International Association
for Cryptologic Research

In the *Distributed Secret Sharing Generation* (DSG) problem $n$ parties wish to obliviously sample a secret-sharing of a random value $s$ taken from some finite field, without letting any of the parties learn $s$. *Distributed Key Generation* (DKG) is a closely related variant of the problem in which, in addition to their private shares, the parties also generate a public ``commitment'' $g^s$ to the secret. Both DSG and DKG are central primitives in the domain of secure multiparty computation and threshold cryptography.

In this paper, we study the communication complexity of DSG and DKG. Motivated by large-scale cryptocurrency and blockchain applications, we ask whether it is possible to obtain protocols in which the communication per party is a constant that does not grow with the number of parties. We answer this question to the affirmative in a model where broadcast communication is implemented via a public bulletin board (e.g., a ledger). Specifically, we present a constant-round DSG/DKG protocol in which the number of bits that each party sends/receives from the public bulletin board is a constant that depends only on the security parameter and the field size but does not grow with the number of parties $n$. In contrast, in all existing solutions at least some of the parties send $\Omega(n)$ bits.

Our protocol works in the near-threshold setting. Given arbitrary privacy/correctness parameters $0<\tau_p<\tau_c<1$, the protocol tolerates up to $\tau_p n$ actively corrupted parties and delivers shares of a random secret according to some $\tau_p n$-private $\tau_c n$-correct secret sharing scheme, such that the adversary cannot bias the secret or learn anything about it. The protocol is based on non-interactive zero-knowledge proofs, non-interactive commitments and a novel secret-sharing scheme with special robustness properties that is based on Low-Density Parity-Check codes. As a secondary contribution, we extend the formal MPC-based treatment of DKG/DSG, and study new aspects of Affine Secret Sharing Schemes.

Recent attacks and applications have led to the need for symmetric encryption schemes that, in addition to providing the usual authenticity and privacy, are also committing. In response, many committing authenticated encryption schemes have been proposed. However, all known schemes, in order to provide s bits of committing security, suffer an expansion---this is the length of the ciphertext minus the length of the plaintext---of 2s bits. This incurs a cost in bandwidth or storage. (We typically want s=128, leading to 256-bit expansion.) However, it has been considered unavoidable due to birthday attacks. We show how to bypass this limitation. We give authenticated encryption (AE) schemes that provide s bits of committing security, yet suffer expansion only around s as long as messages are long enough, namely more than s bits. We call such schemes succinct. We do this via a generic, ciphertext-shortening transform called SC: given an AE scheme with 2s-bit expansion, SC returns an AE scheme with s-bit expansion while preserving committing security. SC is very efficient; an AES-based instantiation has overhead just two AES calls. As a tool, SC uses a collision-resistant invertible PRF called HtM, that we design, and whose analysis is technically difficult. To add the committing security that SC assumes to a base scheme, we also give a transform CTY that improves Chan and Rogaway's CTX. Our results hold in a general framework for authenticated encryption, called AE3, that includes both AE1 (also called AEAD) and AE2 (also called nonce-hiding AE) as special cases, so that we in particular obtain succinctly-committing AE schemes for both these settings.

The Bluetooth protocol for wireless connection between devices comes with several security measures to protect confidentiality and integrity of data. At the heart of these security protocols lies the Secure Simple Pairing, wherewith the devices can negotiate a shared key before communicating sensitive data. Despite the good intentions, the Bluetooth security protocol has repeatedly been shown to be vulnerable, especially with regard to active attacks on the Secure Simple Pairing.

We propose here a mechanism to limit active attacks on the Secure Connections protocol (the more secure version of the Secure Simple Pairing protocol), without infringing on the current Bluetooth protocol stack specification. The idea is to run an authentication protocol, like a classical challenge-response step for certified keys, within the existing infrastructure, even at a later, more convenient point in time. We prove that not only does this authentication step ensure freshness of future encryption keys, but an interesting feature is that it—a posteriori—also guarantees security of previously derived encryption keys. We next argue that this approach indeed prevents a large set of known attacks on the Bluetooth protocol.

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth++, Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation $x^e$ requires at least $\log_2 e$ sequential multiplications.

In this work, we analyze the security of these algebraic VDF candidates. In particular, we show that the latency of exponentiation can be reduced using parallel computation, against the preliminary assumptions.

We study elastic SNARKs, a concept introduced by the elegant work of Gemini (EUROCRYPTO 2022). The prover of elastic SNARKs has multiple configurations with different time and memory tradeoffs and the output proof is independent of the chosen configuration. In addition, during the execution of the protocol, the space-efficient prover can pause the protocol and save the current state. The time-efficient prover can then resume the protocol from that state. Gemini constructs an elastic SNARK for R1CS.

We present Epistle, an elastic SNARK for Plonk constraint system. For an instance with size $N$, in the time-efficient configuration, the prover uses $O_{\lambda} (N)$ cryptographic operations and $O(N)$ memory; in the space-efficient configuration, the prover uses $O_{\lambda} (N \log N)$ cryptographic operations and $O(\log N)$ memory. Compared to Gemini, our approach reduces the asymptotic time complexity of the space-efficient prover by a factor of $\log N$. The key technique we use is to make the toolbox for multivariate PIOP provided by HyperPlonk (EUROCRYPTO 2023) elastic, with the most important aspect being the redesign of each protocol in the toolbox in the streaming model. We implement Epistle in Rust. Our benchmarks show that Epistle maintains a stable memory overhead of around $1.5$ GB for instance sizes exceeding $2^{21}$, while the time overhead shows a linear growth trend.

Differential-linear cryptanalysis was introduced by Langford and Hellman in 1994 and has been extensively studied since then. In 2019, Bar-On et al. presented the Differential-Linear Connectivity Table (DLCT), which connects the differential part and the linear part, thus an attacked cipher is divided to 3 subciphers: the differential part, the DLCT part, and the linear part. In this paper, we firstly present an accurate mathematical formula which establishes a relation between differential-linear and truncated differential cryptanalysis. Using the formula, the bias estimate of a differential-linear distinguisher can be converted to the probability calculations of a series of truncated differentials. Then, we propose a novel and natural concept, the TDT, which can be used to accelerate the calculation of the probabilities of truncated differentials. Based on the formula and the TDT, we propose two novel approaches for estimating the bias of a differential-linear distinguisher. We demonstrate the accuracy and efficiency of our new approaches by applying them to 5 symmetric-key primitives: Ascon, Serpent, KNOT, AES, and CLEFIA. For Ascon and Serpent, we update the best known differential-linear distinguishers. For KNOT AES, and CLEFIA, for the first time we give the theoretical differential-linear biases for different rounds.

The shuffle model has recently emerged as a popular setting for differential privacy, where clients can communicate with a central server using anonymous channels or an intermediate message shuffler. This model was also explored in the context of cryptographic tasks such as secure aggregation and private information retrieval (PIR). However, this study was almost entirely restricted to the stringent notion of information-theoretic security.

In this work, we study computationally secure aggregation protocols and PIR in the shuffle model. Our starting point is the insight that the previous technique of shuffling additive shares can be improved in the computational setting. We show that this indeed holds under the standard learning parity with noise (LPN) assumption, but even better efficiency follows from plausible conjectures about the multi-disjoint syndrome decoding (MDSD) problem that we introduce and study in this work.

We leverage the above towards improving the efficiency of secure aggregation and PIR in the shuffle model. For secure aggregation of long vectors, our protocols require $9\times$-$25\times$ less communication than the previous information-theoretic solutions. Our PIR protocols enjoy the simplicity and concrete efficiency benefits of multi-server PIR while only requiring a single server to store the database. Under the MDSD assumption, they improve over recent single-server PIR constructions by up to two orders of magnitude.

One of the most promising avenues for realizing scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. Such a cycle consists of two elliptic curves E/GF(p) and E'/GF(q) that both have a low embedding degree and also satisfy q = #E and p = #E'. These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first proposed for use in proof systems, no new constructions of 2-cycles have been found.

In this paper, we generalize the notion of cycles of pairing-friendly elliptic curves to study cycles of pairing-friendly abelian varieties, with a view towards realizing more efficient pairing-based SNARKs. We show that considering abelian varieties of dimension larger than 1 unlocks a number of interesting possibilities for finding pairing-friendly cycles, and we give several new constructions that can be instantiated at any security level.

We design and implement a novel post-quantum signature scheme based on the Legendre PRF, named Loquat. Prior to this work, efficient approaches for constructing post-quantum signatures with comparable security assumptions mainly used the MPC-in-the-head paradigm or hash trees. Our method departs from these paradigms and, notably, is SNARK-friendly, a feature not commonly found in earlier designs. Loquat requires significantly fewer computational operations for verification than other symmetric-key-based post-quantum signature schemes that support stateless many-time signing. Notably, the performance of Loquat remains practical even when employing algebraic hash functions. Our Python-based implementations of Loquat demonstrate a signature size of 46KB, with a signing time of 5.04 seconds and a verification time of merely 0.21 seconds. Instantiating the random oracle with an algebraic hash function results in the R1CS constraints for signature verification being about 148K, 7 to 175 times smaller than those required for state-of-the-art MPC-in-the-head-based signatures and 3 to 9 times less than those for SPHINCS+ [Bernstein et al. CCS’19].

We explore two applications of Loquat. First, we incorporate it into the ID-based ring signature scheme [Buser et al. ACNS’22], achieving a significant reduction in signature size from 1.9 MB to 0.9 MB with stateless signing and practical master key generation. Our second application presents a SNARK-based aggregate signature scheme. We use the implementations of Aurora [Ben-Sasson et al. EC’19] and Fractal [Chiesa et al. EC’20] to benchmark our aggregate signature’s performance. Our findings show that aggregating 32 Loquat signatures using Aurora results in a proving time of about 7 minutes, a verification time of 66 seconds, and an aggregate signature size of 197 KB. Furthermore, by leveraging the recursive proof composition feature of Fractal, we achieve an aggregate signature with a constant size of 145 KB, illustrating Loquat’s potential for scalability in cryptographic applications.

We use pairings over elliptic curves to give a collusion-resistant traitor tracing scheme where the sizes of public keys, secret keys, and ciphertexts are independent of the number of users. Prior constructions from pairings had size $\Omega(N^{1/3})$. Our construction is non-black box.

Homomorphic encryption can address key privacy challenges in cloud-based outsourcing by enabling potentially untrusted servers to perform meaningful computation directly on encrypted data. While most homomorphic encryption schemes offer addition and multiplication over ciphertexts natively, any non-linear functions must be implemented as costly polynomial approximations due to this restricted computational model. Nevertheless, the CGGI cryptosystem is capable of performing arbitrary univariate functions over ciphertexts in the form of lookup tables through the use of programmable bootstrapping. While promising, this procedure can quickly become costly when high degrees of precision are required. To address this challenge, we propose Ripple: a framework that introduces different approximation methodologies based on discrete wavelet transforms (DWT) to decrease the number of entries in homomorphic lookup tables while maintaining high accuracy. Our empirical evaluations demonstrate significant error reduction compared to plain quantization methods across multiple non-linear functions. Notably, Ripple improves runtime performance for several realistic benchmarks, such as logistic regression and cross-correlation, among others.

Boolean Searchable Symmetric Encryption (SSE) enables secure outsourcing of databases to an untrusted server in encrypted form and allows the client to execute secure Boolean queries involving multiple keywords. The leakage of keyword pair result pattern (KPRP) in a Boolean search poses a significant threat, which reveals the intersection of documents containing any two keywords involved in a search and can be exploited by attackers to recover plaintext information about searched keywords (USENIX Security’16). However, existing KPRP-hiding schemes either rely on Bloom filters (S&P’14, CCS’18), leading to high false positive search results (where non-matching documents could be erroneously identified as matches) that hinder the extension to multi-client settings (CCS’13), or require excessive server storage (PETS’23), making them impractical for large-scale sparse databases.

In this paper, we introduce Hidden Boolean Search (HBS), the first KPRP-hiding Boolean SSE scheme with both negligible false positives (essential for satisfying the standard correctness definition of SSE) and low server storage requirements. HBS leverages a novel cryptographic tool called Result-hiding Filter (RH-filter). It distinguishes itself as the first tool that supports computationally correct membership queries with hiding results at nearly constant overhead. With the help of RH-filter, compared to the most efficient KPRP-hiding scheme (CCS’18) in terms of overall storage and search efficiency, HBS surpasses it across all performance metrics, mitigates false positives, and achieves significantly stronger query expressiveness. We further extend HBS to the dynamic setting, resulting in a scheme named DHBS, which maintains KPRP-hiding while ensuring forward and backward privacy—two critical security guarantees in the dynamic setting.

Direct Anonymous Attestation (DAA) allows a (host) device with a Trusted Platform Module (TPM) to prove that it has a certified configuration of hardware and software whilst preserving the privacy of the device. All deployed DAA schemes are based on classical security assumptions. Despite a long line of works proposing post-quantum designs, the vast majority give only theoretical schemes and where concrete parameters are computed, their efficiency is far from practical. Our first contribution is to define collaborative, segregated, non-interactive zero knowledge (CoSNIZK). This notion generalizes the property of collaborative zero-knowledge as formalised by Ozdemir and Boneh (USENIX ’22) so that the zero-knowledge property need only apply to a subset of provers during collaborative proof generation. This if of particular interest for proxy-cryptography in which part of an expensive but sensitive computation may be delegated to another party. We give a lattice-based CoSNIZK based on the highly efficient proof framework in (Crypto ’22).

Our main contribution is the construction of a DAA based on the hardness of problems over module lattices as well as the ISISf assumption recently introduced by Bootle et al. (Crypto ’23). A key component of our work is the CoSNIZK construction which allows the TPM and host to jointly create attestations whilst protecting TPM key material from a potentially corrupt host. We prove the security of our DAA scheme according to the well-established UC definition of Camenisch et al. (PKC ’16). Our design achieves DAA signatures more than 1.5 orders of magnitude smaller than previous works at only 38KB making it the first truly practical candidate for post-quantum DAA.

We explore the problem of preventing length leakage in oblivious data access mechanisms with passive persistent adversaries. Designing mechanisms that prevent both access pattern and length leakage requires navigating a three-way tradeoff between storage footprint, bandwidth footprint, and the information leaked to the adversary. We establish powerful lower bounds on achievable storage and bandwidth footprints for a variety of leakage profiles, and present constructions that perfectly or near-perfectly match the lower bounds.

In a federated learning (FL) system, decentralized data owners (clients) could upload their locally trained models to a central server, to jointly train a global model. Malicious clients may plant backdoors into the global model through uploading poisoned local models, causing misclassification to a target class when encountering attacker-defined triggers. Existing backdoor defenses show inconsistent performance under different system and adversarial settings, especially when the malicious updates are made statistically close to the benign ones. In this paper, we first reveal the fact that planting subsequent backdoors with the same target label could significantly help to maintain the accuracy of previously planted back- doors, and then propose a novel proactive backdoor detection mechanism for FL named BackdoorIndicator, which has the server inject indicator tasks into the global model leveraging out-of-distribution (OOD) data, and then utilizing the fact that any backdoor samples are OOD samples with respect to benign samples, the server, who is completely agnostic of the potential backdoor types and target labels, can accurately detect the presence of backdoors in uploaded models, via evaluating the indicator tasks. We perform systematic and extensive empirical studies to demonstrate the consistently superior performance and practicality of BackdoorIndicator over baseline defenses, across a wide range of system and adversarial settings.

Multivariate Cryptography is one of the main candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate polynomials $\mathcal{F}$ (often quadratic). The secret polynomials $\mathcal{F}$ posses a trapdoor that allows the legitimate user to find a solution of the corresponding system, while the public polynomials $\mathcal G=\mathcal S\circ\mathcal F\circ\mathcal T$ look like random polynomials. The polynomials $\mathcal G$ and $\mathcal F$ are said to be affine equivalent. In this article, we present a more general way of constructing a multivariate scheme by considering the CCZ equivalence, which has been introduced and studied in the context of vectorial Boolean functions.

We present the first comprehensive approach for detecting and analyzing symmetric cryptographic primitives in gate-level descriptions of hardware. To capture both ASICs and FPGAs, we model the hardware as a directed graph, where gates become nodes and wires become edges. For modern chips, those graphs can easily consist of hundreds of thousands of nodes. More abstractly, we find subgraphs corresponding to cryptographic primitives in a potentially huge graph, the sea-of-gates, describing an entire chip. As we are particularly interested in unknown cryptographic algorithms, we cannot rely on searching for known parts such as S-boxes or round constants. Instead, we are looking for parts of the chip that perform highly local computations. A major result of our work is that many symmetric algorithms can be reliably located and sometimes even identified by our approach, which we call HAWKEYE. Our findings are verified by extensive experimental results, which involve SPN, ARX, Feistel, and LFSR-based ciphers implemented for both FPGAs and ASICs. We demonstrate the real-world applicability of HAWKEYE by evaluating it on OpenTitan's Earl Grey chip, an open-source secure micro-controller design. HAWKEYE locates all major cryptographic primitives present in the netlist comprising 424341 gates in 44.3 seconds.

In this paper, we study the computation of complex mathematical functions in statements executed on top of zero-knowledge proofs (ZKP); these functions may include roots, exponentials and logarithms, trigonometry etc. While existing approaches to these functions in privacy-preserving computations (and sometimes also in general-purpose processors) have relied on polynomial approximation, more powerful methods are available for ZKP. In this paper, we note that in ZKP, all algebraic functions are exactly computable. Recognizing that, we proceed to the approximation of transcendental functions with algebraic functions. We develop methods of approximation, instantiate them on a number of common transcendental functions, and benchmark their precision and efficiency in comparison with best polynomial approximations.

As an applied cryptographer, you’ll be pushing the boundaries of cryptographic knowledge along with the Zircuit core research team. You will work together with Zircuit’s elite and tight-knit team to tackle new theoretical problems using cryptography and apply existing cryptographic systems in innovative ways.

Zircuit’s cryptographic problems mainly revolve around zero knowledge proofs (zk-SNARK specifically). We do not expect mastery in all zero knowledge proof systems, but mastery in at least one is required. You should have a strong theoretical background and be comfortable reading and writing code.

If this sounds like you, then we highly encourage you to apply!

Expertise

Mastery of at least one zk-SNARK/zk-STARK proof system

Ability to code and develop software. Experience in least one major programming language and familiarity with versioning software

Ability to read and interpret academic papers

Ability to communicate complex ideas effectively and bridge the gap between theory and practice

Nice to have - familiarity with Circom for writing zero knowledge circuits

Nice to have - familiarity with existing designs of zero knowledge applications in blockchain.

Compensation & Perks

A competitive salary that matches your experience, plus performance bonuses and token grants

Work from anywhere, 100% remote, and flexible working hours

Generous paid time off, including maternity/paternity leave

Retirement/pension plan

Free gym membership, or any virtual alternative of your choice

Join all-expenses-paid retreats in exotic/exclusive locations with the team

Closing date for applications:

Contact: candidate-upload-to-job-rlPL6O4rdXfOvml@inbox.ashbyhq.com

More information: https://jobs.ashbyhq.com/Zircuit/64780490-7248-4e56-8d20-3c29161c6634

We are recruiting a postdoc to work with us (Razvan Barbulescu and Alice Pellet-Mary) on quantum cryptanalysis. More precisely, we are interested in

• quantum cryptanalysis of lattice problems (LWE, SIS, shortest vector problem, ...)
• quantum cryptanalysis of pre-quantum cryptography (e.g., optimizing quantum algorithms for discrete logarithm and factorization)

The starting date is flexible, between September 2024 and September 2025.

The deadline for application is June 30th.

More information about the position and how to apply are available at https://apelletm.pages.math.cnrs.fr/page-perso/documents/positions/HQI_post-doc.pdf

Closing date for applications:

Contact: Alice Pellet-Mary (alice.pellet-mary@math.u-bordeaux.fr) and Razvan Barbulescu (razvan.barbulescu@math.u-bordeaux.fr)

More information: https://apelletm.pages.math.cnrs.fr/page-perso/documents/positions/HQI_post-doc.pdf