Hasina Andriambelo, Hery Zo Andriamanohisoa, Naghmeh Moradpoor
Federated learning enables collaborative model training without sharing raw data, but practical deployments increasingly require verifiable guarantees that clients compute updates correctly. Zero-knowledge proofs can provide such guarantees, yet existing approaches face scalability limits due to the combined cost of polynomial commitments and fast Fourier transform (FFT) intensive verification. Pairing-based schemes offer compact proofs but incur high prover and verifier overhead, while hash-based constructions reduce algebraic cost at the expense of rapidly growing proof sizes. This paper proposes Hybrid-Commit, a polynomial commitment architecture for Binius zero-knowledge proofs that aligns cryptographic primitives with the algebraic structure of federated learning workloads. The scheme separates verification into additive and multiplicative phases: linear aggregation is handled using batched additive commitments optimized for binary fields, while non-linear constraints are verified via hash-based commitments over sparsely selected FFT domains. Proofs from multiple clients are combined through recursive aggregation while preserving non-interactivity. Experiments demonstrate scalability in prover time and proof size (near-constant prover time across 4–11 clients; 160 bytes per client representing 341× and 813× reductions vs. FRI-PCS and Orion), although verification time (762 ms per client) does not scale favorably, making the scheme suitable for bandwidth-constrained scenarios. The scheme achieves under 2% end-to-end training overhead with no impact on model accuracy, indicating that workload-aware commitment design can improve specific scalability dimensions of zero-knowledge verification in federated learning systems.
Defensive publication establishing prior art for proof-first digital identity systems using prime-indexed state evolution, zero-knowledge proofs, and silence-by-default semantics. This specification defines the Meta-Theorem of Prime Identity (MTPI), an architectural framework requiring cryptographic proof for every state transition. Core components include: Prime-Indexed Recursive Tensor Mathematics (PIRTM) with contractive dynamics guarantee; prime-gated activation with drift bounds δ(t) ≤ 0.3; Conscious Sovereignty Layer (CSL) with ethical tensor field commutation relations; Archivum append-only audit schema; and conformance requirements including Surveillance Fork detection. Reference implementations provided in Solidity and Circom 2.1. Mathematical foundations, alternative embodiments, and public domain designations included for maximum prior art scope. Keywords: zero-knowledge proofs, prime-indexed identity, verifiable computation, AI safety, defensive publication, proof-first computing, MTPI, PIRTM, CSL
Open access
2 source records
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Zero-Knowledge (ZK) proof systems are cryptographic protocols that can (with overwhelming probability) demonstrate that the pair $(X, W)$ is in a relation $R$ without revealing information about the private input $W$. This membership checking is captured by a complex arithmetic circuit: a set of polynomial equations over a finite field. ZK programming languages, like Noir, have been proposed to simplify the description of these circuits. A developer can write a Noir program using traditional high-level constructs that can be compiled into a lower-level ACIR (Abstract Circuit Intermediate Representation), which is essentially a high-level description of an arithmetic circuit. In this paper, we formalise some of the ACIR language using SMT-LIB and its extended theory of finite fields. We use this formalisation to create an open-source formal verifier for the Noir language using the SMT solver cvc5. Our verifier can be used to check whether Noir programs behave appropriately. For instance, it can be used to check whether a Noir program has been properly constrained, that is, the finite-field polynomial equations generated truly capture the intended relation. We evaluate our verifier over 4 distinct sets of Noir programs, demonstrating its practical applicability and identifying a hard-to-check constraint type that charts an improvement path for our verification framework.
The Internet of Medical Things (IoMT) enables real-time health monitoring and intelligent clinical decision-making by continuously collecting and processing sensitive physiological data from wearable, implantable, and edge-connected devices. However, this data aggregation paradigm introduces critical privacy and security challenges, including data leakage, aggregator misbehavior, and adversarial attacks, while existing frameworks often fail to simultaneously ensure confidentiality, verifiability, and efficiency. To address these limitations, we propose MedGuard, a novel end-to-end secure data aggregation framework for IoMT that synergistically integrates Fully Homomorphic Encryption (FHE) based on the CKKS scheme and Groth16 zero-knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs). MedGuard enables healthcare providers to perform complex analytical queries, such as statistical analysis, anomaly detection, and trend forecasting, directly on encrypted data without decryption, ensuring compliance with privacy regulations. By allowing edge nodes to generate cryptographic proofs of correct computation and enabling cloud-based verification, MedGuard eliminates reliance on trusted intermediaries and mitigates insider threats. Our comprehensive evaluation, conducted in a high-fidelity OMNeT++ 6.0.1 simulation environment with 1,000 IoMT devices, 100 edge nodes, and an Amazon EC2 c5.4xlarge cloud server, uses a hybrid dataset combining real-world and GMM-augmented synthetic data. Results show that MedGuard achieves an end-to-end latency of 64.8 ms, a 13.3% improvement over state-of-the-art baselines, communication efficiency of 1.465 GB/s, per-query energy consumption of 1.489 mJ, and sustained throughputs of 1,200 packets/s, 120 aggregates/s, and 1,200 queries/s. These performance gains, combined with a robust [Formula: see text] security level, demonstrate that MedGuard delivers scalable, verifiable, and privacy-preserving analytics for next-generation smart healthcare systems.
A sharing framework based on Zero-Knowledge Proof (ZKP) and Proxy Re-encryption (PRE) technologies offers a promising solution for sharing Student Electronic Academic Records (SEARs). As core credentials in the education sector, student records are characterized by strong identity binding, the need for long-term retention, frequent cross-institutional verification, and sensitive information. Compared with electronic health records and government archives, they face more complex security, privacy protection, and storage scalability challenges during sharing. These records not only contain sensitive data such as personal identity and academic performance but also serve as crucial evidence in key scenarios such as further education, employment, and professional title evaluation. Leakage or tampering could have irreversible impacts on a student’s career development. Furthermore, traditional blockchain technology faces storage capacity limitations when storing massive academic records, and existing general electronic record sharing solutions struggle to meet the high-frequency verification demands of educational authorities, universities, and employers for academic data. This study proposes a dedicated sharing framework for students’ electronic academic records, leveraging PRE technology and the distributed ledger characteristics of blockchain to ensure transparency and immutability during sharing. By integrating the InterPlanetary File System (IPFS) with Ethereum Smart Contract (SC), it addresses blockchain storage bottlenecks, enabling secure storage and efficient sharing of academic records. Relying on optimized ZKP technology, it supports verifying the authenticity and integrity of records without revealing sensitive content. Furthermore, the introduction of gate circuit merging, constant folding techniques, Field-Programmable Gate Array (FPGA) hardware acceleration, and the efficient Bulletproofs algorithm alleviates the high computational complexity of ZKP, significantly reducing proof generation time. The experimental results demonstrate that the framework, while ensuring strong privacy protection, can meet the cross-scenario sharing needs of student records and significantly improve sharing efficiency and security. Therefore, this method exhibits superior security and performance in privacy-preserving scenarios. This framework can be applied to scenarios such as cross-institutional academic certification, employer background checks, and long-term management of academic records by educational authorities, providing secure and efficient technical support for the sharing of electronic academic credentials in the digital education ecosystem.
We propose a novel digital signature cryptosystem that exploits the concept of the brute-force problem. To ensure the security of the cryptosystem, we employed several mechanisms: sharing a common secret for factorable permutations, associating permutations with the message being signed, and confirming knowledge of the shared secret using a zero-knowledge proof. We developed a secret-sharing theory based on homomorphic matrix transformations for factorized permutations. The inverse matrix transformation for computing the shared secret is determined by secret parameters, which results in incompletely defined functionality and gives rise to a brute-force cryptanalysis problem. Randomization of session keys using a message hash and random parameters guarantees the uniqueness of each signature, even for identical messages. We employed a zero-knowledge authentication protocol to confirm knowledge of the shared secret, thereby protecting the verifier against unauthorized signature imposition. The LINEture cryptosystem is built on linear matrix algebra and does not rely on a computationally hard problem. High security is achieved through the appropriate selection of matrix transformation dimensions. Matrix computations potentially offer low operational costs for signature generation and verification.
Chimeremma Sandra Amadi, Simeon Okechukwu Ajakwe, Taesoo Jun
Secure and auditable data sharing in large-scale Internet of Things (IoT) environments remains a significant challenge due to weak trust coordination, limited scalability, and susceptibility to emerging quantum attacks. This study introduces a hybrid blockchain-based framework that integrates post-quantum cryptography with intelligent anomaly detection to ensure end-to-end data integrity and resilience. The proposed system utilizes Hyperledger Fabric for permissioned device lifecycle management and Ethereum for public auditability of encrypted telemetry, thereby providing both private control and transparent verification. Device identities are established using quantum-entropy-seeded credentials and safeguarded with lattice-based encryption to withstand quantum adversaries. A convolutional long short-term memory (CNN–LSTM) model continuously monitors device behavior, facilitating real-time trust scoring and autonomous revocation via smart contract triggers. Experimental results demonstrate 97.4% anomaly detection accuracy and a 0.968 F1-score, supporting up to 1000 transactions per second with cross-chain latency below 6 s. These findings indicate that the proposed architecture delivers scalable, quantum-resilient, and computationally efficient data sharing suitable for mission-critical IoT deployments.
We present Y.I.N.-LLM, a privacy-preserving training architecture for Large Language Models that mathematically guarantees non-memorization of training data. The core innovation is the mandatory DP→ZK→HE ordering (Differential Privacy → Zero-Knowledge Proof → Homomorphic Encryption) applied to transformer gradients during training. Key results: (1) 2.3% accuracy loss at ε=1.0 privacy versus 15-40% with standard DP-SGD; (2) zero extractable training data across all tested attack vectors; (3) native GDPR Article 17 "right to be forgotten" compliance via cryptographic gradient subtraction; (4) EU AI Act Article 50 transparency compliance through verifiable privacy proofs. The Non-Memorization Theorem establishes that for any model M trained with Y.I.N.-LLM parameters (ε, δ), the probability of verbatim reproduction is bounded: P[M outputs y | x ∈ training] ≤ e^ε · P[M outputs y | x ∉ training]. This transforms copyright defense from argument to mathematics. Y.I.N.-LLM addresses the $10B+ memorization litigation crisis (NYT v. OpenAI, Getty v. Stability AI, Authors Guild v. OpenAI) by providing the first mathematically verifiable non-memorization guarantee with practical accuracy preservation. Patent Protected: U.S. Provisional Application 63/946,118 (filed December 21, 2025).
Federated Learning enables large-scale collaborative training across distributed devices. However, in massive-scale Internet-of-Things (IoT) deployments, ensuring the trustworthy sensor-level operations remains a critical challenge. We introduce a hierarchical framework that combines a three-tier architecture (devices → gateways → server) with a high-speed recursive proof system to enforce scalable zero-knowledge proofs (ZKPs). At the device level, each proof serves as a unified cryptographic commitment, binding the device’s identity, local data integrity, and training correctness into a single attestation. These proofs are then individually verified at intermediate gateways, and compressed into a single, succinct proof using a folding scheme inspired by Nova [1] - a state-of-the-art system that can excel at this task at best. The server then verifies a small number of batched proofs before aggregation, reducing workload (∼ 571× in data load) by replacing hundreds of thousands of individual proof and model update transmissions with just one per gateway. Our fully implemented R1CS precursor demonstrates resilience against various vectors (e.g., backdoor-style attacks,) achieves a ∼ 34× verification speedup on a 105-device network, and maintains both strong security and model performance. Our prototype, evaluated on an Internet-of-Vehicles (IoV) use case, demonstrates that recursive proofs add succinct overhead while providing scalable, robust integrity guarantees against adversarial environments.
With the advancement of sensing technology, the use of spatial information from LiDAR and similar measurement devices such as a depth camera is rapidly expanding. However, 3D spatial data contains trade secrets such as facility layouts and equipment configurations, making direct sharing a significant business risk. Additionally, from the perspective of data distribution between companies, a mechanism to prove the value of data utilization before purchase is essential. Existing approaches using trusted third parties or conventional encryption require data disclosure for utility verification, failing to achieve both confidentiality and value assessment simultaneously. Therefore, this study proposes a distributed platform that enables secure data exchange between organizations while ensuring confidentiality of 3D spatial information using cryptographic methods. The system operates on a Hyperledger Fabric-based permissioned blockchain to establish trust through immutable proof verification records for data distribution, and enables verification of data utility without disclosing any original data through zero-knowledge proof technology. Specifically, we implement a proprietary algorithm that generates feature values with concealed coordinates while preserving the geometric characteristics of the spatial information. Each participating organization generates feature values from spatial information and records proofs of the validity of this process on the blockchain, allowing other organizations not only to search for useful spatial information based on the feature values but also to verify the reliability of the feature values themselves. This enables previously difficult applications such as collaborative digital twin construction with competitors in manufacturing and logistics industries. Through empirical experiments, we clarify practical processing speeds in a consortium of multiple organizations, confirming the applicability in enterprise environments.
Yuxin Xia, Ziyang Ji, Jie Zhang, Wanxin Li · 7 authors
Abstract Non-Fungible Token (NFT) creators use digital signatures to ensure the ownership, authenticity, integrity, and nonrepudiation of their digital works. However, if the private key is compromised, an attacker can generate unauthorized NFTs by using the creator’s private key to issue valid signatures. These valid but unauthorized signatures will be accepted in the NFT market and cannot be revoked. Even if the NFT creators update their private-public key pairs, they cannot deny the NFTs generated by the attacker. To mitigate these risks, we propose revocable signature by introducing commitment mechanism and an Auxiliary Embedded Key ( AEK ) into the signature, while the regular verification process does not involve this AEK . If a valid but unauthorized signature is detected and needs to be revoked, AEK will be disclosed to perform the revocation operation. To illustrate the application of revocable signatures in NFT, we design and implement a revocable Elliptic Curve Digital Signature Algorithm (ECDSA) scheme with provable security. Experimental evaluations on the FIPS-recommended elliptic curves show that the performance of revocable ECDSA is comparable to the basic ECDSA, with additional 0.0303 s (P-256 curve) and 0.15 USD gas fee in Remix VM for revoking a signature.
Open access
Cryptography and Data Security
Cryptography and Residue Arithmetic
Physical Unclonable Functions (PUFs) and Hardware Security
SNARKs enable compact proofs that an NP statement is true and that the prover knows a valid witness. They have become a key building block in modern smart contract applications, including rollups and privacy-focused cryptocurrencies. In the widely used Groth16 framework, however, long statements incur high costs. A common workaround is to pass the statement’s hash to the SNARK and move the statement into the witness. The smart contract then hashes the statement first, and the circuit that is proven additionally checks consistency of the hash and the statement. Unfortunately, virtually any hash function is expensive to call either in a smart contract (in terms of gas) or in the proven circuit (in terms of prover time). We demonstrate a novel solution to this dilemma, which we call hybrid compression. Our method allows us to use two different hash functions—one optimized for the proof circuit, and another optimized for on-chain verification—thereby combining the efficiency advantages of both. We define a clean and simple security property of the two hash functions to which our security reduces in the standard model, namely, joint UHF hardness. We then show the plausibility of this assumption in the random oracle model. Our benchmarks show that it achieves near-optimal performance in both gas usage and prover time. As an example, compressing an 8 KB statement with our approach results in a 10-second prover time and a smart contract spending 270K gas, whereas the existing approaches either need a much longer proof generation (290 seconds for SHA-256 hashing) or a much more expensive contract (5M gas for Poseidon hashing). Along the way, we develop a two-party protocol of independent interest in communication complexity: an efficient deterministic method for checking input equality when the two parties do not share the same hash function.
In recent years, the number-theoretic transform (NTT) has become increasingly common in cryptography, in part due to multiple lattice-based cryptographic schemes being selected for standardization during the NIST PQC competition. Indeed, polynomial multiplications are one of the most computing intensive operations in these schemes and the NTT is crucial in decreasing the performance cost. The NTT also appears in other areas such as fully homomorphic encryption (FHE) and zero-knowledge proofs (ZKP) which are increasingly used in privacy-preserving applications. In this paper, we show how to formally specify the NTT in the Rocq proof assistant, and how we used this specification to automatically derive formally verified implementations of both complete and incomplete NTTs for multiple cryptographic schemes.
The ongoing transition to post-quantum cryptography has highlighted the need for digital signature schemes offering diverse performance and security trade-offs. Among the candidates in NIST’s ongoing post-quantum signature standardisation process is FAEST, a scheme built upon the Vector Oblivious Linear Evaluation in-the-Head (VOLEitH) paradigm introduced in 2023. VOLEitH enables efficient zero-knowledge proofs with competitive signature sizes under conservative assumptions, allowing FAEST to rely primarily on the one-wayness of the Advanced Encryption Standard (AES). Despite their promising efficiency, VOLEitH-based signature schemes have remained relatively unexplored from a physical security perspective. In this paper, we present the first side-channel security evaluation. Specifically, we demonstrate two single-trace, deep learning-assisted power analysis attacks on the masked implementation of FAEST by Aranha, Degn, Eilath, Nielsen, and Scholl. These attacks exploit leakage from witness bits and VOLE tag computations, recovering the full secret key with success probability above 0.99 from a single signature on an ARM Cortex-M4 processor. We further analyse how the VOLEitH construction enables profiling of VOLE tags without knowledge of the secret key and how even partial leakage of these tags compromises security. Finally, we discuss practical countermeasures to mitigate such leakages and strengthen the physical resilience of VOLEitH-based signature implementations.
Address verification and spend limit checks in card and instant payment systems expose cardholder ZIP codes and velocity histories to gateways and intermediaries, which increases the privacy impact of breaches. At the same time, issuers rely on these checks to control fraud within strict two to three hundred millisecond authorization budgets. This paper presents ZK-AVS, a design that replaces plaintext AVS and spend limit evaluation with zero knowledge proofs produced on the customer device and verified at the payment gateway. The issuer stores commitments to the cardholder ZIP and per window spend counters, and the device proves that its ZIP matches the committed value and that the proposed transaction keeps cumulative spend within the configured limit, without revealing the underlying values. We instantiate a synthetic workload of fifty thousand transactions and show that AVS mismatch and limit pressure carry useful fraud signal that can be exposed as proof outcomes. The design is structured to fit within sub three hundred millisecond budgets on commodity devices, while removing direct exposure of address and spend history data at the gateway and keeping changes largely at endpoints.
The explosive gains of FinTech-enabled digital payments have raised concerns about transaction privacy, the leaking of identity information and regulatory compliance on public blockchains. Existing privacy-preserving payment solutions either have a high computational overhead or do not offer controlled auditability as demanded by financial regulators. This research addresses the problem of ensuring good privacy of transactions while guaranteeing lawful transparency of decentralized payment systems. The goal is to create a blockchain payment framework that incorporates zero-knowledge proof (ZKP) which will ensure payer anonymity, transaction unlinkability and selective regulatory disclosure. The proposed method combines cryptographic identity commitments, private transaction circuits with zk-SNARK and gas optimized smart contract verification with controlled audit proofs. The framework is tested on the Private-FinPay data set that contains two million transactions. Experimental results indicate that the proposed ZKP-FinPay can achieve$\mathbf{1, 2 0 0}$transactions per second, verification latency of$\mathbf{1 2 0}$ms, anonymity set of 50,000 users, and 0.5% probability of privacy leakage, which is better than the five state-of-the-art privacypreserving payment protocols. These findings confirm the viability of regulatory-compliant privacy preservation of FinTech blockchain systems as being technically feasible and practically scalable.
Kamil Ježek, Seongho Jeong, Yeonsoo Kim, Bernhard Scholz · 5 authors
Ethereum’s smart contracts operate on directly addressable storage that is represented as tries. The performance of the Ethereum Virtual Machine (EVM) suffers from slow storage access due to trie encoding, which hampers transaction throughput and scalability. To mitigate the Ethereum storage performance bottleneck, we propose a new storage representation for the EVM that supports asynchronous trie construction. Without changing the Ethereum protocol, we add a flat representation called Storage Replica to improve performance. Storage Replica provides a fast lookup of values in the program’s main thread, while a worker thread prepares the tries for subsequent cryptographic calculations. With a storage overhead of less than 5% (i.e., 10 GB), we achieve up to a 6× speedup in processing smart contracts and a 4× speedup in block commits for the initial 9 M blocks of the Ethereum blockchain.
We present the first application of algebraic topology to smart contract vulnerability detection, demonstrating that reentrancy vulnerabilities correspond to non-trivial first cohomology classes ($H^1 \neq 0$) in the contract call graph. Using the Eden Scanner's Hensel obstruction test, we identified a critical vulnerability in the Inverse Finance FiRM Convex sDola-scrvUSD Market contract (address \texttt{0x63D27fC9d463Ed727676367D3F818999962737E8}) within 48 hours of its addition to the Immunefi bug bounty scope. The vulnerability affects approximately \$605,500 in total value locked and enables direct theft of user collateral through a reentrancy attack via the \texttt{liquidate()} $\to$ \texttt{escrow.pay()} $\to$ callback path. We provide mathematical proof of exploitability through the Regularization Theorem and validate with a fork test against Ethereum mainnet. \end{abstract}
The growing threat of cyber-attacks and the fast development of quantum computing have rendered conventional methods of cryptography to be inadequate in ensuring the security of data transmission. In order to resolve this issue, this paper will present a Hybrid Quantum-Safe Cryptographic Framework, a mixture of Post-Quantum Cryptography (PQC), Blockchain, and Zero-Knowledge Proofs (ZKP) to achieve secure, verifiable, and privacy-preserving data sharing. The system utilises quantum resistance based on lattice-based encryption, decentralized identity and tamper-proof storage based on blockchain, and authentication based on ZKP, which does not reveal sensitive user information. Moreover, a Tamil-based linguistic encryption layer that is integrated with AES-256-GCM is added to increase the cryptographic complexity and security of localization. The experimental analysis of the system run on a Windows-based platform proves that the system can encrypt a 1 MB file on average time of 1.9 seconds, at the same time being highly secure and scalable. The access control based on the ZKP had an accuracy of verification 99.2 and the AI-based anomaly detector had an accuracy of detection 96.8 and low rate of false-positive. These findings prove that the proposed framework provides an effective, quantum-resistant, and privacy-aware implementation that can be used in secure systems like e-governance, legal documentation, sensitive data sharing systems.
Centralized exchanges (CEXs) dominate cryptocurrency markets due to liquidity and low latency, but their opaque internal ledgers create custodial risk. Meanwhile, privacy concerns motivate private exchanges that blind the platform to user balances and order flow. Recent work such as Pisces [1] explores private and compliable exchanges, but one critical piece in compliance, public verifiable full solvency, remains unresolved. When liabilities are hidden from the platform, the platform cannot construct plaintext-based commitments and cannot be trusted to disclose complete liability sets at audit time, creating a fundamental privacy–solvency conflict. We address this conflict by designing two systems that enforce both solvency and platform-side privacy: * **Audit-then-Check Private and Solvent Exchange System:** Uses an RSA accumulator to provide constant-size membership witnesses; users verify inclusion after the auditor publishes an audit snapshot, and omission yields publicly verifiable evidence. * **Certify-then-Audit Private and Solvent Exchange System:** Eliminates user participation by introducing trusted hardware that certifies each transaction acceptance via a monotonic counter log, enabling the auditor to verify completeness without learning transaction contents. We provide rigorous security analysis that formally establish privacy against a malicious platform and solvency soundness against a malicious user-platform coalition. We implement both schemes and evaluate performance against the state-of-the-art baselines. Our prototype achieves average per-procedure computation under 35 ms, communication bounded by 14 KB per operation. For solvency verification, our online prover time remains nearly constant across user scales, achieving a 41.6× speedup over the state of the art and a 268.6× speedup over deployed baselines at $N = 2^{14}$ users, demonstrating that frequent auditing remains feasible at scale.
This study examines whether Ethereum’s market-wide influence strengthened relative to Bitcoin following the Ethereum Berlin upgrade in April 2021. Using one-minute Binance spot data for Bitcoin, Ethereum, and major large-cap cryptocurrencies, we estimate Granger-causality tests and vector autoregressions around the upgrade. The results suggest that Bitcoin retained its benchmark role, but Ethereum’s marginal contribution to short-horizon price discovery increased after Berlin. This shift is especially evident in high-liquidity states, where lagged Ethereum returns became stronger predictors of Bitcoin and other large-cap cryptocurrency returns. The evidence indicates that protocol-level developments may alter the hierarchy of information transmission in crypto markets at the margin, without overturning Bitcoin’s broader benchmark status.