International Association
for Cryptologic Research

Zero-knowledge Succinct Non-interactive ARguments of Knowledge (zkSNARKs) allow a prover to convince a verifier of the correct execution of a large computation in private and easily-verifiable manner. These properties make zkSNARKs a powerful tool for adding accountability, scalability, and privacy to numerous systems such as blockchains and verifiable key directories. Unfortunately, existing zkSNARKs are unable to scale to large computations due to time and space complexity requirements for the prover algorithm. As a result, they cannot handle real-world instances of the aforementioned applications. In this work, we introduce Hᴇᴋᴀᴛᴏɴ, a zkSNARK that overcomes these barriers and can efficiently handle arbitrarily large computations. We construct Hᴇᴋᴀᴛᴏɴ via a new "distribute-and-aggregate" framework that breaks up large computations into small chunks, proves these chunks in parallel in a distributed system, and then aggregates the resulting chunk proofs into a single succinct proof. Underlying this framework is a new technique for efficiently handling data that is shared between chunks that we believe could be of independent interest. We implement a distributed prover for Hᴇᴋᴀᴛᴏɴ, and evaluate its performance on a compute cluster. Our experiments show that Hᴇᴋᴀᴛᴏɴ achieves strong horizontal scalability (proving time decreases linearly as we increase the number of nodes in the cluster), and is able to prove large computations quickly: it can prove computations of size $2^{35}$ gates in under an hour, which is much faster than prior work.

Finally, we also apply Hᴇᴋᴀᴛᴏɴ to two applications of real-world interest: proofs of batched insertion for a verifiable key directory and proving correctness of RAM computations. In both cases, Hᴇᴋᴀᴛᴏɴ is able to scale to handle realistic workloads with better efficiency than prior work.

In recent years, there have been several constructions combining FHE with SNARGs to add integrity guarantees to FHE schemes. Most of these works focused on improving efficiency, while the precise security model with regards to client side input privacy has remained understudied. Only recently it was shown by Manulis and Nguyen (Eurocrypt'24) that this combination does not yield IND-CCA1 security. So an interesting open question is: does the SNARG actually add any meaningful security to input privacy? We address this question in this note and give a security definition that meaningfully captures the security of the FHE plus SNARG construction.

This article presents an innovative project for a Central Bank Digital Currency (CBDC) infrastructure. Focusing on security and reliability, the proposed architecture: (1) employs post-quantum cryptography (PQC) algorithms for long-term security, even against attackers with access to cryptographically-relevant quantum computers; (2) can be integrated with a Trusted Execution Environment (TEE) to safeguard the confidentiality of transaction contents as they are processed by third-parties; and (3) uses Distributed Ledger Technology (DLT) to promote a high level of transparency and tamper resistance for all transactions registered in the system. Besides providing a theoretical discussion on the benefits of this architecture, we experimentally evaluate its components. Namely, as PQC algorithms, we consider three signature schemes being standardized by the National Institute of Standards and Technology (NIST), CRYSTALS-Dilithium, Falcon, and SPHINCS+. Those algorithms are integrated into the Hyperledger Besu (DLT) and executed both inside and outside an Intel SGX TEE environment. According to our results, CRYSTALS-Dilithium-2 combined with classical secp256k1 signatures leads to the shortest execution times when signing blocks in the DLT, reaching 1.68ms without the TEE, and 2.09ms with TEE. The same combination also displays the best results for signature verifications, achieving 0.5ms without a TEE and 1.98ms with a TEE. We also describe the main aspects of the evaluation methodology and the next steps in validating the proposed infrastructure. The conclusions drawn from our experiments is that the combination of PQC and TEE promises highly secure and effective DLT-based CBDC scenarios, ready to face the challenges of the digital financial future and potential quantum threats.

We show that the Chunka-Banerjee-Goswami authentication and key agreement scheme [Wirel. Pers. Commun., 117, 1361-1385, 2021] fails to keep user anonymity, not as claimed. It only keeps pseudonymity. Anonymous actions are designed to be unlinkable to any entity, but pseudonymous actions can be traced back to a certain entity. We also find the scheme is insecure against offline dictionary attack.

Functional bootstrapping in FHE schemes such as FHEW and TFHE allows the evaluation of a function on an encrypted message, in addition to noise reduction. Implementing programs that directly use functional bootstrapping is challenging and error-prone. In this paper, we propose a heuristic that automatically maps Boolean circuits to functional bootstrapping instructions. Unlike other approaches, our method does not limit the encrypted data plaintext space to a power-of-two size, allowing the instantiation of functional bootstrapping with smaller parameters. Furthermore, the negacyclic property of functional bootstrapping is exploited to extend the plaintext space. Despite the inherently greedy nature of the heuristic, experimental results show that the mapped circuits exhibit a significant reduction in evaluation time. Furthermore, our heuristic was able to achieve a $45\%$ improvement in evaluation time when applied to manually implemented Trivium and Kreyvium circuits.

Compilers often weaken or even discard software-based countermeasures commonly used to protect programs against side-channel attacks; worse, they may also introduce vulnerabilities that attackers can exploit. The solution to this problem is to develop compilers that preserve these countermeasures. Prior work establishes that (a mildly modified version of) the CompCert and Jasmin formally verified compilers preserve constant-time, an information flow policy that ensures that programs are protected against cache side-channel attacks. However, nothing is known about preservation of speculative constant-time, a strengthening of the constant-time policy that ensures that programs are protected against Spectre v1 attacks. We first show that preservation of speculative constant-time fails in practice by providing examples of secure programs whose compilation is not speculative constant-time using GCC (GCC -O0 and GCC -O1) and Jasmin. Then, we define a proof-of-concept compiler that distills some of the critical passes of the Jasmin compiler and use the Coq proof assistant to prove that it preserves speculative constant-time. Finally, we patch the Jasmin speculative constant-time type checker and demonstrate that all cryptographic implementations written in Jasmin can be fixed with minimal impact.

In recent years, formal verification has emerged as a crucial method for assessing security against Side-Channel attacks of masked implementations, owing to its remarkable versatility and high degree of automation. However, formal verification still faces technical bottlenecks in balancing accuracy and efficiency, thereby limiting its scalability. Former efficient tools like \textsf{maskVerif} and CocoAlma are often inaccurate when verifying schemes utilizing properties of Boolean functions. Later, SILVER addressed the accuracy issue, albeit at the cost of significantly reduced speed and scalability compared to \textsf{maskVerif}. Consequently, there is a pressing need to develop formal verification tools that are both efficient and accurate for designing secure schemes and evaluating implementations. This paper's primary contribution lies in proposing several approaches to develop a more efficient and scalable formal verification tool called \textsf{Prover}, which is built upon SILVER. Firstly, inspired by the auxiliary data structures proposed by Eldib et al. and optimistic sampling rule of maskVerif, we introduce two reduction rules aimed at diminishing the size of observable sets and secret sets in statistical independence checks. These rules substantially decrease, or even eliminate, the need for repeated computation of probability distributions using Reduced Ordered Binary Decision Diagrams (ROBDDs), a time-intensive procedure in verification. Subsequently, we integrate one of these reduction rules into the uniformity check to mitigate its complexity. Secondly, we identify that variable ordering significantly impacts efficiency and optimize it for constructing ROBDDs, resulting in much smaller representations of investigated functions. Lastly, we present the algorithm of \textsf{Prover}, which efficiently verifies the security and uniformity of masked implementations in probing model with or without the presence of glitches. Experimental results demonstrate that our proposed tool \textsf{Prover} offers a superior balance between efficiency and accuracy compared to other state-of-the-art tools (CocoAlma, maskVerif, and SILVER). It successfully verifies a design that SILVER could not complete within the allocated time, whereas CocoAlma and maskVerif encounter issues with false positives.

Making the most of TFHE programmable bootstrapping to evaluate functions or operators otherwise difficult to perform with only the native addition and multiplication of the scheme is a very active line of research. In this paper, we systematize this approach and apply it to build an 8-bit FHE processor abstraction, i.e., a software entity that works over FHE-encrypted 8-bits data and presents itself to the programmer by means of a conventional-looking assembly instruction set. In doing so, we provide several homomorphic LUT dereferencing operators based on variants on the tree-based method and show that they are the most efficient option for manipulating encryptions of 8-bit data (optimally represented as two base 16 digits). We then systematically apply this approach over a set of around 50 instructions, including, notably, conditional assignments, divisions, or fixed-point arithmetic operations. We then conclude the paper by testing the approach on several simple algorithms, including the execution of a neuron with a sigmoid activation function over 16-bit precision. Finally, this work reveals that a very limited set of functional bootstrapping patterns is versatile and efficient enough to achieve general-purpose FHE computations beyond the boolean circuit approach. As such, these patterns may be an appropriate target for further works on advanced software optimizations or hardware implementations.

A common misconception is that the computational abilities of circuits composed of additions and multiplications are restricted to simple formulas only. Such arithmetic circuits over finite fields are actually capable of computing any function, including equality checks, comparisons, and other highly non-linear operations. While all those functions are computable, the challenge lies in computing them efficiently. We refer to this search problem as arithmetization. Arithmetization is a key problem in secure computation, as techniques like homomorphic encryption and secret sharing compute arithmetic circuits rather than the high-level programs that programmers are used to. The objective in arithmetization has typically been to minimize the number of multiplications (multiplicative size), as multiplications in most secure computation techniques are significantly more expensive to compute than additions. However, the multiplicative depth of a circuit arguably plays an even more important role in deciding the computational cost: For homomorphic encryption, it strongly affects the choice of cryptographic parameters and the number of bootstrapping operations required, which are orders of magnitude more expensive to compute than multiplications. In fact, if we can limit the multiplicative depth of a circuit such that we do not need to perform any bootstrapping, we can omit the large bootstrapping keys required to perform them all together. We argue that arithmetization should be treated as a multi-objective minimization problem, in which a trade-off can be made between a circuit's multiplicative size and depth. We present efficient depth-aware arithmetization methods for many primitive operations such as exponentiation, univariate functions, equality checks, comparisons, and ANDs and ORs, which take into account that squaring can be cheaper than arbitrary multiplications, and we study how to compose them.

Exploiting the notion of carries, we obtain improved upper bounds for the length of the shortest addition chains $\iota(2^n-1)$ producing $2^n-1$. Most notably, we show that if $2^n-1$ has carries of degree at most $$\kappa(2^n-1)=\frac{1}{2}(\iota(n)-\lfloor \frac{\log n}{\log 2}\rfloor+\sum \limits_{j=1}^{\lfloor \frac{\log n}{\log 2}\rfloor}\{\frac{n}{2^j}\})$$ then the inequality $$\iota(2^n-1)\leq n+1+\sum \limits_{j=1}^{\lfloor \frac{\log n}{\log 2}\rfloor}\bigg(\{\frac{n}{2^j}\}-\xi(n,j)\bigg)+\iota(n)$$ holds for all $n\in \mathbb{N}$ with $n\geq 4$, where $\iota(\cdot)$ denotes the length of the shortest addition chain producing $\cdot$, $\{\cdot\}$ denotes the fractional part of $\cdot$ and where $\xi(n,1):=\{\frac{n}{2}\}$ with $\xi(n,2)=\{\frac{1}{2}\lfloor \frac{n}{2}\rfloor\}$ and so on.

Event date: 17 December to 19 December 2024
Submission deadline: 16 August 2024
Notification: 11 October 2024

Help us build the leading wallet infrastructure for the multi-trillion-dollar digital asset industry. Work closely with our top leadership, including the CTO, CPO, and Head of Security, and collaborate with a talented team of Cryptographers, Security Engineers and Protocol Engineers. We’re looking for a Lead Cryptographer with expertise in developing secure, efficient cryptographic protocols focused namely on multi-party computation, threshold cryptography, and post-quantum cryptography. You will collaborate with library developers and solutions architects to enhance our cryptographic solutions, aligning them with the company’s needs and objectives.

As a Lead Cryptographer, you will:
• Carry out fundamental and applied research with the research team.
• Act as a powerhouse of ideas on all cryptographic and research issues.
• Collaborate with the research and engineering team on technical research tasks.

  More information on Dfns Labs and its affiliated projects: dfns.co/labs

  Closing date for applications:

  Contact: Christopher Grilhault des Fontaines chris@dfns.co

  More information: https://www.welcometothejungle.com/en/companies/dfns/jobs/lead-cryptographer_paris?q=577351ed68dbf939d46f6cf0a1b9fc04&o=f45742ac-fac0-4c1b-8afc-7968f5378d33

As a system developer, you will contribute to the creation of a complex decentralized system involving smart contract technology, offchain communication protocols, and identity management. CIMA.Science is a startup company whose mission is the innovative application of decentralized consensus protocols through both horizontal and vertical integration across a wide range of technologies. A key initiative is the creation of an autonomous transaction platform that allows individuals to securely conduct transactions with others across jurisdictional boundaries, establishing trust and legal certainty without the need for intermediaries. Additionally, individuals can opt for a decentralized identity, facilitating their proper integration into the commerce stream. Our goal is to bring the blockchain technology to people in an inclusive manner, with little environment impact, and with high security and resilience objectives. The plan is to build up a R&D team. We will release open source software and nurture expertise. We follow and contribute to cutting edge research. We work on the Unlimitrust Campus in Prilly with tight connections with academic partners.

Closing date for applications:

Contact: Alfio Lanuto (OBJECT: System developer)

More information: https://cima.science

Summary

As a Cryptographic Engineer in Applied Cryptography, you will play a vital role in developing and implementing cryptographic solutions. You'll work alongside a team of talented individuals, contributing to various projects ranging from prototyping new cryptographic products to optimizing existing ones. You will collaborate closely with software architects, product managers, and other team members to successfully deliver high-quality cryptographic solutions that meet market demands.

You will need to have a strong foundation in engineering principles and a keen interest in cryptography. This role offers an exciting opportunity to work on cutting-edge technologies while continuously learning and growing in applied cryptography.

Duties

As a Cryptographic Engineer, you'll play a pivotal role in implementing Zero-Knowledge (ZK) circuits tailored for integration within the Midnight chain. Your focus will involve leveraging recursive proof technologies, particularly those based on Halo2, to create proofs regarding the Midnight state. These proofs are designed to interface with other ecosystems, such as Cardano, providing a secure and efficient means to interact and exchange information across platforms. Your duties will include:

Working with teams across time zones

Working independently on software development tasks

Being proactive and requiring minimal supervision or mentoring to complete tasks

Contribute to the development and delivery of cryptographic products

Assist in prototyping new cryptographic solutions

Implement cryptographic primitives according to established specifications

Collaborate with team members to review cryptographic protocols and proposed primitives

Document code and APIs clearly and comprehensively

Adhere to software engineering best practices during the development process

Closing date for applications:

Contact: Marios Nicolaides

More information: https://apply.workable.com/io-global/j/E68F9E4337/

These positions are supported by the prestigious Australian Research Council Laureate Fellowship on "Secure Cloud Computing from Cryptography: The Rise of Pragmatic Cryptography". You will contribute to research conducted at the Institute of Cybersecurity and Cryptology, focusing on cryptography particularly with the application on developing secure cloud computing. You will also be supervising PhD students. The Institute of Cybersecurity and Cryptology at the University of Wollongong is a premier research institute that conducts research in cybersecurity and cryptology. The institute was awarded the Excellence of Research Assessment with score 5 (well above the world standard) for cryptography research, which is the only score given to a University in Australia. Please apply online (not via email)

Closing date for applications:

Contact: Prof. Willy Susilo

More information: https://www.uow.edu.au/about/jobs/jobs-available/#en/sites/CX_1/requisitions/preview/4659/?

Event date: 23 June to 26 June 2025
Submission deadline: 9 September 2024
Notification: 11 November 2024

Event date: 9 January to 11 February 2025
Submission deadline: 15 August 2024
Notification: 30 September 2024

Event date: 8 April to 10 April 2025
Submission deadline: 25 October 2024
Notification: 6 January 2025

Event date: 13 August to 15 August 2025

Event date: 16 December to 20 December 2024