, extremely lossy functions, and, depending on the scheme, also other (but polynomial and comparatively mild) assumptions. All of these assumptions are implied by polynomially secure iO and the (non-polynomial, but very well-investigated) exponential DDH assumption. Previously, all the above applications required to assume the subexponential security of iO (and more standard assumptions).
2019
PKC
On Tightly Secure Primitives in the Multi-instance Setting
Dennis Hofheinz Ngoc Khanh Nguyen
We initiate the study of general tight reductions in cryptography. There already exist a variety of works that offer tight reductions for a number of cryptographic tasks, ranging from encryption and signature schemes to proof systems. However, our work is the first to provide a universal definition of a tight reduction (for arbitrary primitives), along with several observations and results concerning primitives for which tight reductions have not been known.Technically, we start from the general notion of reductions due to Reingold, Trevisan, and Vadhan (TCC 2004), and equip it with a quantification of the respective reduction loss, and a canonical multi-instance extension to primitives. We then revisit several standard reductions whose tight security has not yet been considered. For instance, we revisit a generic construction of signature schemes from one-way functions, and show how to tighten the corresponding reduction by assuming collision-resistance from the used one-way function. We also obtain tightly secure pseudorandom generators (by using suitable rerandomisable hard-core predicates), and tightly secure lossy trapdoor functions.
2019
EUROCRYPT
Designated-Verifier Pseudorandom Generators, and Their Applications 📺
Geoffroy Couteau Dennis Hofheinz
We provide a generic construction of non-interactive zero-knowledge (NIZK) schemes. Our construction is a refinement of Dwork and Naor’s (FOCS 2000) implementation of the hidden bits model using verifiable pseudorandom generators (VPRGs). Our refinement simplifies their construction and relaxes the necessary assumptions considerably.As a result of this conceptual improvement, we obtain interesting new instantiations:A designated-verifier NIZK (with unbounded soundness) based on the computational Diffie-Hellman (CDH) problem. If a pairing is available, this NIZK becomes publicly verifiable. This constitutes the first fully secure CDH-based designated-verifier NIZKs (and more generally, the first fully secure designated-verifier NIZK from a non-generic assumption which does not already imply publicly-verifiable NIZKs), and it answers an open problem recently raised by Kim and Wu (CRYPTO 2018).A NIZK based on the learning with errors (LWE) assumption, and assuming a non-interactive witness-indistinguishable (NIWI) proof system for bounded distance decoding (BDD). This simplifies and improves upon a recent NIZK from LWE that assumes a NIZK for BDD (Rothblum et al., PKC 2019).
2019
ASIACRYPT
Dual-Mode NIZKs from Obfuscation
Dennis Hofheinz Bogdan Ursu
Two standard security properties of a non-interactive zero-knowledge (NIZK) scheme are soundness and zero-knowledge. But while standard NIZK systems can only provide one of those properties against unbounded adversaries, dual-mode NIZK systems allow to choose dynamically and adaptively which of these properties holds unconditionally. The only known dual-mode NIZK schemes are Groth-Sahai proofs (which have proved extremely useful in a variety of applications), and the FHE-based NIZK constructions of Canetti et al. and Peikert et al, which are concurrent and independent to this work. However, all these constructions rely on specific algebraic settings.Here, we provide a generic construction of dual-mode NIZK systems for all of NP. The public parameters of our scheme can be set up in one of two indistinguishable ways. One way provides unconditional soundness, while the other provides unconditional zero-knowledge. Our scheme relies on subexponentially secure indistinguishability obfuscation and subexponentially secure one-way functions, but otherwise only on comparatively mild and generic computational assumptions. These generic assumptions can be instantiated under any one of the DDH, $$k$$-LIN, DCR, or QR assumptions.As an application, we reduce the required assumptions necessary for several recent obfuscation-based constructions of multilinear maps. Combined with previous work, our scheme can be used to construct multilinear maps from obfuscation and a group in which the strong Diffie-Hellman assumption holds. We also believe that our work adds to the understanding of the construction of NIZK systems, as it provides a conceptually new way to achieve dual-mode properties.
2018
EUROCRYPT
2018
CRYPTO
On Tightly Secure Non-Interactive Key Exchange 📺
Julia Hesse Dennis Hofheinz Lisa Kohl
We consider the reduction loss of security reductions for non-interactive key exchange (NIKE) schemes. Currently, no tightly secure NIKE schemes exist, and in fact Bader et al. (EUROCRYPT 2016) provide a lower bound (of $$\varOmega (n^2)$$, where $$n$$ is the number of parties an adversary interacts with) on the reduction loss for a large class of NIKE schemes.We offer two results: the first NIKE scheme with a reduction loss of $$n/2$$ that circumvents the lower bound of Bader et al., but is of course still far from tightly secure. Second, we provide a generalization of Bader et al.’s lower bound to a larger class of NIKE schemes (that also covers our NIKE scheme), with an adapted lower bound of $$n/2$$ on the reduction loss. Hence, in that sense, the reduction for our NIKE scheme is optimal.
2018
PKC
Interactively Secure Groups from Obfuscation
Thomas Agrikola Dennis Hofheinz
We construct a mathematical group in which an interactive variant of the very general Uber assumption holds. Our construction uses probabilistic indistinguishability obfuscation, fully homomorphic encryption, and a pairing-friendly group in which a mild and standard computational assumption holds. While our construction is not practical, it constitutes a feasibility result that shows that under a strong but generic, and a mild assumption, groups exist in which very general computational assumptions hold. We believe that this grants additional credibility to the Uber assumption.
2018
ASIACRYPT
Identity-Based Encryption Tightly Secure Under Chosen-Ciphertext Attacks
Dennis Hofheinz Dingding Jia Jiaxin Pan
We propose the first identity-based encryption (IBE) scheme that is (almost) tightly secure against chosen-ciphertext attacks. Our scheme is efficient, in the sense that its ciphertext overhead is only seven group elements, three group elements more than that of the state-of-the-art passively (almost) tightly secure IBE scheme. Our scheme is secure in a multi-challenge setting, i.e., in face of an arbitrary number of challenge ciphertexts. The security of our scheme is based upon the standard symmetric external Diffie-Hellman assumption in pairing-friendly groups, but we also consider (less efficient) generalizations under weaker assumptions.
2018
PKC
Graded Encoding Schemes from Obfuscation
We construct a graded encoding scheme (GES), an approximate form of graded multilinear maps. Our construction relies on indistinguishability obfuscation, and a pairing-friendly group in which (a suitable variant of) the strong Diffie–Hellman assumption holds. As a result of this abstract approach, our GES has a number of advantages over previous constructions. Most importantly: We can prove that the multilinear decisional Diffie–Hellman (MDDH) assumption holds in our setting, assuming the used ingredients are secure (in a well-defined and standard sense). Hence, our GES does not succumb to so-called “zeroizing” attacks if the underlying ingredients are secure.Encodings in our GES do not carry any noise. Thus, unlike previous GES constructions, there is no upper bound on the number of operations one can perform with our encodings. Hence, our GES essentially realizes what Garg et al. (EUROCRYPT 2013) call the “dream version” of a GES. Technically, our scheme extends a previous, non-graded approximate multilinear map scheme due to Albrecht et al. (TCC 2016-A). To introduce a graded structure, we develop a new view of encodings at different levels as polynomials of different degrees.
2017
EUROCRYPT
Adaptive Partitioning 📺
Dennis Hofheinz
2017
CRYPTO
2017
CRYPTO
2017
TCC
2016
EUROCRYPT
2016
TCC
2016
TCC
2016
TCC
2016
TCC
2016
ASIACRYPT
2016
TCC
2016
TCC
2015
JOFC
2015
JOFC
2015
JOFC
2015
TCC
2015
PKC
2015
ASIACRYPT
2014
CRYPTO
2014
PKC
2014
TCC
2013
PKC
2013
CRYPTO
2013
EUROCRYPT
2013
EUROCRYPT
2013
JOFC
Polynomial Runtime and Composability
We devise a notion of polynomial runtime suitable for the simulation-based security analysis of multi-party cryptographic protocols. Somewhat surprisingly, straightforward notions of polynomial runtime lack expressivity for reactive tasks and/or lead to an unnatural simulation-based security notion. Indeed, the problem has been recognized in previous works, and several notions of polynomial runtime have already been proposed. However, our new notion, dubbed reactive polynomial time, is the first to combine the following properties: it is simple enough to support simple security/runtime analyses,it is intuitive in the sense that all intuitively feasible protocols and attacks (and only those) are considered polynomial-time,it supports secure composition of protocols in the sense of a universal composition theorem. We work in the Universal Composability (UC) protocol framework. We remark that while the UC framework already features a universal composition theorem, we develop new techniques to prove secure composition in the case of reactively polynomial-time protocols and attacks.
2012
EUROCRYPT
2012
CRYPTO
2012
PKC
2012
PKC
2012
JOFC
Bonsai Trees, or How to Delegate a Lattice Basis
We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area. Applications of bonsai trees include an efficient, stateless ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and the first hierarchical identity-based encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional number-theoretic cryptography.
2012
JOFC
Programmable Hash Functions and Their Applications
Dennis Hofheinz Eike Kiltz
We introduce a new combinatorial primitive called programmable hash functions (PHFs). PHFs can be used to program the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard model realizations of PHFs (with different parameters).The programmability makes PHFs a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps.
2011
ASIACRYPT
2011
JOFC
2010
TCC
2010
JOFC
2010
EUROCRYPT
2010
EUROCRYPT
2010
EUROCRYPT
2009
EUROCRYPT
2009
EUROCRYPT
2009
CRYPTO
2008
EUROCRYPT
2008
CRYPTO
2007
ASIACRYPT
2007
CRYPTO
2007
TCC
2006
EUROCRYPT
2005
TCC
2004
TCC
2003
PKC

Program Committees

Crypto 2021
TCC 2019
TCC 2019 (Program chair)
Eurocrypt 2018
PKC 2017
Crypto 2017
Eurocrypt 2016
TCC 2015
TCC 2014
Crypto 2013
Eurocrypt 2012
TCC 2012
Asiacrypt 2011
Asiacrypt 2010
TCC 2008