Every correction for backtest overfitting depends on N, the number of strategies a researcher tried. The deflated Sharpe ratio needs it. So do multiple-testing haircuts and the probability of backtest overfitting. And N is supplied by the researcher. Nobody has ever been able to check it. VTR-1 is an open standard that makes N a structural property of a cryptographic proof. The full set of candidate strategies is committed before evaluation, and N is the leaf count of that commitment. The winning result is forced in-circuit to be the maximum of the committed set. The anti-overfitting statistics are then recomputed inside a zero-knowledge proof, on committed price data, net of a committed cost floor. Any party can re-derive every asserted property in milliseconds against their own copy of the data. No trust is placed in the issuer at any step, and the strategy is never revealed. The standard sets out three conformance levels, a verification procedure, and an adversary model naming seven attack classes. Its normative appendices pin the estimators, the fixed-point arithmetic and the commitment constructions closely enough that an independent implementation can reproduce a credential exactly. Forty-one numbered requirements let a conformance claim be contradicted. Nine known-answer conformance vectors are published with it, so a second implementation can be tested against something. The standard is equally explicit about what it will not certify: future returns, capacity, market impact, and any strategy whose result depends on fills the committed data cannot justify. The reference implementation's first published verdict refused its own author's flagship strategy, deflated below significance and published permanently. Published under CC BY 4.0. Anyone may implement it, including competitors of its steward.
We explore the design and analysis of post-quantum cryptographic primitives with an emphasis on two angles. First, diversity of assumptions, by building and analysing cryptography that does not rely on structured lattices. Second, diversity of functionalities, focusing on various primitives that extend beyond standard encryption. Motivated by the rapid development of quantum computing and the consequent threat to classical public-key cryptography, we therefore consider two families of post-quantum assumptions: isogeny-based and code-equivalence problems from which we build and analyse various primitives. In the first part, we focus on isogeny-based cryptography. We start our study with digital signatures derived from SIDH squares and investigate their security by analysing a range of attack vectors, including higher-dimensional attack strategies (known as SIDH attacks), and consequently propose suitable parameters. Building on the powerful constructive tools that the SIDH attacks became, we design an updatable public-key encryption scheme from a variant of FESTA, a public-key encryption scheme by Basso, Maino and Pope, enabling an efficient instantiation of this primitive that allows an unbounded number of updates. Finally, we investigate isogeny-based group actions and propose a framework for general-purpose zero-knowledge proofs. The second part focuses on code-based cryptography, particularly tensor group actions and code-equivalence problems. We first analyze and break a commitment scheme based on a structured tensor isomorphism problem, and we propose a secure fix. Then, we study variants of code-equivalence problems that underlie the security of two blind signature schemes. For one variant, we provide a reduction to a standard problem, whilst for another one we show that its security has been largely over-estimated. Overall, this thesis contributes to the development of a diverse suite of post-quantum primitives by providing new constructions, security analyses, and insights into the use of alternative assumptions beyond lattice-based systems.
Zero-Knowledge Proofs (ZKPs), particularly zk- SNARKs, are extensively employed in privacy-sensitive applications, but proof generation in such protocols imposes significant computational overhead. A major performance bottleneck is Multi-Scalar Multiplication (MSM), a highly compute-intensive operation on elliptic curves. While existing work focuses on specialized curves such as BLS12-377, which support more efficient elliptic curve arithmetic, there is limited exploration of MSM on general-purpose curves such as BLS12-381, which lack such optimizations and make parallelization more difficult. It faces the following challenges: imbalanced resource usage in modular multipliers, performance disparity between elliptic curve operations, and under-utilization of point addition unit in scheduling. To tackle these challenges, we propose FlexMSM, a flexible and scalable FPGA-based accelerator to accelerate MSM. FlexMSM innovates three techniques. First, we present a reconfigurable modular multiplier based on our proposed Hybrid-Weight Modular Multiplication algorithm, which strikes a balance between hardware cost and the number of MSM cores deployed on a single FPGA. Second, we propose a unified point addition scheme and design a fully pipelined point addition (PADD) unit. This design eliminates timing mismatch between pipeline stages and shortens the critical path. Third, we introduce dual-decoupled scheduling strategy for the bucket aggregation phase in Pippenger algorithm, which reduces pipeline stalls and improves the utilization of the PADD unit in MSM. To the best of our knowledge, FlexMSM is the first work to support up to double MSM cores for BLS12-381 curve on a single Xilinx UltraScale+ VU13P FPGA, leading to remarkable performance enhancements compared to existing works for input sizes from 218to 226. For the degree of 220, FlexMSM with two cores on a single FPGA achieves speedups of 19.29× over Hardcaml, 8.57× over if-ZKP, 2.14× over OPTIMSM on FPGA, 6.57× over ASIC-based work PipeZK, and 9.29× over GPU-based work GZKP.
Abstract Bilinear pairings have emerged as a fundamental tool in public-key cryptography, enabling advanced protocols such as identity-based encryption, short signatures, and zero-knowledge proofs. This paper focuses on optimizing pairing computations on curves with embedding degree 2, addressing both theoretical foundations and practical implementations. We propose an optimized double-and-add ladder algorithm that leverages the technique of y -coordinate recovery, achieving superior performance for the Tate pairing on supersingular curves and the Omega pairing on non-supersingular curves. Our method is implemented based on the RELIC cryptographic library, demonstrating significant efficiency improvements over Miller’s algorithm. Specifically, it reduces the number of base field multiplications (respectively CPU clock cycles) by 17.53 % (respectively 13.58 %) for the reduced Tate pairing on supersingular curves with a 1536-bit field size and by 12.37 % (respectively 8.39 %) for the Omega pairing on non-supersingular curves of the same size. This work establishes the first comprehensive implementation framework for cubical-based pairing computations on curves with embedding degree 2, providing quantified optimizations for practical cryptographic deployment.
Nishanth Shet, R. Chinmai, Preethi Preethi, Y. V. Srinivasa Murthy
Abstract As quantum computing grows, the security of RSA and ECC offers is becoming increasingly flush. A novel Quantum Resistant Multipath CryptoGraph protocol (QR-MCP) has been proposed in this work, which is a multi-layered security framework that combines lattice-based cryptography, SPHINCS+ post-quantum signatures, onion routing, with AI-driven anomaly detection for long lifetime security and privacy of data. Encrypting messages in multiple paths increases security as larger network attackers cannot intercept an entire message. Ledgering on the blockchain is also used for integrity verification for the protocol, and the protocol also uses AI models to detect anomalies in real-time. QR-MCP has shown to be resilient to simulated cyber attacks such as man-in-the-middle, traffic analysis as well as collusion based decryption. Future scalability to new threats will gain strength with the introduction of homomorphic encryption and zero-knowledge proof (ZKP).
The growing use of biometric authentication systems has raised serious concerns about the privacy and security of sensitive user data. Zero-Knowledge Proofs (ZKPs) provide a cryptographic solution that allows authentication without revealing the actual biometric templates. However, applying them in practice is often difficult due to the computational complexity of the circuits involved. It is commonly assumed that only simple metrics, such as Hamming distance, are suitable for these limited environments, while arithmetic metrics like Euclidean distance are considered too "heavy" or slow. This research challenges that assumption by comparing the performance of both metrics within a Groth16 Zero-Knowledge framework. For our methodology, we used a ResNet18 neural network to generate fixed-length biometric data (embeddings). To make this data compatible with the cryptographic system, we used a quantization strategy for the Euclidean metric and a binarization strategy for the Hamming metric. The experiments, conducted using the Circom compiler and snarkjs library, show very little difference in performance between the two approaches. The Euclidean circuit required 577 constraints, which is only 9% more than the 529 constraints of the Hamming circuit. Furthermore, both methods had an average proof generation time of approximately 0.5 seconds on standard hardware. These findings empirically prove that high-accuracy Euclidean comparisons can be used efficiently in Zero-Knowledge protocols. This allows developers to focus on biometric precision without sacrificing cryptographic performance.
We introduce the ω-Protocol, a zero-knowledge proof framework for the verification of elliptic curve–based homomorphic digital signatures. The protocol is constructed on top of the Elliptic Curve Homomorphic Digital Signature Algorithm (EHDSA) and enables zero-knowledge verification of signature validity while preserving signer privacy. The core contribution of the ω-Protocol is a signature-integrated zero-knowledge construction that combines homomorphic properties of EHDSA with algebraic commitment mechanisms over elliptic curve groups. We formalize the protocol model and define security notions capturing zero-knowledge, soundness, and unlinkability of signature verification. Under standard cryptographic assumptions over elliptic curve groups, we prove that the ω-Protocol achieves zero-knowledge and unforgeability-preserving verification without revealing signature components or ephemeral key material. We further analyze the computational complexity of the protocol and show that it incurs only minimal overhead compared to standard EHDSA verification. Our results establish a principled cryptographic framework for zero-knowledge verification of homomorphic digital signatures and provide a foundation applicable to privacy-preserving authentication and verification protocols.
Michael Adjedj, Constantin Blokh, Geoffroy Couteau, Arik Galansky · 6 authors
We present a novel protocol for two-party ECDSA that achieves two rounds (a single back-and-forth communication) at the cost of a single oblivious linear function evaluation (OLE). In comparison, the previous work of Boneh, Haitner, Lindell, and Segev (EUROCRYPT 2025) achieves two rounds but requires expensive zero-knowledge proofs on top of the OLE. We demonstrate this by proving that in the generic group model, any adversary capable of generating forgeries for our protocol can be transformed into an adversary that finds preimages for the ECDSA message digest function (e.g., the SHA family). Interestingly, our analysis is closely related to, and has ramifications for, the ‘presignatures’ mode of operation—Canetti, Gennaro, Goldfeder, Makriyannis, and Peled (CCS 2020), Groth and Shoup (EUROCRYPT 2022).Motivated by applications to embedded cryptocurrency wallets, where a single server maintains distinct, shared public keys with separate clients (i.e., a star-shaped topology), and with the goal of minimizing communication, we instantiate our protocol using Paillier encryption and suitable zero-knowledge proofs. To reduce computational overhead, we thoroughly optimize all components of our protocol under sound cryptographic assumptions, specifically small-exponent variants of RSA-style assumptions.Finally, we implement our protocol and provide benchmarks. At the 128-bit security level, the signing phase requires approximately 50 ms of computation time on a standard linux machine, and 2 KB of bandwidth.
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Pierpaolo Della Monica, Ivan Visconti, Andrea Vitaletti, Marco Zecchini
An essential requirement for the large-scale adoption of Web3 is enabling users to benefit from their data even within already deployed systems. This raises an important open question: how can existing, widely adopted software verify that a user has retrieved specific data from a TLS server? Impressive scientific results (e.g., DECO [CCS20] and the work of Xie et al. [USENIX24]) and industrial products (TLSNotary) have recently made progress in the above challenging direction. However, while they nicely leave TLS servers untouched, the retrieved data is then used in computations with verifiers that are required to run some advanced non-standardized cryptographic schemes (e.g., ZK-SNARKs), which clearly limits the large-scale adoption of the proposed technologies. In this paper, building on top of previous approaches and relying on the recent concept of Predicate Blind Signatures of Fuchsbauer and Wolf [Eurocrypt24], we bypass the limits of prior work by presenting ACTS a distributed architecture that, while still leaving TLS servers untouched, it allows a user to show possession of data retrieved from TLS servers simply requiring that the software of the verifier can check a standard signature. Our contributions include a round-optimal predicate blind signature protocol that produces standard RSA-PSS signatures. We show how this primitive can be integrated into the DECO architecture (and its successors) to certify data retrieved from TLS servers. Furthermore, we have optimized our construction to make it practical on commodity hardware for a large and significant class of policies implemented by the notary (i.e., the actor that is in charge of obliviously certifying TLS data, therefore preserving data confidentiality). We provide an experimental evaluation on the simple but powerful enough use case of a PDF document downloaded from a TLS server and encoded into an AES-GCM ciphertext. The user will then get a certified PDF through a standard PADES signature added obliviously to the PDF along with some metadata by a notary service. The resulting standard signed PDF document can be transparently verified using off-the-shelf PDF readers. Our experimental validation demonstrates that our architecture is suitable for real-world deployment in concrete scenarios.
Dharmesh Dhabliya, Aditya Lavhale, Sunil Thakur, R. M. Gomathi · 6 authors
In modern cryptography, improving the cryptographic security of Zero-Knowledge Proofs (ZKP) has become a compelling trend. Traditional models like the zk-SNARK and zk-STARK has shown strong security but are accompanied by the inherent issues of computational complexity and proof size. This work presents the Algebraic Zero-Knowledge Proof (AZKP) framework, using algebraic structures and integration of elliptic curves to optimize proof creation and verification. The suggested approach fills in key gaps found in the current methodologies, such as huge computational overhead and enormous proof sizes. Prime factorization in algebraic groups and ring homomorphisms of the AZKP framework is used to achieve small proof size without sacrificing computational efficiency. Comparing AZKP with zk-SNARK and zk-STARK models, experimental evaluation was applied to four critical performance metrics. generation time of proof, verification time, size of proof, and computational overhead. Results show that the AZKP is able to make a 48% decrease in proof generation duration and 20% increase in verification speed in comparison to zk-SNARK. Also, AZKP incurred lower computational cost than zk-STARK, with a proof size that is manageable. These results highlight the prospect of AZKP in cryptographic use where high-speed low-latency verification operations are desired. Further research will integrate AZKP in blockchain environments in order to increase real-time transaction validation.
Fully Homomorphic Encryption (FHE) enables computation on encrypted data with end-to-end confidentiality; however, its practical adoption remains limited by substantial computational costs...
Blockchain technology enables tamper-resistant and transparent data management, but it continues to face pressing challenges related to security and performance. Existing blockchain applications predominantly rely on software-based implementations, which are susceptible to side-channel analysis (SCA) attacks and constrained by the limited efficiency of general-purpose processors. This thesis addresses these challenges by leveraging Field-Programmable Gate Array (FPGA) technology to develop hardware-based solutions that strengthen cryptographic security and accelerate blockchain execution. Three major hardware contributions are presented: an Ethereum hardware wallet resistant to SCA, a hybrid Ethereum–Bitcoin hardware wallet supporting both Hierarchical Deterministic (HD) and Non-Deterministic (ND) modes, and a hardware-accelerated Ethereum Virtual Machine (EVM). The first contribution, EthVault, introduces the first complete hardware architecture of an Ethereum HD cold wallet and its FPGA implementation. EthVault integrates a side-channel resistant elliptic curve cryptography (ECC) design, the first hardware realization of the child key derivation (CKD) function, and resource-conscious implementations of key cryptographic algorithms, including ECDSA, HMAC-SHA-512, PBKDF2, SECP256K1, elliptic curve point operations, and the Ethereum checksum algorithm, resulting in a secure, compact wallet. The second contribution, HardVault, presents the first FPGA-based hybrid Ethereum–Bitcoin cold wallet architecture. Supporting both HD and ND key generation methods, HardVault improves resource efficiency by reusing cryptographic primitives common to Ethereum and Bitcoin, including RIPEMD-160, CKD, and SHA-256. This reuse minimizes hardware overhead, enabling a lightweight and energy-efficient solution. A detailed power–performance evaluation further demonstrates HardVault’s superior efficiency, with measurable improvements over commercial wallets such as Trezor One. The third contribution, EVMx, proposes a single-core FPGA-based EVM that offloads smart contract execution from full and archival nodes to a dedicated hardware accelerator. EVMx preserves full compatibility with the EVM’s stack-based semantics while introducing performance optimizations such as lightweight pipelining, simplified opcode decoding, dynamic corner-case handling, and selective parallelism. Experimental results show significant speedups for both individual opcodes and complete smart contract execution compared to CPU-based and prior FPGA designs. Furthermore, integration strategies are discussed to enable scalable adoption of EVMx within existing Ethereum clients. Overall, this thesis demonstrates that FPGA-based designs can substantially strengthen blockchain ecosystems by enhancing both security (EthVault and HardVault) and computational performance (EVMx), thereby paving the way for more secure, efficient, and practical blockchain deployments.
Cryptographic Implementations and Security
Cryptography and Residue Arithmetic
Physical Unclonable Functions (PUFs) and Hardware Security
Zero-knowledge proof (ZKP) is a cryptographic protocol that allows a prover to convince verifiers that a computation is correctly executed without disclosing the prover’s secret. ZKP has been deployed in various privacy-preserving applications. However, the proof generation is notably inefficient on general-purpose processors. Multi-scalar multiplication (MSM) and polynomial computation (POLY), including number theoretic transform (NTT), are two of the most computation-intensive parts in proof generation. Recently, separate accelerators for MSM and POLY (mostly NTT) have been proposed. Unfortunately, separate accelerators may have poor resource utilization since MSM and POLY cannot be performed concurrently. To address this challenge, we propose Exa, a unified hardware architecture for MSM and POLY. It enables MSM and POLY to share computational resources and memory resources through decoupling dataflow control, computation, and memory. We design a novel unified functional unit (FU) array that can support both POLY operation and point addition (PADD) for MSM. In addition, we propose a 3-D NTT implementation and an adaptive MSM implementation on the FU array using a domain-specific instruction set architecture (ISA). Exa is scalable and can be efficiently orchestrated by our proposed runtime system. Compared with the separate accelerators for MSM and NTT, Exa occupies 47% less chip area. Compared to state-of-the-art accelerator PipeZK, Exa achieves up to$20.68 \times $and$4.58 \times $improvement for NTT and MSM, respectively, while occupying a chip area that is$2.6 \times $smaller. For end-to-end applications, Exa can achieve a speedup of$6.5 \times $on average than software implementation.
Людмила Василівна Ковальчук, Микола Юрійович Кузнєцов, Алла Антонівна Шумська
Розглядається модель функціонування блокчейну, що ґрунтується на протоколі консенсусу Proof-of-Stake, а саме — протоколі Ouroboros Praos. Кожен створений блок стає видимим усім стейкхолдерам з певною затримкою, або часом синхронізації, що є випадковою величиною з натуральними значеннями та заданим дискретним розподілом. Можливе розгалуження блокчейну внаслідок того, що слотлідер може не бачити останній створений блок. Тому в разі утворення нового блока формується посилання на раніше створений видимий блок. Ще однією причиною потенційного розгалуження є наявність декількох слотлідерів у одному й тому самому таймслоті, оскільки у разі застосування протоколу Ouroboros Praos така можливість є. Множина всіх блоків блокчейну, які були будь-коли створені (зважаючи й на ті, що не увійшли до історії блокчейну згідно з правилом «довшої гілки»), утворює дерево, гілками якого є ланцюги блоків, пов’язаних між собою посиланнями. Запропоновано застосовувати алгоритм методу Монте-Карло для оцінки таких характеристик дерева: середня довжина найдовшої гілки, середня ефективність процедури генерації блоків, середня довжина найдовшого розгалуження, а також розподіли відповідних випадкових величин. Числові приклади ілюструють високу точність отриманих оцінок за незначних витрат часу на обчислення.