International Association
for Cryptologic Research

https://aztec.network/

We’re creating a general-purpose private smart contract layer for Ethereum, affectionately dubbed ‘Aztec 3’.

We utilise bleeding-edge cryptography in our tech stack to realise private transactions on a public blockchain network, particularly in the realm of zero-knowledge cryptography.

As a result we possess a world-class R&D team that has co-authored the Plonk, Plookup and Zeromorph protocols. Plonk in particular is rapidly becoming an industry standard ZK-SNARK technology.

We are looking for experienced cryptographers to expand our R&D team and allow us to further enhance the state-of-the-art when it comes to generating proofs of private computation.

Role focus:

* Research techniques to improve both the constant and asymptotic performance of our cryptographic protocols

* Perform literature reviews to identify new developments that could improve the Prover/Verifier efficiency of our cryptographic protocols (or replace them entirely)

* Develop security proofs for our ZK-SNARK circuit architectures

* Liaise with our applied cryptographers to assist them with implementing our cryptographic protocols in software

Required experience:

* PhD-level qualification in cryptography or a related field

* Named author in one or more papers in the field of zero-knowledge cryptography

* Ability to read and understand software implementations of cryptographic protocols written in C++

* Familiarity with algorithms, data structures and basic programming concepts

* Able to provide clear and constructive feedback for more junior cryptographers / applied cryptographers, mentoring where necessary

What we offer:

* A highly competitive compensation package (including equity)

* Flexible and remote work environment

* 25 days holiday + bank holidays annually

* An opportunity to work at the cutting edge of blockchain and FinTech with a world class cryptography and engineering team

Closing date for applications:

Contact: travis@aztecprotocol.com

More information: https://boards.eu.greenhouse.io/aztec/jobs/4098527101

Full Time =nil; Foundation has been at the forefront of Ethereum scalability solutions since 2018. With a mission to overcome the Ethereum scalability challenge, the team has been working on cutting-edge products such as =nil;’s native Proof Market, zkLLVM, and Placeholder, combining advanced cryptography, zero-knowledge technology, and database management systems. Now we are looking for an experienced Cryptographer, who has an experience or a strong interest in developing zkProof systems. Responsibilities - Developing cryptography algorithms design including proof system design. - Design circuits for protocols’ state proofs for a proof system. - Academic writing. - Security analysis. - Research other solutions related to proof-system\circuits\other cryptography tasks. Qualifications - MS with major in Applied Math or equivalent experience. - Deep expertise in cryptographic algorithms and primitives. - Peer-reviewed publications in cryptography, distributed systems, proof systems. - Proven experience in ZK proof techniques (for example, Groth16, Plonk, STARKs, Marlin). - The language is English, so you’re supposed to be at least B2 level. As part of our hiring process, one of the key stages involves completing a test assignment. You can familiarize yourself with it by following this link https://nilfoundation.notion.site/Applicant-Challenge-Cryptography-Researcher-at-nil-Foundation-2dd2b4535ac14847a69ea46091b78442?pvs=74 Should you be interested, you are welcome to undertake this task and submit the link to your completed assignment along with your application. Alternatively, you may respond with your resume and opt to commence the assignment after engaging with our team. Benefits Apply to discuss your benefit package, including health insurance, language courses, relocation support or other care the company may provide.

Closing date for applications:

Contact: Alex Aristides - Alexisaristdes@nil.foundation

More information: https://nil.foundation/careers/jobs?jobId=eKBawSyO9EDP

We are seeking a highly motivated candidate for a PhD in Cybersecurity. This project aims to advance the field of healthcare cybersecurity through innovative and scalable solutions. The candidate will focus on the security and privacy of healthcare systems, including but not limited to developing decentralized, secure, and privacy-preserving methods for sharing health data.

Starting date: The position is available from January 1, 2025. An earlier commencement might be possible.

Application deadline: October 7, 2024.

We offer:

• Fully funded position for three years
• No teaching obligations
• Stimulating research environment
• Competitive salary and benefits, starting salary from NOK 532,200

More information is available at bit.ly/phd25

Closing date for applications:

Contact: Mohsen Toorani (mohsen.toorani@usn.no)

More information: https://bit.ly/phd25

Multi-party private set union (MPSU) protocol enables $m$ $(m > 2)$ parties, each holding a set, to collectively compute the union of their sets without revealing any additional information to other parties. There are two main categories of MPSU protocols: The first builds on public-key techniques. All existing works in this category involve a super-linear number of public-key operations, resulting in poor practical efficiency. The second builds on oblivious transfer and symmetric-key techniques. The only existing work in this category is proposed by Liu and Gao (ASIACRYPT 2023), which features the best concrete performance among all existing protocols, despite its super-linear computation and communication. Unfortunately, it does not achieve the standard semi-honest security, as it inherently relies on a non-collusion assumption, which is unlikely to hold in practice. Therefore, the problem of constructing a practical MPSU protocol based on oblivious transfer and symmetric-key techniques in standard semi-honest model remains open. Furthermore, there is no MPSU protocol achieving both linear computation and linear communication complexity, which leaves another unresolved problem. In this work, we resolve these two open problems.

- We propose the first MPSU protocol based on oblivious transfer and symmetric-key techniques in the standard semi-honest model. This protocol is $4.9-9.3 \times$ faster than Liu and Gao in the LAN setting. Concretely, our protocol requires only $3.6$ seconds in online phase for 3 parties with sets of $2^{20}$ items each. - We propose the first MPSU protocol achieving both linear computation and linear communication complexity, based on public-key operations. This protocol has the lowest overall communication costs and shows a factor of $3.0-36.5\times$ improvement in terms of overall communication compared to Liu and Gao.

We implement our protocols and conduct an extensive experiment to compare the performance of our protocols and the state-of-the-art. To the best of our knowledge, our implementation is the first correct and secure implementation of MPSU that reports on large-size experiments.

The one-time pad cipher is renowned for its theoretical perfect security, yet its practical deployment is primarily hindered by the key-size and distribution challenge. This paper introduces a novel approach to key distribution called q-stream, designed to make symmetric-key cryptography, and the one-time pad cipher in particular, a viable option for contemporary secure communications, and specifically, post-quantum cryptography, leveraging quantum noise and combinatorics to ensure secure and efficient key-distribution between communicating parties. We demonstrate that our key-distribution mechanism has a variable, yet quantifiable hardness of at least 504 bits, established from immutable mathematical laws, rather than conjectured-intractability, and how we overcome the one-time pad key-size issue with a localised quantum-noise seeded key-generation function, having a system hardness of at least 2304 bits, while introducing sender authentication and message integrity. Whilst the proposed solution has potential applications in fields requiring very high levels of security, such as military communications and large financial transactions, we show from our research with a prototype of q-stream, that it is sufficiently practical and scaleable for use in common browser-based web-applications, without any modification to the browser (i.e. plug-ins), running above SSL/TLS at the application level, where in tests, it achieved a key-distribution rate of around 7 million keys over a 5 minute surge-window, in a single (multi-threaded) instance of q-stream.

We show that the data storage scheme [IEEE/ACM Trans. Netw., 2023, 31(4), 1550-1565] is flawed due to the false secret sharing protocol, which requires that some random $4\times 4$ matrixes over the finite field $F_p$ (a prime $p$) are invertible. But we find its mathematical proof for invertibility is incorrect. To fix this flaw, one needs to check the invertibility of all 35 matrixes so as to generate the proper 7 secret shares.

Oblivious Transfer (OT) is a fundamental cryptographic primitive, becoming a crucial component of a practical secure protocol. OT is typically implemented in software, and one way to accelerate its running time is by using hardware implementations. However, such implementations are vulnerable to side-channel attacks (SCAs). On the other hand, protecting interactive protocols against SCA is highly challenging because of their longer secrets (which include inputs and randomness), more complicated design, and running multiple instances. Consequently, there are no truly practical leakage-resistant OT protocols yet.

In this paper, we introduce two tailored indistinguishability-based security definitions for leakage-resilient OT, focusing on protecting the sender's state. Second, we propose a practical semi-honest secure OT protocol that achieves these security levels while minimizing the assumptions on the protocol's building blocks and the use of a secret state. Finally, we extend our protocol to support sequential composition and explore efficiency-security tradeoffs.

Matrix congruential generators is an important class of pseudorandom number generators. In this paper we show how to predict a class of Matrix congruential generators matrix congruential generators with unknown parameters. Given a few truncated digits of high-order bits output by a matrix congruential generator, we give a method based on lattice reduction to recover the parameters and the initial state of the generator.

Clustering is a crucial unsupervised learning method extensively used in the field of data analysis. For analyzing big data, outsourced computation is an effective solution but privacy concerns arise when involving sensitive information. Fully homomorphic encryption (FHE) enables computations on encrypted data, making it ideal for such scenarios. However, existing privacy-preserving clustering based on FHE are often constrained by the high computational overhead incurred from FHE, typically requiring decryption and interactions after only one iteration of the clustering algorithm. In this work, we propose a more efficient approach to evaluate the one-hot vector for the index of the minimum in an array with FHE, which fully exploits the parallelism of single-instruction-multiple-data of FHE schemes. By combining this with FHE bootstrapping, we present a practical FHE-based k-means clustering protocol whose required round of interactions between the data owner and the server is optimal, i.e., accomplishing the entire clustering process on encrypted data in a single round. We implement this protocol using the CKKS FHE scheme. Experiments show that our protocol significantly outperforms the state-of-the-art FHE-based k-means clustering protocols on various public datasets and achieves comparable accuracy to plaintext result. Additionally, We adapt our protocol to support mini-batch k-means for large-scale datasets and report its performance.

We propose a generalization of Zhandry’s compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry’s technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to represent the permutation in the oracle’s database. As an application of our framework, we show that the one-round sponge construction is unconditionally preimage resistant in the random permutation model. This proves a conjecture by Unruh.

Strike-lists are a common technique for rollback and replay prevention in protocols that require that clients remain anonymous or that their current position in a state machine remain confidential. Strike-lists are heavily used in anonymous credentials, e-cash schemes, and trusted execution environments, and are widely deployed on the web in the form of Privacy Pass (PoPETS '18) and Google Private State Tokens. In such protocols, clients submit pseudorandom tokens associated with each action (e.g., a page view in Privacy Pass) or state transition, and the token is added to a server-side list to prevent reuse.

Unfortunately, the size of a strike-list, and hence the storage required by the server, is proportional to the total number of issued tokens, $N \cdot t$, where $N$ is the number of clients and $t$ is the maximum number of tickets per client. In this work, we ask whether it is possible to realize a strike-list-like functionality, which we call the anonymous tickets functionality, with storage requirements proportional to $N \log(t)$.

For the anonymous tickets functionality we construct a secure protocol from standard assumptions that achieves server storage of $O(N)$ ciphertexts, where each ciphertext encrypts a message of length $O(\log(t))$. We also consider an extension of the strike-list functionality where the server stores an arbitrary state for each client and clients advance their state with some function $s_i\gets f(s_{i-1},\mathsf{auxinput})$, which we call the anonymous outsourced state-keeping functionality. In this setting, malicious clients are prevented from rolling back their state, while honest clients are guaranteed anonymity and confidentiality against a malicious server. We achieve analogous results in this setting for two different classes of functions.

Our results rely on a new technique to preserve client anonymity in the face of selective failure attacks by a malicious server. Specifically, our protocol guarantees that misbehavior of the server either (1) does not prevent the honest client from redeeming a ticket or (2) provides the honest client with an escape hatch that can be used to simulate a redeem in a way that is indistinguishable to the server.

A dot-product proof (DPP) is a simple probabilistic proof system in which the input statement $\mathbf{x}$ and the proof $\boldsymbol{\pi}$ are vectors over a finite field $\mathbb{F}$, and the proof is verified by making a single dot-product query $\langle \mathbf{q},(\mathbf{x} \| \boldsymbol{\pi}) \rangle$ jointly to $\mathbf{x}$ and $\boldsymbol{\pi}$. A DPP can be viewed as a 1-query fully linear PCP. We study the feasibility and efficiency of DPPs, obtaining the following results:

- Small-field DPP. For any finite field $\mathbb{F}$ and Boolean circuit $C$ of size $S$, there is a DPP for proving that there exists $\mathbf{w}$ such that $C(\mathbf{x}, \mathbf{w})=1$ with a proof $\boldsymbol{\pi}$ of length $S\cdot\mathsf{poly}(|\mathbb{F}|)$ and soundness error $\varepsilon=O(1 / \sqrt{|\mathbb{F}|})$. We show this error to be asymptotically optimal. In particular, and in contrast to the best known PCPs, there exist strictly linear-length DPPs over constant-size fields.

- Large-field DPP. If $|\mathbb{F}|\ge\mathsf{poly}(S/\varepsilon)$, there is a similar DPP with soundness error $\varepsilon$ and proof length $O(S)$ (in field elements).

The above results do not rely on the PCP theorem and their proofs are considerably simpler. We apply our DPP constructions toward two kinds of applications.

- Hardness of approximation. We obtain a simple proof for the NP-hardness of approximating MAXLIN (with dense instances) over any finite field $\mathbb{F}$ up to some constant factor $c>1$, independent of $\mathbb{F}$. Unlike previous PCP-based proofs, our proof yields exponential-time hardness under the exponential time hypothesis (ETH).

- Succinct arguments. We improve the concrete efficiency of succinct interactive arguments in the generic group model using input-independent preprocessing. In particular, the communication is comparable to sending two group elements and the verifier's computation is dominated by a single group exponentiation. We also show how to use DPPs together with linear-only encryption to construct succinct commit-and-prove arguments.

EagleSign is one of the 40 “Round 1 Additional Signatures” that is accepted for consideration in the supplementary round of the Post-Quantum Cryptography standardization process, organized by NIST. Its design is based on structured lattices, and it boasts greater simplicity and performance compared to the two lattice signatures already selected for standardization: Falcon and Dilithium.

In this paper, we show that those claimed advantages come at the cost of security. More precisely, we show that the distribution of EagleSign signatures leaks information about the private key, to the point that only a few hundred signatures on arbitrary known messages suffice for a full key recovery, for all proposed parameters.

A related vulnerability also affects EagleSign-V2, a subsequent version of the scheme specifically designed to thwart the initial attack. Although a larger number of signatures is required for key recovery, the idea of the attack remains largely similar. Both schemes come with proofs of security that we show are flawed.

The SHA-3 standard consists of four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, and two extendable-output functions (XOFs), called SHAKE128 and SHAKE256. In this paper, we study the collision resistance of the SHA-3 instances. By analyzing the nonlinear layer, we introduce the concept of maximum difference density subspace, and develop a new target internal difference algorithm by probabilistic linearization. We also exploit new strategies for optimizing the internal differential characteristic. Further more, we figure out the expected size of collision subsets in internal differentials, by analyzing the collision probability of the digests rather than the intermediate states input to the last nonlinear layer. These techniques enhance the analysis of internal differentials, leading to the best collision attacks on four round-reduced variants of the SHA-3 instances. In particular, the number of attacked rounds is extended to 5 from 4 for SHA3-384, and to 6 from 5 for SHAKE256.

Payment channels are one of the most prominent off-chain scaling solutions for blockchain systems. However, regulatory institutions have difficulty embracing them, as the channels lack insights needed for Anti-Money Laundering (AML) auditing purposes. Our work tackles the problem of a formal reliable and controllable inspection of off-ledger payment channels, by offering a novel approach for maintaining and reliably auditing statistics of payment channels. We extend a typical trustless Layer 2 protocol and provide a lightweight and scalable protocol such that: - every state channel is provably auditable w.r.t. a configurable set of policy queries, such that a regulator can retrieve reliable insights about the channel; - no information beyond the answers to auditing queries is leaked; - the cryptographic operations are inexpensive, the setup is simple, and storage complexity is independent of the transaction graph's size. We present a concrete protocol, based on Hydra Isomorphic State Channels (FC'21), and tie the creation of a state channel to real-world identifiers, both in a plain and privacy-preserving manner. For this, we employ verifiable credentials for decentralized identifiers, specifically verifiable Legal Entity Identifiers (vLEI) that increasingly gain traction for financial service providers and regulated institutions.

Enhanced pqsigRM is a code-based hash-and-sign scheme proposed to the second National Institute of Standards and Technology call for post-quantum signatures. The scheme is based on the $(U,U+V)$-construction and it enjoys remarkably small signature lengths, about $1$KBytes for a security level of $128$ bits. Unfortunately we show that signatures leak information about the underlying $(U,U+V)$-structure. It allows to retrieve the private-key with~$100, 000$ signatures.

The aim of an algebraic attack is to find the secret key by solving a collection of relations that describe the internal structure of a cipher for observations of plaintext/cipher-text pairs. Although algebraic attacks are addressed for cryptanalysis of block and stream ciphers, there is a limited understanding of the impact of algebraic representation of the cipher on the efficiency of solving the resulting collection of equations. In this paper, we investigate on how different S-box representations affect the complexity of algebraic attacks, in an empirical manner. In the literature some algebraic properties are intuitively proposed to evaluate optimality of an algebraic description of S-boxes for algebraic cryptanalysis. In this paper, we compare different S-box representation for algebraic cryptanalysis with doing experiments with SR family of block ciphers. We also show that the so-called \textit{Forward-Backward} representation which is in contrast with all mentioned criteria for optimal representations criteria, practically gives better results than the compliant representations. We also compare the representations for both $GF(2)$ and $GF(2^n)$ fields.

Model quantization has become a common practice in machine learning (ML) to improve efficiency and reduce computational/communicational overhead. However, adopting quantization in privacy-preserving machine learning (PPML) remains challenging due to the complex internal structure of quantized operators, which leads to inefficient protocols under the existing PPML frameworks.

In this work, we propose a new PPML paradigm that is tailor-made for and can benefit from quantized models. Our main observation is that lookup tables can ignore the complex internal constructs of any functions which can be used to simplify the quantized operator evaluation. We view the model inference process as a sequence of quantized operators, and each operator is implemented by a lookup table. We then develop an efficient private lookup table evaluation protocol, and its online communication cost is only $\log n$, where $n$ is the size of the lookup table. On a single CPU core, our protocol can evaluate $2^{15}$ tables with 8-bit input and 8-bit output per second.

The resulting PPML framework for quantized models offers extremely fast online performance. The experimental results demonstrate that our quantization strategy achieves substantial speedups over SOTA PPML solutions, improving the online performance by $40\sim 60 \times$ w.r.t. convolutional neural network (CNN) models, such as AlexNet, VGG16, and ResNet18, and by $10\sim 25 \times$ w.r.t. large language models (LLMs), such as GPT-2, GPT-Neo, and Llama2.

Event date: 11 September to 13 September 2024

The authors of Jolt [AST24] pioneered a unique method for creating zero-knowledge virtual machines, known as the lookup singularity. This technique extensively uses lookup tables to create virtual machine circuits. Despite Jolt’s performance being twice as efficient as the previous state-of-the-art1 , there is potential for further enhancement.

The initial release of Jolt uses Spartan [Set20] and Hyrax [WTs+ 18] as their backend, leading to two constraints. First, Hyrax employs Pedersen commitment to build inner product arguments, which requires elliptic curve operations. Second, the verification of a Hyrax commitment takes square root time $O(\sqrt{N})$ relative to the circuit size $N$ . This makes the recursive verification of a Jolt proof impractical, as the verification circuit would need to execute all the Hyrax verification logic in-circuit. A later version of Jolt includes Zeromorph [KT23] and HyperKZG as their commitment backend, making the system recursion-friendly, as now the recursive verifier only needs to perform $O(\log N)$ operations, but at the expense of a need for a trusted setup.

Our scheme, Jolt-b, addresses these issues by transitioning to the extension field of the Goldilocks and using the Basefold commitment scheme [ZCF23], which has an $O(\log^2 N)$ verifier time. This scheme mirrors the modifications of Plonky2 over the original Plonk [GWC19]: it transitions from EC fields to the Goldilocks field; it replaces the EC-based commitment scheme with an encoding-based commitment scheme.

We implemented Jolt-b, along with an optimized version of the Basefold scheme. Our benchmarks show that at a cost of 2.47x slowdown for the prover, we achieve recursion friendliness for the original Jolt. In comparison with other recursion-friendly Jolt variants, our scheme is 1.24x and 1.52x faster in prover time than the Zeromorph and HyperKZG variants of Jolt, respectively.