International Association
for Cryptologic Research

This paper compares the relative strengths of prominent security notions for onion encryption within the Tor setting, specifically focusing on CircuitHiding (EUROCRYPT 2018, an anonymity flavor notion) and OnionAE (PETS 2018, a stateful authenticated encryption flavor notion). Although both are state-of-the-art, Tor-specific notions, they have exhibited different definitional choices, along with variations in complexity and usability. By employing an indirect approach, we compare them using a set of onion layer-centric notions: IND\$-CPA, IPR/IPR$^+$, and INT-sfCTXT, to compare with the two, respectively. Since the same notion set that implies OnionAE does not imply CircuitHiding, and vice versa, this leads to the conclusion that OnionAE and CircuitHiding are mutually separable. Therefore, neither notion fully expresses satisfactory security on its own. Importantly, IND\$-CPA, IPR$^+$ (a stronger variant of IPR), and INT-sfCTXT collectively and strictly imply OnionAE and CircuitHiding. Given their onion layer-centric and thus simpler nature, this provides a practical approach to simultaneously satisfying CircuitHiding and OnionAE. Finally, we thoroughly discuss how the results presented in this paper impact the design and evaluation of onion encryption schemes for Tor. While the formal treatment of (general) public-key onion routing has been relatively well-studied, formal treatment tailored to Tor remains insufficient, and thus our work narrows this gap.

In this paper, we present Trilithium: a protocol for distributed key generation and signing compliant with FIPS 204 (ML-DSA). Our protocol allows two parties, "server" and "phone" with assistance of correlated randomness provider (CRP) to produce a standard ML-DSA signature. We prove our protocol to be secure against a malicious server or phone in the universal composability (UC) model, introducing some novel techniques to argue the security of two-party secure computation protocols with active security against one party, but only active privacy against the other. We provide an implementation of our protocol in Rust and benchmark it, showing the practicality of the protocol.

The paper analyzes the security of two recently proposed code-based cryptosystems that employ encryption of the form $y = m G_{\text{pub}} + eE_{pub}$: the Krouk-Kabatiansky-Tavernier (KKT) cryptosystem and the Lau-Ivanov-Ariffin-Chin-Yap (LIACY) cryptosystem. We demonstrate that the KKT cryptosystem can be reduced to a variant of the McEliece scheme, where a small set of columns in the public generator matrix is replaced with random ones. This reduction implies that the KKT cryptosystem is vulnerable to existing attacks on Wieschebrink's encryption scheme, particularly when Generalized Reed-Solomon (GRS) codes are used. In addition, we present a full key-recovery attack on the LIACY cryptosystem by exploiting its linear-algebraic structure and leveraging distinguishers of subcodes of GRS codes. Our findings reveal critical vulnerabilities in both systems, effectively compromising their security despite their novel designs.

As artificial intelligence plays an increasingly important role in decision-making within critical infrastructure, ensuring the authenticity and integrity of neural networks is crucial. This paper addresses the problem of detecting cloned neural networks. We present a method for identifying clones that employs a combination of metrics from both the information and physical domains: output predictions, probability score vectors, and power traces measured from the device running the neural network during inference. We compare the effectiveness of each metric individually, as well as in combination. Our results show that the effectiveness of both the information and the physical domain metrics is excellent for a clone that is a near replica of the target neural network. Furthermore, both the physical domain metric individually and the hybrid approach outperformed the information domain metrics at detecting clones whose weights were extracted with low accuracy. The presented method offers a practical solution for verifying neural network authenticity and integrity. It is particularly useful in scenarios where neural networks are at risk of model extraction attacks, such as in cloud-based machine learning services.

We show that Montgomery ladders compute pairings as a by-product, and explain how a small adjustment to the ladder results in simple and efficient algorithms for the Weil and Tate pairing on elliptic curves using cubical arithmetic. We demonstrate the efficiency of the resulting cubical pairings in several applications from isogeny-based cryptography. Cubical pairings are simpler and more performant than pairings computed using Miller's algorithm: we get a speed-up of over 40% for use-cases in SQIsign, and a speed-up of about 7% for use-cases in CSIDH. While these results arise from a deep connection to biextensions and cubical arithmetic, in this article we keep things as concrete (and digestible) as possible. We provide a concise and complete introduction to cubical arithmetic as an appendix.

Multisignature schemes are crucial for secure operations in digital wallets and escrow services within smart contract platforms, particularly in the emerging post-quantum era. Existing post-quantum multisignature constructions either do not address the stringent requirements of the Quantum Random Oracle Model (QROM) or fail to achieve practical efficiency due to suboptimal parameter choices.

In this paper, we present a novel Dilithium-based multisignature scheme designed to be secure in the QROM and optimized for practical use. Our scheme operates over the polynomial ring $\mathbb{Z}_q[X]/(x^n+1)$ with $q \equiv 1 \pmod{2n}$, enabling full splitting of the ring and allowing for efficient polynomial arithmetic via the Number Theoretic Transform (NTT). This structure not only ensures post-quantum security but also bridges the gap between theoretical constructs and real-world implementation needs.

We further propose a new hardness assumption, termed $\nu$-SelfTargetMSIS, extending SelfTargetMSIS (Eurocrypt 2018) to accommodate multiple challenge targets. We prove its security in the QROM and leverage it to construct a secure and efficient multisignature scheme. Our approach avoids the limitations of previous techniques, reduces security loss in the reduction, and results in a more compact and practical scheme suitable for deployment in post-quantum cryptographic systems.

Bilinear pairings constitute a cornerstone of public-key cryptography, where advancements in Tate pairings and their efficient variants have emerged as a critical research domain within cryptographic science. Currently, the computation of pairings can be effectively implemented through three distinct algorithmic approaches: Miller’s algorithm, the elliptic net algorithm (as developed by Stange), and cubical-based algorithms (as proposed by Damien Robert). Biextensions are the geometric object underlying the arithmetic of pairings, and all three approaches can be seen as a different way to represent biextension elements. In this paper, we revisit the biextension geometric point of view for pairing computation and investigate in more detail the cubical representation for pairing-based cryptography. Utilizing the twisting isomorphism, we derive explicit formulas and algorithmic frameworks for the ate pairing and optimal ate pairing computations. Additionally, we present detailed formulas and introduce an optimized shared cubical ladder algorithm for super-optimal ate pairings. Through concrete computational analyses, we compare the performance of our cubical-based methods with the Miller's algorithm on various well-known families of pairing-friendly elliptic curves. Our results demonstrate that the cubical-based algorithm outperforms the Miller's algorithm by bits in certain specific situations, establishing its potential as an alternative for pairing computation.

Fully Homomorphic Encryption (FHE) enables computation on encrypted data without decryption, demonstrating significant potential for privacy-preserving applications. However, FHE faces several challenges, one of which is the significant plaintext-to-ciphertext expansion ratio, resulting in high communication overhead between client and server. The transciphering technique can effectively address this problem by first encrypting data with a space-efficient symmetric cipher, then converting symmetric ciphertext to FHE ciphertext without decryption.

Numerous FHE-friendly symmetric ciphers and transciphering methods have been developed by researchers, each with unique advantages and limitations. These often require extensive knowledge of both symmetric cryptography and FHE to fully grasp, making comparison and selection among these schemes challenging. To address this, we conduct a comprehensive survey of over 20 FHE-friendly symmetric ciphers and transciphering methods, evaluating them based on criteria such as security level, efficiency, and compatibility. We have designed and executed experiments to benchmark the performance of the feasible combinations of symmetric ciphers and transciphering methods across various application scenarios. Our findings offer insights into achieving efficient transciphering tailored to different task contexts. Additionally, we make our example code available open-source, leveraging state-of-the-art FHE implementations.

In this paper, we investigate the Extended Gabidulin (EG) codes and the Interleaved EG (IEG) codes, and enhance the Rank Quasi-Cyclic (RQC) encryption scheme. Our primary contribution is the development of a general decoding algorithm for (I)EG codes, for which we precisely provide the DFR, bound the decoding capacity, and estimate the decoding complexity. As the core tool, we demonstrate that the Linear Reconstruction (LR) problem derived from the decoding (I)EG codes problem can be probabilistically solved, enabling (I)EG codes to achieve arbitrarily small DFRs, decode up to the rank Gilbert-Varshamov bound (even close to the minimal distance), and decode by the Welch-Berlekamp like algorithm. An interesting and important byproduct is that we demonstrate that decoding interleaved Gabidulin codes can be achieved deterministically by solving the LR problem. We finally apply the EG codes to improve RQC (NIST PQC & Asiacrypt 2023). For 128-bit security, our optimized RQC reduces bandwidth by 69 % and 34 % compared to the original versions, respectively. The scheme also achieves at least 50% improvement in efficiency and mitigates MM algebraic attacks (as discussed in Eurocrypt 2020, Asiacrypt 2020 & 2023) as EG codes facilitate schemes operating over smaller finite fields. Overall, our scheme outperforms code-based schemes of NIST PQC Round 4 submissions, such as HQC, BIKE, and Classic McEliece, in terms of bandwidth. A conservative parameters set still remains competitive bandwidths.

Due to their widespread applications in decentralized and privacy preserving technologies, commitment schemes have become increasingly important cryptographic primitives. With a wide variety of applications, many new constructions have been proposed, each enjoying different features and security guarantees. In this paper, we systematize the designs, features, properties, and applications of vector commitments (VCs). We define vector, polynomial, and functional commitments and we discuss the relationships shared between these types of commitment schemes. We first provide an overview of the definitions of the commitment schemes we will consider, as well as their security notions and various properties they can have. We proceed to compare popular constructions, taking into account the properties each one enjoys, their proof/update information sizes, and their proof/commitment complexities. We also consider their effectiveness in various decentralized and privacy preserving applications. Finally, we conclude by discussing some potential directions for future work.

Johnson and Lindenstrauss (Contemporary Mathematics, 1984) showed that for $n > m$, a scaled random projection $\mathbf{A}$ from $\mathbb{R}^n$ to $\mathbb{R}^m$ is an approximate isometry on any set $S$ of size at most exponential in $m$. If $S$ is larger, however, its points can contract arbitrarily under $\mathbf{A}$. In particular, the hypergrid $([-B, B] \cap \mathbb{Z})^n$ is expected to contain a point that is contracted by a factor of $\kappa_{\mathsf{stat}} = \Theta(B)^{-1/\alpha}$, where $\alpha = m/n$. We give evidence that finding such a point exhibits a statistical-computational gap precisely up to $\kappa_{\mathsf{comp}} = \widetilde{\Theta}(\sqrt{\alpha}/B)$. On the algorithmic side, we design an online algorithm achieving $\kappa_{\mathsf{comp}}$, inspired by a discrepancy minimization algorithm of Bansal and Spencer (Random Structures \& Algorithms, 2020). On the hardness side, we show evidence via a multiple overlap gap property (mOGP), which in particular captures online algorithms; and a reduction-based lower bound, which shows hardness under standard worst-case lattice assumptions.

As a cryptographic application, we show that the rounded Johnson-Lindenstrauss embedding is a robust property-preserving hash function (Boyle, Lavigne and Vaikuntanathan, TCC 2019) on the hypergrid for the Euclidean metric in the computationally hard regime. Such hash functions compress data while preserving $\ell_2$ distances between inputs up to some distortion factor, with the guarantee that even knowing the hash function, no computationally bounded adversary can find any pair of points that violates the distortion bound.

A proof of reserves (PoR) protocol enables a cryptocurrency exchange to prove to its users that it owns a certain amount of coins, as a first step towards proving that it is solvent. We present the design, implementation, and security analysis of MProve-Nova, a PoR protocol for Monero that leverages the Nova recursive SNARK to achieve two firsts (without requiring any trusted setup). It is the first Monero PoR protocol that reveals only the number of outputs owned by an exchange; no other information about the outputs or their key images is revealed. It is also the first Monero PoR protocol where the proof size and proof verification time are constant, i.e. they are independent of the number of outputs on the Monero blockchain and the number of outputs owned by the exchange. To achieve constant verification times, MProve-Nova requires a pre-processing step which creates two Merkle trees from all the outputs and key images on the Monero blockchain.

MProve-Nova consists of two Nova-based subprotocols, a reserves commitment generator (RCG) protocol used to compute a commitment to the total reserves owned by an exchange and a non-collusion (NC) protocol used to prove non-collusion between two exchanges. For the RCG protocol, we observed proof sizes of about 28 KB and verification times of 4.3 seconds. For the NC protocol, we observed proof sizes of about 24 KB and verification times of 0.2 seconds. Proving times for both protocols increase linearly with the number of outputs owned by the exchange but remain independent of the number of outputs on the Monero blockchain. On average, the RCG protocol required about 42 minutes per 1000 outputs and the NC protocol required about 5 minutes per 1000 outputs.

Generalized secret sharing (GSS), which accommodates monotone access structures, has been under-explored in distributed computing over the past decades. In this paper, we propose the publicly verifiable generalized secret sharing (PVGSS) scheme, enhancing the applicability of GSS in transparent systems. PVGSS not only enables a dealer to share a secret with fine-grained access structures, but also allows anyone to verify whether the dealer and shareholders are acting honestly or not. We begin by introducing two approaches to implement GSS schemes: one based on recursive Shamir secret sharing and another utilizing linear secret sharing scheme (LSSS). Then, we present PVGSS constructions by integrating non-interactive zero-knowledge proofs into the GSS schemes. Further, we prove that the proposed PVGSS schemes achieve IND1-secrecy under DDH assumption. To showcase the practical applicability of PVGSS schemes, we implement a decentralized exchange (DEX) protocol that enables fair atomic swaps of ERC-20 tokens. A sophisticated access structure is devised to: (1) enable fair atomic swaps during normal protocol execution, and (2) incorporate fault-tolerant passive watchers to provide accountable arbitration when disputes occur. Our benchmarks on the BN128 curve demonstrate the computational efficiency of PVGSS schemes, while Ethereum gas cost analysis confirms the viability of the DEX implementation.

We consider adversaries able to perform a nonzero but small number of discrete logarithm computations, as would be expected with near-term quantum computers. Schemes with public parameters consisting of a few group elements are now at risk; could an adversary knowing the discrete logarithms of these elements go on to easily compromise the security of many users? We study this question for known schemes and find, across them, a perhaps surprising variance in the answers. In a first class are schemes, including Okamoto and Katz-Wang signatures, that we show fully retain security even when the discrete logs of the group elements in their parameters are known to the adversary. In a second class are schemes like Cramer-Shoup encryption and the SPAKE2 password-authenticated key exchange protocol that we show retain some partial but still meaningful and valuable security. In the last class are schemes we show by attack to totally break. The distinctions uncovered by these results shed light on the security of classical schemes in a setting of immediate importance, and help make choices moving forward.

Can a dealer share a secret without knowing the shareholders? We provide a positive answer to this question by introducing the concept of an attribute-based secret sharing (AB-SS) scheme. With AB-SS, a dealer can distribute a secret based on attributes rather than specific individuals or shareholders. Only authorized users whose attributes satisfy a given access structure can recover the secret. Furthermore, we introduce the concept of attribute-based publicly verifiable secret sharing (AB-PVSS). An AB-PVSS scheme allows external users to verify the correctness of all broadcast messages from the dealer and shareholders, similar to a traditional PVSS scheme. Additionally, AB-SS (or AB-PVSS) distinguishes itself from traditional SS (or PVSS) by enabling a dealer to generate shares according to an arbitrary monotone access structure. To construct an AB-PVSS scheme, we first implement a decentralized ciphertext-policy attribute-based encryption (CP-ABE) scheme. The proposed CP-ABE scheme offers a smaller ciphertext size and requires fewer computational operations, although it is not fully-fledged as a trade-off. We then incorporate non-interactive zero-knowledge (NIZK) proofs to enable public verification of the CP-ABE ciphertext. Based on the CP-ABE and NIZK proofs, we construct an AB-PVSS primitive. Furthermore, we present an intuitive implementation of optimistic fair exchange based on the AB-PVSS scheme. Finally, we conduct security analysis and comprehensive experiments on the proposed CP-ABE and AB-PVSS schemes. The results demonstrate that both schemes exhibit plausible performance compared to related works.

Recent advancements in Large Language Models (LLMs) have transformed communication, yet their role in secure messaging remains underexplored, especially in surveillance-heavy environments. At the same time, many governments all over the world are proposing legislation to detect, backdoor, or even ban encrypted communication. That emphasizes the need for alternative ways to communicate securely and covertly over open channels. We propose a novel cryptographic embedding framework that enables covert Public Key or Symmetric Key encrypted communication over public chat channels with human-like produced texts. Some unique properties of our framework are: 1. It is LLM agnostic, i.e., it allows participants to use different local LLM models independently; 2. It is pre- or post-quantum agnostic; 3. It ensures indistinguishability from human-like chat-produced texts. Thus, it offers a viable alternative where traditional encryption is detectable and restricted.

Whilst many key exchange and digital signature methods use the NIST P256 (secp256r1) and secp256k1 curves, there is often a demand for increased security. With these curves, we have a 128-bit security. These security levels can be increased to 256-bit security with NIST P-521 Curve 448 and Brainpool-P512. This paper outlines a new curve - Eccfrog512ck2 - and which provides 256-bit security and enhanced performance over NIST P-521. Along with this, it has side-channel resistance and is designed to avoid weaknesses such as related to the MOV attack. It shows that Eccfrog512ck2 can have a 61.5% speed-up on scalar multiplication and a 33.3% speed-up on point generation over the NIST P-521 curve.

Abstract—Anonymous token schemes are cryptographic protocols for limiting the access to online resources to credible users. The resource provider issues a set of access tokens to the credible user that they can later redeem anonymously, i.e., without the provider being able to link their redemptions. When combined with credibility tests such as CAPTCHAs, anonymous token schemes can significantly increase user experience and provider security, without exposing user access patterns to providers. Current anonymous token schemes such as the Privacy Pass protocol by Davidson et al. rely on oblivious pseudorandom functions (OPRFs), which let server and user jointly compute randomly looking access tokens. For those protocols, token issuing costs are linear in the number of requested tokens. In this work, we propose a new approach for building anonymous token schemes. Instead of relying on two-party computation to realize a privacy-preserving pseudorandom function evaluation, we propose to offload token generation to the user by using group verifiable random functions (GVRFs). GVRFs are a new cryptographic primitive that allow users to produce verifiable pseudorandomness. Opposed to standard VRFs, verification is anonymous within the group of credible users. We give a construction of group VRFs from the Dodis-Yampolskiy VRF and Equivalence- Class Signatures, based on pairings and a new Diffie- Hellman inversion assumption that we analyze in the Generic Group Model. Our construction enjoys compact public keys and proofs, while evaluation and verification costs are only slightly increased compared to the Dodis-Yampolskiy VRF. By deploying a group VRF instead of a OPRF, we obtain an anonymous token scheme where communication as well as server-side computation during the issuing phase is constant and independent of the number of tokens a user requests. Moreover, by means of our new concept of updatable token policies, the number of unspent tokens in circulation can retrospectively (i.e., even after the credibility check) be decreased or increased in order to react to the current or expected network situation. Our tokens are further countable and publicly verifiable. This comes at the cost of higher computational efforts for token redemption and verification as well as somewhat weaker unlinkability guarantees compared to Privacy Pass.

Mixnets are powerful building blocks for providing anonymity in applications like electronic voting and anonymous messaging. The en- cryption schemes upon which traditional mixnets are built, as well as the zero-knowledge proofs used to provide verifiability, will, however, soon become insecure once a cryptographically-relevant quantum computer is built. In this work, we construct the most compact verifiable mixnet that achieves privacy and verifiability through encryption and zero-knowledge proofs based on the hardness of lattice problems, which are believed to be quantum-safe.

A core component of verifiable mixnets is a proof of shuffle. The starting point for our construction is the proof of shuffle of Aranha et al. (CT- RSA 2021). We first identify an issue with the soundness proof in that work, which is also present in the adaptation of this proof in the mixnets of Aranha et al. (ACM CCS 2023) and Hough et al. (IACR CiC 2025). The issue is that one cannot directly adapt classical proofs of shuffle to the lattice setting due to the splitting structure of the rings used in lattice-based cryptography. This is not just an artifact of the proof, but a problem that manifests itself in practice, and we successfully mount an attack against the implementation of the first of the mixnets. We fix the problem and introduce a general approach for proving shuffles in split- ting rings that can be of independent interest.

The efficiency improvement of our mixnet over prior work is achieved by switching from re-encryption mixnets (as in the works of Aranha et al. and Hough et al.) to decryption mixnets with very efficient layering based on the hardness of the LWE and LWR problems over polynomial rings. The ciphertexts in our scheme are smaller by approximately a factor of 10X and 2X over the aforementioned instantiations, while the linear-size zero-knowledge proofs are smaller by a factor of 4X and 2X.

Key derivation functions (KDFs) are integral to many cryptographic protocols. Their functionality is to turn raw key material, such as a Diffie-Hellman secret, into a strong cryptographic key that is indistinguishable from random. This guarantee was formalized by Krawczyk together with the seminal introduction of HKDF (CRYPTO 2010), in a model where the KDF only takes a single key material input. Modern protocol designs, however, regularly need to combine multiple secrets, possibly even from different sources, with the guarantee that the derived key is secure as long as at least one of the inputs is good. This is particularly relevant in settings like hybrid key exchange for quantum-safe migration. Krawczyk's KDF formalism does not capture this goal, and there has been surprisingly little work on the security considerations for KDFs since then.

In this work, we thus revisit the syntax and security model for KDFs to treat multiple, possibly correlated inputs. Our syntax is assertive: We do away with salts, which are needed in theory to extract from arbitrary sources in the standard model, but in practice, they are almost never used (or even available) and sometimes even misused, as we argue. We use our new model to analyze real-world multi-input KDFs—in Signal's X3DH protocol, ETSI's TS 103 744 standard, and MLS' combiner for pre-shared keys—as well as new constructions we introduce for specialized settings—e.g., a purely blockcipher-based one. We further discuss the importance of collision resistance for KDFs and finally apply our multi-input KDF model to show how hybrid KEM key exchange can be analyzed from a KDF perspective.