International Association
for Cryptologic Research

This article generalizes the widely-used GLV decomposition for scalar multiplication to a broader range of elliptic curves with moderate CM discriminant \( D < 0 \) (up to a few thousand in absolute value). Previously, it was commonly believed that this technique could only be applied efficiently for small \( D \) values (e.g., up to \( 100 \)). In practice, curves with \( j \)-invariant \( 0 \) are most frequently employed, as they have the smallest possible \( D = -3 \). This article participates in the decade-long development of numerous real-world curves with moderate \( D \) in the context of ZK-SNARKs. Such curves are typically derived from others, which limits the ability to generate them while controlling the magnitude of \( D \). The most notable example is so-called "lollipop" curves demanded, among others, in the Mina protocol.

Additionally, the new results are relevant to one of the "classical" curves (with \( D = -619 \)) from the Russian ECC standard. This curve was likely found using the CM method (with overwhelming probability), though this is not explicitly stated in the standard. Its developers seemingly sought to avoid curves with small \( D \) values, aiming to mitigate potential DLP attacks on such curves, and hoped these attacks would not extend effectively to \( D = -619 \). One goal of the present article is to address the perceived disparity between the \( D = -3 \) curves and the Russian curve. Specifically, the Russian curve should either be excluded from the standard for potential security reasons or local software should begin leveraging the advantages of the GLV decomposition.

This work investigates constructions of threshold fully homomorphic encryption with low communication, i.e., with small ciphertexts and small decryption shares. In this context, we discuss in detail the technicalities for achieving full-fledged threshold FHE, and put forward limitations regarding prior works, including an attack against the recent construction of Boudgoust and Scholl [ASIACRYPT 2023]. In light of our observations, we generalize the definition of threshold fully homomorphic encryption by adding an algorithm which allows to introduce additional randomness in ciphertexts before they are decrypted by parties. In this setting, we are able to propose a construction which offers small ciphertexts and small decryption shares.

As dataset sizes continue to grow, users face increasing difficulties in performing processing tasks on their local machines. From this, privacy concerns about data leakage have led data owners to upload encrypted data and utilize secure range queries to cloud servers. To address these challenges, order-revealing encryption (ORE) has emerged as a promising solution for large numerical datasets. Building on this, delegatable order-revealing encryption (DORE) was introduced, allowing operations between encrypted datasets with different secret keys in multi-client ORE environments. DORE operates through authorization tokens issued by the data owner. However, security concerns had arisen about unauthorized users exploiting data without permission, leading to the development of a secure order-revealing encryption scheme (SEDORE). These attacks can result in unauthorized data access and significant financial losses in modern cloud service providers (CSPs) utilizing pay-per-query systems. In addition, efficient delegatable order-revealing encryption (EDORE), which improves speed and storage compared to SEDORE with identical security levels, was also introduced. Although both SEDORE and EDORE were designed to be robust against these attacks, we have identified that they still retain the same vulnerabilities within the same threat model. To address these issues, we propose Verifiable Delegatable Order-Revealing Encryption (VDORE), which protects against attacks by using the Schnorr Signature Scheme to verify the validity of the token that users send. We propose a precise definition and robust proof to improve the unclear definition and insufficient proof regarding token unforgeability in the SEDORE. Furthermore, the token generation algorithm in VDORE provides about a $1.5\times$ speed-up compared to SEDORE.

Quantum computing has attracted substantial attention from researchers across various fields. In case of the symmetric key cryptography, the main problem is posed by the application of Grover's search. In this work, we focus on quantum analysis of the lightweight block cipher LED.

This paper proposes an optimized quantum circuit for LED, minimizing the required number of qubits, quantum gates, and circuit depth. Furthermore, we conduct Grover's attack and Search with Two Oracles (STO) attack on the proposed LED cipher, estimating the quantum resources required for the corresponding attack oracles. The STO attack outperforms the usual Grover's search when the state size is less than the key size. Beyond analyzing the cipher itself (i.e., the ECB mode), this work also evaluates the effectiveness of quantum attacks on LED across different modes of operation.

With the emergence of DeFi, attacks based on re-ordering transactions have become an essential problem for public blockchains. Such attacks include front-running or sandwiching transactions, where the adversary places transactions at a particular place within a block to influence a financial asset’s market price. In the Ethereum space, the value extracted by such attacks is often referred to as miner/maximal extractable value (MEV), which to date is estimated to have reached a value of more than USD 1.3B. A promising approach to protect against MEV is to hide the transaction data so block proposers cannot choose the order in which transactions are executed based on the transactions’ content. This paper describes the cryptographic protocol underlying the Shutter network. Shutter has been available as an open-source project since the end of 2021 and has been running in production since Oct. 2022.

A message authentication code (MAC) is a symmetric-key cryptographic function used to authenticate a message by assigning it a tag. This tag is a short string that is difficult to reproduce without knowing the key. The tag ensures both the authenticity and integrity of the message, enabling the detection of any modifications.

A significant number of existing message authentication codes (MACs) are based on block ciphers (BCs) and tweakable block ciphers (TBCs). These MACs offer various trade-offs in properties, such as data processing rate per primitive call, use of single or multiple keys, security levels, pre- or post-processing, parallelizability, state size, and optimization for short/long queries.

In this work, we propose the $\mathsf{Sonikku}$ family of expanding primitive based MACs, consisting of three instances: $\mathsf{BabySonic}$, $\mathsf{DarkSonic}$, and $\mathsf{SuperSonic}$. The $\mathsf{Sonikku}$ MACs are -- 1) faster than the state-of-the-art TBC-based MACs; 2) secure beyond the birthday bound in the input block size; 3) smaller in state size compared to state-of-the-art MACs; and 4) optimized with diverse trade-offs such as pre/post-processing-free execution, parallelization, small footprint, and suitability for both short and long queries. These attributes make them favorable for common applications as well as ``IoT'' and embedded devices where processing power is limited.

On a Cortex-M4 32-bit microcontroller, $\mathsf{BabySonic}$ with $\mathsf{ForkSkinny}$ achieves a speed-up of at least 2.11x (up to 4.36x) compared to state-of-the-art ZMAC with $\mathsf{SKINNY}$ for 128-bit block sizes and queries of 95B or smaller. $\mathsf{DarkSonic}$ and $\mathsf{SuperSonic}$ with $\mathsf{ForkSkinny}$ achieve a speed-up of at least 1.93x for small queries of 95B or smaller and 1.48x for large queries up to 64KB, respectively, against ZMAC with $\mathsf{SKINNY}$ for both 64- and 128-bit block sizes.

Similar to ZMAC and PMAC2x, we then demonstrate the potential of our MAC family by using $\mathsf{SuperSonic}$ to construct a highly efficient, beyond-birthday secure, stateless, and deterministic authenticated encryption scheme, which we call SonicAE.

Evaluating the security of LWE-based KEMs involves two crucial metrics: the hardness of the underlying LWE problem and resistance to decryption failure attacks, both significantly influenced by the secret key and error distributions. To mitigate the complexity and timing vulnerabilities of Gaussian sampling, modern LWE-based schemes often adopt either the uniform or centered binomial distribution (CBD).

This work focuses on Kyber to evaluate its security under both distributions. Compared with the CBD, the uniform distribution over the same range enhances the LWE hardness but also increases the decryption failure probability, amplifying the risk of decryption failure attacks. We introduce a majority-voting-based key recovery method, and carry out a practical decryption failure attack on Kyber512 in this scenario with a complexity of $2^{37}$.

Building on this analysis, we propose uKyber, a variant of Kyber that employs the uniform distribution and parameter adjustments under the asymmetric module-LWE assumption. Compared with Kyber, uKyber maintains comparable hardness and decryption failure probability while reducing ciphertext sizes. Furthermore, we propose a multi-value sampling technique to enhance the efficiency of rejection sampling under the uniform distribution. These properties make uKyber a practical and efficient alternative to Kyber for a wide range of cryptographic applications.

The rise of microarchitectural attacks has necessitated robust detection and mitigation strategies to secure computing systems. Traditional tools, such as static and dynamic code analyzers and attack detectors, often fall short due to their reliance on predefined patterns and heuristics that lack the flexibility to adapt to new or evolving attack vectors. In this paper, we introduce for the first time a microarchitecture security assistant, built on OpenAI's GPT-3.5, which we refer to as µLAM. This assistant surpasses conventional tools by not only identifying vulnerable code segments but also providing context-aware mitigations, tailored to specific system specifications and existing security measures. Additionally, µLAM leverages real-time data from dynamic Hardware Performance Counters (HPCs) and system specifications to detect ongoing attacks, offering a level of adaptability and responsiveness that static and dynamic analyzers cannot match.

For fine-tuning µLAM, we utilize a comprehensive dataset that includes system configurations, mitigations already in place for different generations of systems, dynamic HPC values, and both vulnerable and non-vulnerable source codes. This rich dataset enables µLAM to harness its advanced LLM natural language processing capabilities to understand and interpret complex code patterns and system behaviors, learning continuously from new data to improve its predictive accuracy and respond effectively in real time to both known and novel threats, making it an indispensable tool against microarchitectural threats. In this paper, we demonstrate the capabilities of µLAM by fine-tuning and testing it on code utilizing well-known cryptographic libraries such as OpenSSL, Libgcrypt, and NaCl, thereby illustrating its effectiveness in securing critical and complex software environments.

Proxy re-encryption (PRE) allows semi-honest party (called proxy) to convert a ciphertext under a public key into a ciphertext under another public key. Due to this functionality, there are various applications such as encrypted email forwarding, key escrow, and securing distributed file systems. Meanwhile, post-quantum cryptography (PQC) is one of the most important research areas because development of quantum computers has been advanced recently. In particular, there are many researches on public key encryption (PKE) algorithms selected/submitted in the NIST (National Institute of Standards and Technology) PQC standardization. However, there is no post-quantum PRE scheme secure against adaptive chosen ciphertext attacks (denoted by CCA security) while many (post-quantum) PRE schemes have been proposed so far. In this paper, we propose a bounded CCA secure PRE scheme based on CRYSTALS-Kyber which is a selected algorithm in the NIST PQC competition. To this end, we present generic constructions of bounded CCA secure PRE. Our generic constructions start from PRE secure against chosen plaintext attacks (denoted by CPA security). In order to instantiate our generic constructions, we present a CPA secure PRE scheme based on CRYSTALS-Kyber.

The proliferation of data outsourcing and cloud services has heightened privacy vulnerabilities. CKKS, among the most prominent homomorphic encryption schemes, allows computations on encrypted data, serving as a critical privacy safeguard. However, performance remains a central bottleneck, hindering widespread adoption. Existing optimization efforts often prioritize latency reduction over throughput performance. This paper presents HI-CKKS, a throughput-oriented High-performance Implementation of CKKS homomorphic encryption, addressing these challenges. Our HI-CKKS introduces a batch-supporting asynchronous execution scheme, effectively mitigating frequent data interactions and high waiting delays between hosts and servers in service-oriented scenarios. We analyze the fundamental (I)NTT primitive, which is critical in CKKS, and develop a hierarchical, hybrid high-throughput implementation. This includes efficient arithmetic module instruction set implementations, unified kernel fusion, and hybrid memory optimization strategies that significantly improve memory access efficiency and the performance of (I)NTT operations. Additionally, we propose a multi-dimensional parallel homomorphic multiplication scheme aimed at maximizing throughput and enhancing the performance of (I)NTT and homomorphic multiplication. In conclusion, our implementation is deployed on the RTX 4090, where we conduct a thorough throughput performance evaluation of HI-CKKS, enabling us to pinpoint the most effective parallel parameter settings. Compared to the CPU implementation, our system achieves throughput increases of $175.08\times$, $191.27\times$, and $679.57\times$ for NTT, INTT, and HMult, respectively. And our throughput performance still demonstrates a significant improvement, ranging from $1.54\times$ to $693.17\times$ compared to the latest GPU-based works.

This paper presents enhanced reductions of the bounded-weight and exact-weight Syndrome Decoding Problem (SDP) to a system of quadratic equations. Over $\mathbb{F}_2$, we improve on a previous work and study the degree of regularity of the modeling of the exact weight SDP. Additionally, we introduce a novel technique that transforms SDP instances over $\mathbb{F}_q$ into systems of polynomial equations and thoroughly investigate the dimension of their varieties. Experimental results are provided to evaluate the complexity of solving SDP instances using our models through Gröbner bases techniques.

We present an efficient and simple multi-party private set intersection cardinality (PSI-CA) protocol that allows several parties to learn the intersection size of their private sets without revealing any other information. Our protocol is highly efficient because it only utilizes the Oblivious Key-Value Store and zero-sharing techniques, without incorporating components such as OPPRF (Oblivious Programmable Pseudorandom Function) which is the main building block of multi-party PSI-CA protocol by Gao et al. (PoPETs 2024). Our protocol exhibits better communication and computational overhead than the state-of-the-art.

To compute the intersection between 16 parties with a set size of $2^{20}$ each, our PSI-CA protocol only takes 5.84 seconds and 326.6 MiB of total communication, which yields a reduction in communication by a factor of up to 2.4× compared to the state-of-the-art multi-party PSI-CA protocol of Gao et al. (PoPETs 2024). We prove that our protocol is secure in the presence of a semi-honest adversary who may passively corrupt any $(t-2)$-out-of-$t$ parties once two specific participants are non-colluding.

Private Set Intersection (PSI) is a cryptographic primitive that allows two parties to obtain the intersection of their private input sets while revealing nothing more than the intersection. PSI and its numerous variants, which compute on the intersection of items and their associated weights, have been widely studied. In this paper, we revisit the problem of finding the best item in the intersection according to weight sum introduced by Beauregard et al. (SCN '22), which is a special variant of PSI.

We present two new protocols that achieve the functionality. The first protocol is based on Oblivious Pseudorandom Function (OPRF), additively homomorphic encryption and symmetric-key encryption, while the second one is based on Decisional Diffie-Hellman (DDH) assumption, additively homomorphic encryption and symmetric-key encryption. Both protocols are proven to be secure against semi-honest adversaries. Compared with the original protocol proposed by Beauregard et al. (abbreviated as the FOCI protocol), which requires all weights in the input sets to be polynomial in magnitude, our protocols remove this restriction.

We compare the performance of our protocols with the FOCI protocol both theoretically and empirically. We find out that the performance of FOCI protocol is primarily affected by the size of the intersection and the values of elements’ weights in intersection when fixing set size, while the performance of ours is independent of these two factors. In particular, in the LAN setting, when the set sizes are $n=10000$, intersection size of $\frac{n}{2}$, the weights of the elements are uniformly distributed as integers from $\left[0, n-1\right]$, our DDH-based protocol has a similar run-time to the FOCI protocol. However, when the weights of the elements belonging to $\left[0, 10n-1\right]$ and $\left[0, 100n-1\right]$, our DDH-based protocol is between a factor $2\times$ and $5\times$ faster than the FOCI protocol.

The Cryptography and Cybersecurity (C2) team at Télécom Paris is looking for an intern in Code-based Cryptography. The objective of the internship would be to design and analyze a post-quantum threshold signature scheme relying on code-based assumptions.

The internship may be followed by a PhD position.

For more information, please visit https://tinyurl.com/2smd2665

Closing date for applications:

Contact: victor[dot]dyseryn[at]telecom-paris[dot]fr

More information: https://victordyseryn.github.io/files/2025_M2_internship_Telecom_Paris_Threshold_Signature_Codes.pdf

Digital predistortion (DPD) is a crucial signal processing technique employed to mitigate the nonlinear distortions introduced by power amplifiers (PAs) in wireless communication systems. These distortions lead to signal degradation, spectral regrowth, and reduced energy efficiency, which are particularly problematic in modern communication systems such as 5G and emerging 6G networks, where stringent linearity requirements coexist with the demand for higher data rates and power efficiency. Traditional DPD algorithms rely on mathematical models and optimization techniques that can struggle to adapt to the increasing complexity of modern communication environments, such as wideband signals, high carrier frequencies, and dynamic operational conditions. Machine learning (ML) offers a transformative approach to DPD by enabling adaptive, efficient, and robust solutions that outperform conventional methods in real-world scenarios.

This project aims to develop AI-optimized digital predistortion algorithms and architectures tailored for modern and future communication systems. The research will focus on designing robust, real-time, and computationally efficient ML-based DPD solutions that adapt to diverse PA characteristics and operational conditions.

Candidate description and eligibility

• A highly motivated candidate with an MEng (or M.Tech)/BEng (or B.Tech) degree or equivalent in electronics and/or electrical engineering, with a strong passion for VLSI for Machine Learning/AI, Communication and Signal Processing is sought herewith.
• Desirable: In addition to above qualifications, expertise and interest in FPGA/ASIC and EDA tools would be advantageous.

To apply please send your motivation letter, CV, and recommendation letters to M.T.Khan@hw.ac.uk. Feel free to reach if you have questions.

Closing date for applications:

Contact: Dr. Mohd. Tasleem Khan

More information: https://microwaves.site.hw.ac.uk/vacancies/

The Cryptography research team at Microsoft Research, Redmond, is looking for PhD student interns for the spring or summer of 2025. Please apply as soon as possible if you are interested in joining us!

For more information and to apply, go to https://jobs.careers.microsoft.com/global/en/job/1791134.

Closing date for applications:

Contact: Karen Easterbrook (keaster@microsoft.com) or Kim Laine (kim.laine@microsoft.com)

Lattice-based succinct arguments allow to prove bounded-norm satisfiability of relations, such as $f(\vec{s}) = \vec{t} \bmod q$ and $\|\vec{s}\|\leq \beta$, over specific cyclotomic rings $\mathcal{O}_\mathcal{K}$, with proof size polylogarithmic in the witness size. However, state-of-the-art protocols require either 1) a super-polynomial size modulus $q$ due to a soundness gap in the security argument, or 2) a verifier which runs in time linear in the witness size. Furthermore, construction techniques often rely on specific choices of $\mathcal{K}$ which are not mutually compatible. In this work, we exhibit a diverse toolkit for constructing efficient lattice-based succinct arguments:

(i) We identify new subtractive sets for general cyclotomic fields $\mathcal{K}$ and their maximal real subfields $\mathcal{K}^+$, which are useful as challenge sets, e.g. in arguments for exact norm bounds. (ii) We construct modular, verifier-succinct reductions of knowledge for the bounded-norm satisfiability of structured-linear/inner-product relations, without any soundness gap, under the vanishing SIS assumption, over any $\mathcal{K}$ which admits polynomial-size subtractive sets. (iii) We propose a framework to use twisted trace maps, i.e. maps of the form $\tau(z) = \frac{1}{N} \cdot \mathsf{Trace}_{\mathcal{K}/\mathbb{Q}}( \alpha \cdot z )$, to embed $\mathbb{Z}$-inner-products as $\mathcal{R}$-inner-products for some structured subrings $\mathcal{R} \subseteq \mathcal{O}_\mathcal{K}$ whenever the conductor has a square-free odd part. (iv) We present a simple extension of our reductions of knowledge for proving the consistency between the coefficient embedding and the Chinese Remainder Transform (CRT) encoding of $\vec{s}$ over any cyclotomic field $\mathcal{K}$ with a smooth conductor, based on a succinct decomposition of the CRT map into automorphisms, and a new, simple succinct argument for proving automorphism relations.

Combining all techniques, we obtain, for example, verifier-succinct arguments for proving that $\vec{s}$ satisfying $f(\vec{s}) = \vec{t} \bmod q$ has binary coefficients, without soundness gap and with polynomial-size modulus $q$.

We further explore the explicit connections between supersingular curve isogenies and Bruhat-Tits trees. By identifying a supersingular elliptic curve $E$ over $\mathbb{F}_p$ as the root of the tree, and a basis for the Tate module $T_\ell(E)$; our main result is that given a vertex $M$ of the Bruhat-Tits tree one can write down a generator of the ideal $I \subseteq \text{End}(E)$ directly, using simple linear algebra, that defines an isogeny corresponding to the path in the Bruhat-Tits tree from the root to the vertex $M$. In contrast to previous methods to go from a vertex in the Bruhat-Tits tree to an ideal, once a basis for the Tate module is set up and an explicit map $\Phi : \text{End}(E) \otimes_{\mathbb{Z}_\ell} \to M_2( \mathbb{Z}_\ell )$ is constructed, our method does not require any computations involving elliptic curves, isogenies, or discrete logs. This idea leads to simplifications and potential speedups to algorithms for converting between isogenies and ideals.

Succinct non-interactive arguments of knowledge (SNARKs) enable a prover to produce a short and efficiently verifiable proof of the validity of an arbitrary NP statement. Recent constructions of efficient SNARKs have led to interest in using them for a wide range of applications, but unfortunately, deployment of SNARKs in these applications faces a key bottleneck: SNARK provers require a prohibitive amount of time and memory to generate proofs for even moderately large statements. While there has been progress in reducing prover time, prover memory remains an issue. In this work, we describe Scribe, a new low-memory SNARK that can efficiently prove large statements even on cheap consumer devices such as smartphones by leveraging a plentiful, but heretofore unutilized, resource: disk storage. In more detail, instead of storing its (large) intermediate state in RAM, Scribe's prover instead stores it on disk. To ensure that accesses to state are efficient, we design Scribe's prover in a *read-write streaming* model of computation that allows the prover to read and modify its state only in a streaming manner.

We implement and evaluate Scribe's prover, and show that, on commodity hardware, it can easily scale to circuits of size $2^{28}$ gates while using only 2GB of memory and incurring only minimal proving latency overhead (10-35%) compared to a state-of-the-art memory-intensive baseline (HyperPlonk [EUROCRYPT 2023]) that requires much more memory. Our implementation minimizes overhead by leveraging the streaming access pattern to enable several systems optimizations that together mask I/O costs.

The Ascon authenticated encryption scheme and hash function of Dobraunig et al (Journal of Cryptology 2021) were recently selected as winner of the NIST lightweight cryptography competition. The mode underlying Ascon authenticated encryption (Ascon-AE) resembles ideas of SpongeWrap, but not quite, and various works have investigated the generic security of Ascon-AE, all covering different attack scenarios and with different bounds. This work systemizes knowledge on the mode security of Ascon-AE, and fills gaps where needed. We consider six mainstream security models, all in the multi-user setting: (i) nonce-respecting security, reflecting on the existing bounds of Chakraborty et al (ASIACRYPT 2023, ACISP 2024) and Lefevre and Mennink (SAC 2024), (ii) nonce-misuse resistance, observing a non-fixable flaw in the proof of Chakraborty et al (ACISP 2024), (iii) nonce-misuse resilience, delivering missing security analysis, (iv) leakage resilience, delivering a new security analysis that supersedes the informal proof sketch (though in a different model) of Guo et al (ToSC 2020), (v) state-recovery security, expanding on the analysis of Lefevre and Mennink, and (vi) release of unverified plaintext, also delivering missing security analysis. We also match all bounds with tight attacks. As a bonus, we systemize the knowledge on Ascon-Hash and Ascon-PRF (but there are no technical novelties here).