## CryptoDB

### Fabrice Benhamouda

#### Publications

Year
Venue
Title
2021
EUROCRYPT
Motivated by the goal of designing versatile and flexible secure computation protocols that at the same time require as little interaction as possible, we present new multiparty reusable Non-Interactive Secure Computation (mrNISC) protocols. This notion, recently introduced by Benhamouda and Lin (TCC 2020), is essentially two-round Multi-Party Computation (MPC) protocols where the first round of messages serves as a reusable commitment to the private inputs of participating parties. Using these commitments, any subset of parties can later compute any function of their choice on their respective inputs by just sending a single message to a stateless evaluator, conveying the result of the computation but nothing else. Importantly, the input commitments can be computed without knowing anything about other participating parties (neither their identities nor their number) and they are reusable across any number of desired computations. We give a construction of mrNISC that achieves standard simulation security, as classical multi-round MPC protocols achieve. Our construction relies on the Learning With Errors (LWE) assumption with polynomial modulus, and on the existence of a pseudorandom function (PRF) in $\mathsf{NC}^1$. We achieve semi-malicious security in the plain model and malicious security by further relying on trusted setup (which is unavoidable for mrNISC). In comparison, the only previously known constructions of mrNISC were either using bilinear maps or using strong primitives such as program obfuscation. We use our mrNISC to obtain new Multi-Key FHE (MKFHE) schemes with threshold decryption: - In the CRS model, we obtain threshold MKFHE for $\mathsf{NC}^1$ based on LWE with only {\em polynomial} modulus and PRFs in $\mathsf{NC}^1$, whereas all previous constructions rely on LWE with super-polynomial modulus-to-noise ratio. - In the plain model, we obtain threshold levelled MKFHE for $\mathsf{P}$ based on LWE with {\em polynomial} modulus, PRF in $\mathsf{NC}^1$, and NTRU, and another scheme for constant number of parties from LWE with sub-exponential modulus-to-noise ratio. The only known prior construction of threshold MKFHE (Ananth et al., TCC 2020) in the plain model restricts the set of parties who can compute together at the onset.
2021
EUROCRYPT
We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem mod p in polynomial time for $l > log p$ dimensions. Our algorithm can be combined with Wagner's attack, and leads to a sub-exponential solution for any dimension $l$ with best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto--Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe--Okamoto, and conditional blind signatures such as ZGP17. Schemes for e-cash and anonymous credentials (such as Anonymous Credentials Light) inspired from the above are also affected.
2021
TCC
Secure multiparty computation (MPC) enables $n$ parties, of which up to $t$ may be corrupted, to perform joint computations on their private inputs while revealing only the outputs. Optimizing the asymptotic and concrete costs of MPC protocols has become an important line of research. Much of this research focuses on the setting of an honest majority, where $n \ge 2t+1$, which gives rise to concretely efficient protocols that are either information-theoretic or make a black-box use of symmetric cryptography. Efficiency can be further improved in the case of a {\em strong} honest majority, where $n>2t+1$. Motivated by the goal of minimizing the communication and latency costs of MPC with a strong honest majority, we make two related contributions. \begin{itemize}[leftmargin=*] \item {\bf Generalized pseudorandom secret sharing (PRSS).} Linear correlations serve as an important resource for MPC protocols and beyond. PRSS enables secure generation of many pseudorandom instances of such correlations without interaction, given replicated seeds of a pseudorandom function. We extend the PRSS technique of Cramer et al.\ (TCC 2015) for sharing degree-$d$ polynomials to new constructions leveraging a particular class of combinatorial designs. Our constructions yield a dramatic efficiency improvement when the degree $d$ is higher than the security threshold $t$, not only for standard degree-$d$ correlations but also for several useful generalizations. In particular, correlations for locally converting between slot configurations in share packing'' enable us to avoid the concrete overhead of prior works. \item {\bf Cheap straggler resilience.} In reality, communication is not fully synchronous: protocol executions suffer from variance in communication delays and occasional node or message-delivery failures. We explore the benefits of PRSS-based MPC with a strong honest majority toward robustness against such failures, in turn yielding improved latency delays. In doing so we develop a novel technique for defending against a subtle double-dipping'' attack, which applies to the best existing protocols, with almost no extra cost in communication or rounds. \end{itemize} Combining the above tools requires further work, including new methods for batch verification via distributed zero-knowledge proofs (Boneh et al., CRYPTO 2019) that apply to packed secret sharing. Overall, our work demonstrates new advantages of the strong honest majority setting, and introduces new tools---in particular, generalized PRSS---that we believe will be of independent use within other cryptographic applications.
2021
JOFC
We consider the following basic question: to what extent are standard secret sharing schemes and protocols for secure multiparty computation that build on them resilient to leakage? We focus on a simple local leakage model, where the adversary can apply an arbitrary function of a bounded output length to the secret state of each party, but cannot otherwise learn joint information about the states. We show that additive secret sharing schemes and high-threshold instances of Shamir’s secret sharing scheme are secure under local leakage attacks when the underlying field is of a large prime order and the number of parties is sufficiently large. This should be contrasted with the fact that any linear secret sharing scheme over a small characteristic field is clearly insecure under local leakage attacks, regardless of the number of parties. Our results are obtained via tools from Fourier analysis and additive combinatorics. We present two types of applications of the above results and techniques. As a positive application, we show that the “GMW protocol” for honest-but-curious parties, when implemented using shared products of random field elements (so-called “Beaver Triples”), is resilient in the local leakage model for sufficiently many parties and over certain fields. This holds even when the adversary has full access to a constant fraction of the views. As a negative application, we rule out multiparty variants of the share conversion scheme used in the 2-party homomorphic secret sharing scheme of Boyle et al. (in: Crypto, 2016).
2020
TCC
Blockchains are gaining traction and acceptance, not just for cryptocurrencies, but increasingly as an architecture for distributed computing. In this work we seek solutions that allow a \emph{public} blockchain to act as a trusted long-term repository of secret information: Our goal is to deposit a secret with the blockchain, specify how it is to be used (e.g., the conditions under which it is released), and have the blockchain keep the secret and use it only in the specified manner (e.g., release only it once the conditions are met). This simple functionality enables many powerful applications, including signing statements on behalf of the blockchain, using it as the control plane for a storage system, performing decentralized program-obfuscation-as-a-service, and many more. Using proactive secret sharing techniques, we present a scalable solution for implementing this functionality on a public blockchain, in the presence of a mobile adversary controlling a small minority of the participants. The main challenge is that, on the one hand, scalability requires that we use small committees to represent the entire system, but, on the other hand, a mobile adversary may be able to corrupt the entire committee if it is small. For this reason, existing proactive secret sharing solutions are either non-scalable or insecure in our setting. We approach this challenge via "player replaceability", which ensures the committee is anonymous until after it performs its actions. Our main technical contribution is a system that allows sharing and re-sharing of secrets among the members of small dynamic committees, without knowing who they are until after they perform their actions and erase their secrets. Our solution handles a fully mobile adversary corrupting roughly 1/4 of the participants at any time, and is scalable in terms of both the number of parties and the number of time intervals.
2020
TCC
Reducing interaction in Multiparty Computation (MPC) is a highly desirable goal in cryptography. It is known that 2-round MPC can be based on the minimal assumption of 2-round Oblivious Transfer (OT) [Benhamouda and Lin, Garg and Srinivasan, EC 2018], and 1-round MPC is impossible in general. In this work, we propose a natural hybrid'' model, called \emph{multiparty reusable Non-Interactive Secure Computation (mrNISC)}. In this model, parties publish encodings of their private inputs $x_i$ on a public bulletin board, once and for all. Later, any subset $I$ of them can compute \emph{on-the-fly} a function $f$ on their inputs $\vec x_I = {\{x_i\}}_{i \in I}$ by just sending a single message to a stateless evaluator, conveying the result $f(\vec x_I)$ and nothing else. Importantly, the input encodings can be \emph{reused} in any number of on-the-fly computations, and the same classical simulation security guaranteed by multi-round MPC, is achieved. In short, mrNISC has a minimal yet tractable'' interaction pattern. We initiate the study of mrNISC on several fronts. First, we formalize the model of mrNISC protocols, and present both a UC security definition and a game-based security definition. Second, we construct mrNISC protocols in the plain model with semi-honest and semi-malicious security based on pairing groups. Third, we demonstrate the power of mrNISC by showing two applications: non-interactive MPC (NIMPC) with reusable setup and a distributed version of program obfuscation. At the core of our construction of mrNISC is a witness encryption scheme for a special language that verifies Non-Interactive Zero-Knowledge (NIZK) proofs of the validity of computations over committed values, which is of independent interest.
2019
PKC
Multi-client functional encryption (MCFE) is a more flexible variant of functional encryption whose functional decryption involves multiple ciphertexts from different parties. Each party holds a different secret key and can independently and adaptively be corrupted by the adversary. We present two compilers for MCFE schemes for the inner-product functionality, both of which support encryption labels. Our first compiler transforms any scheme with a special key-derivation property into a decentralized scheme, as defined by Chotard et al. (ASIACRYPT 2018), thus allowing for a simple distributed way of generating functional decryption keys without a trusted party. Our second compiler allows to lift an unnatural restriction present in existing (decentralized) MCFE schemes, which requires the adversary to ask for a ciphertext from each party. We apply our compilers to the works of Abdalla et al. (CRYPTO 2018) and Chotard et al. (ASIACRYPT 2018) to obtain schemes with hitherto unachieved properties. From Abdalla et al., we obtain instantiations of DMCFE schemes in the standard model (from DDH, Paillier, or LWE) but without labels. From Chotard et al., we obtain a DMCFE scheme with labels still in the random oracle model, but without pairings.
2019
ASIACRYPT
Due to the vast number of successful related-key attacks against existing block-ciphers, related-key security has become a common design goal for such primitives. In these attacks, the adversary is not only capable of seeing the output of a function on inputs of its choice, but also on related keys. At Crypto 2010, Bellare and Cash proposed the first construction of a pseudorandom function that could provably withstand such attacks based on standard assumptions. Their construction, as well as several others that appeared more recently, have in common the fact that they only consider linear or polynomial functions of the secret key over complex groups. In reality, however, most related-key attacks have a simpler form, such as the XOR of the key with a known value. To address this problem, we propose the first construction of RKA-secure pseudorandom function for XOR relations. Our construction relies on multilinear maps and, hence, can only be seen as a feasibility result. Nevertheless, we remark that it can be instantiated under two of the existing multilinear-map candidates since it does not reveal any encodings of zero. To achieve this goal, we rely on several techniques that were used in the context of program obfuscation, but we also introduce new ones to address challenges that are specific to the related-key-security setting.
2019
ASIACRYPT
We present a new generic construction of multi-client functional encryption (MCFE) for inner products from single-input functional inner-product encryption and standard pseudorandom functions. In spite of its simplicity, the new construction supports labels, achieves security in the standard model under adaptive corruptions, and can be instantiated from the plain DDH, LWE, and Paillier assumptions. Prior to our work, the only known constructions required discrete-log-based assumptions and the random-oracle model. Since our new scheme is not compatible with the compiler from Abdalla et al. (PKC 2019) that decentralizes the generation of the functional decryption keys, we also show how to modify the latter transformation to obtain a decentralized version of our scheme with similar features.
2019
JOFC
In this paper, we revisit the security of factoring-based signature schemes built via the Fiat–Shamir transform and show that they can admit tighter reductions to certain decisional complexity assumptions such as the quadratic-residuosity, the high-residuosity, and the $\phi$ ϕ -hiding assumptions. We do so by proving that the underlying identification schemes used in these schemes are a particular case of the lossy identification notion introduced by Abdalla et al. at Eurocrypt 2012. Next, we show how to extend these results to the forward-security setting based on ideas from the Itkis–Reyzin forward-secure signature scheme. Unlike the original Itkis–Reyzin scheme, our construction can be instantiated under different decisional complexity assumptions and has a much tighter security reduction. Moreover, we also show that the tighter security reductions provided by our proof methodology can result in concrete efficiency gains in practice, both in the standard and forward-security setting, as long as the use of stronger security assumptions is deemed acceptable. Finally, we investigate the design of forward-secure signature schemes whose security reductions are fully tight.
2018
EUROCRYPT
2018
CRYPTO
We consider the following basic question: to what extent are standard secret sharing schemes and protocols for secure multiparty computation that build on them resilient to leakage? We focus on a simple local leakage model, where the adversary can apply an arbitrary function of a bounded output length to the secret state of each party, but cannot otherwise learn joint information about the states.We show that additive secret sharing schemes and high-threshold instances of Shamir’s secret sharing scheme are secure under local leakage attacks when the underlying field is of a large prime order and the number of parties is sufficiently large. This should be contrasted with the fact that any linear secret sharing scheme over a small characteristic field is clearly insecure under local leakage attacks, regardless of the number of parties. Our results are obtained via tools from Fourier analysis and additive combinatorics.We present two types of applications of the above results and techniques. As a positive application, we show that the “GMW protocol” for honest-but-curious parties, when implemented using shared products of random field elements (so-called “Beaver Triples”), is resilient in the local leakage model for sufficiently many parties and over certain fields. This holds even when the adversary has full access to a constant fraction of the views. As a negative application, we rule out multi-party variants of the share conversion scheme used in the 2-party homomorphic secret sharing scheme of Boyle et al. (Crypto 2016).
2018
PKC
Hash Proof Systems or Smooth Projective Hash Functions (SPHFs) are a form of implicit arguments introduced by Cramer and Shoup at Eurocrypt’02. They have found many applications since then, in particular for authenticated key exchange or honest-verifier zero-knowledge proofs. While they are relatively well understood in group settings, they seem painful to construct directly in the lattice setting.Only one construction of an SPHF over lattices has been proposed in the standard model, by Katz and Vaikuntanathan at Asiacrypt’09. But this construction has an important drawback: it only works for an ad-hoc language of ciphertexts. Concretely, the corresponding decryption procedure needs to be tweaked, now requiring q many trapdoor inversion attempts, where q is the modulus of the underlying Learning With Errors (LWE) problem.Using harmonic analysis, we explain the source of this limitation, and propose a way around it. We show how to construct SPHFs for standard languages of LWE ciphertexts, and explicit our construction over a tag-IND-CCA2 encryption scheme à la Micciancio-Peikert (Eurocrypt’12). We then improve our construction and our analysis in the case where the tag is known in advance or fixed (in the latter case, the scheme is only IND-CPA) with a super-polynomial modulus, to get a stronger type of SPHF, which was never achieved before for any language over lattices.Finally, we conclude with applications of these SPHFs: password-based authenticated key exchange, honest-verifier zero-knowledge proofs, and a relaxed version of witness encryption.
2018
TCC
2017
PKC
2017
PKC
2017
CRYPTO
2017
CRYPTO
2017
JOFC
2016
EUROCRYPT
2016
PKC
2015
PKC
2015
EUROCRYPT
2015
CRYPTO
2015
CRYPTO
2015
ASIACRYPT
2014
CRYPTO
2014
ASIACRYPT
2013
PKC
2013
PKC
2013
CRYPTO
2013
ASIACRYPT

Crypto 2021
PKC 2021
Asiacrypt 2021
Eurocrypt 2020
Crypto 2018
Eurocrypt 2017
PKC 2017