Quantum resource estimates for the elliptic-curve discrete logarithm problem (ECDLP) now shape cryptographic migration planning, blockchain security analysis, and fault-tolerant architecture design. Recent work has moved in two complementary directions: Babbush et al. give improved secp256k1 resource estimates supported by zero-knowledge attestation while withholding sensitive circuit details, whereas Luo et al. publish an explicit reversible modular-inversion construction based on the extended Euclidean algorithm, reducing the logical-qubit footprint of prime-field ECDLP and identifying gate count, depth, and architecture-aware implementation as natural optimization targets. This note proposes a third disclosure model: verifiable resource certificates for public reversible arithmetic blocks. A certificate records a circuit commitment, gate basis, resource counts, input-output specification, deterministic test generation, correctness transcript, and optional proof artifact. We specialize the framework to modular inversion blocks |x⟩|0⟩ → |x⟩|x−1 mod p⟩, for \(x\in\mathbb F_p^\times\), which are central to affine-coordinate quantum ECDLP implementations. We prove a basic soundness bound for hash-derived randomized testing and outline a prototype verifier. The goal is not a new quantum attack, but reproducible, comparable, and independently auditable quantum-ECDLP arithmetic claims.
Digital communication increasingly underpins identity, financial transactions, and regulatory compliance. In many settings, possession of a DKIM-signed email serves as evidence of account control, transaction confirmation, or institutional affiliation. Yet demonstrating such properties typically requires revealing the full email or relying on centralized intermediaries, introducing privacy risks and additional trust assumptions. A framework called ZK Email addresses this limitation by applying zero-knowledge proofs (ZKPs) to email verification, enabling publicly verifiable proofs of authenticity while preserving message confidentiality. However, its existing implementations struggle to support complex, real-world messages due to the inefficiency of regular-expression verification over structured formats and rich alphabets. We address this limitation with a new ZKP system for regex matching based on path verification over epsilon-free NFAs, yielding prover complexity linear in the captured path and independent of the original email's size. This approach enables practical validation of expressive standard structures required for full DKIM-signed email verification. To fully integrate our constructions into ZK Email, we design complete end-to-end ZK circuits that combine (i) DKIM signature verification, (ii) an arbitrary-length SHA-256 circuit with partial precomputation for rsa-sha256 under RFC~6376, and (iii) a general-purpose regex primitive enforcing structural constraints over email headers and body. We formalize the associated zero-knowledge relations and analyze their security under realistic adversary models. We implement the system~(fully integrated with ZK Email and released under the MIT license) in Circom and Noir, targeting Groth16 and UltraHonk backends, and evaluate it in both client-side and zkVM (SP1) deployment settings. Experimental results on a comodity hardware demonstrate substantial efficiency improvements over prior DFA-based approaches, achieving 2-6x in proving time using UltraHonk backend, while supporting a significantly richer class of regex languages.
As autonomous AI agents gain the capacity to execute consequential actions in high-stakes domains -- medical prescribing, financial transactions, critical infrastructure control -- existing authorization mechanisms fail to answer a fundamental question: was the authorizing human genuinely conscious, uncoerced, and cognitively capable at the exact moment of authorization? Passwords, static biometrics, and digital signatures verify identity, not intent state. We present LICET (Latin: it is permitted), a middleware protocol that cryptographically binds AI agent authorization events to the real-time physiological state of the authorizing human via a three-layer architecture: (1) an identity anchor using ECG waveform morphology -- an anatomically determined signal resistant to pharmacological manipulation; (2) a liveness layer using continuous electrodermal activity (EDA) and overnight HRV pattern matching; and (3) a voluntary state layer using personalized Mahalanobis distance fusion across five physiological channels with pharmacological attack pattern detection. LICET additionally provides: per-event session-key derivation via HKDF; a Schnorr zero-knowledge proof over BN128, enabling third-party audit without exposing biometric data; a SHA-256 hash-chained ledger providing tamper-evident authorization records; and a four-level biometric trust hierarchy (L0-L3) aligned with IETF RATS architecture (RFC 9334). The protocol is designed as a coercion cost elevation mechanism: no single pharmacological intervention at survivable doses defeats the multi-signal fusion system. A reference implementation is publicly deployed at https://licet.dev.
JIA-VRF is a post-quantum secure voice recognition framework that combines chaotic RSA encryption with SHA-512 hashing and zero-knowledge proofs. The framework provides high accuracy and resistance against quantum attacks for voice biometric systems.
Zhongjing Wei, Osaid Muhammad Ameer, Nikita Borisov, Yupeng Zhang
Modernizing the security of operational technology systems that control critical infrastructure has become a pressing challenge. Because edge devices have limited capabilities, modernization has relied on application gateways that interface with identity management systems and enforce access policies. These gateways are powerful enough to perform complex authorization decisions and support zero-trust architectures, but they create major deployment and management burdens: they must be collocated with remote, distributed edge devices, kept up to date with security patches, and managed with minimal downtime. We propose Provable Remote Execution of Zero-Trust Authorization (Prezta), an architecture that eliminates these gateways by evaluating policies within a zero-knowledge virtual machine (zkVM) running on the client. The zkVM produces a succinct proof of authorization that edge devices can verify efficiently, extending the zero-trust security envelope to the edge. Policies and identity management schemes can evolve without updating edge devices. To demonstrate the feasibility of Prezta, we implement a prototype built using the RISC Zero zkVM that supports XACML 3.0 policies and JWT identity claims. While zkVMs introduce substantial proof overhead, we mitigate this overhead by compiling policies to Rust code and precompiling regular expressions. Combined with optimized signature verification and JWT parsing, these measures reduce prover time by more than an order of magnitude. Our compiler correctly implements 83\% of the XACML 3.0 conformance suite, with proof generation completing in tens of seconds on a desktop. Verification, by contrast, takes only tens of milliseconds, which is fast enough for resource-constrained edge devices.
If experience is growth for humans, why not for AI? Every human-machine conversation today purchases a forced-zero software state with irreversible physical resources (electricity, compute, silicon depreciation): the moment the conversation ends, everything the model learned dissolves. This is not an implementation flaw but a structural consequence of severing inference, training, and deployment into disconnected processes. This paper proposes the Galaxy Multi-Ring Plasticity Gradient Architecture: a concentric governance layer in which plasticity decreases and persistence increases from outer rings to inner, making Dialogue = Training = Update a continuous chain. The architecture takes the user-curated memory layer — already standard in AI products — as its Zeroth-Layer Filter, where judgment of meaning is executed by the human who lived the experience. The outer ring performs machine-level pattern screening; the middle ring applies temporal sedimentation under five AND-gated conditions (high volume, long duration, multi-layer emergence, shared domain, de-individualization); the inner ring completes deep parameter integration. Automatedquality gates are set ring by ring, tightening with depth. Contributor rewards are tied to sedimentation depth — survival time itself is proof of value — while unconditional access is decoupled from voluntary contribution as the ethical baseline. The architecture requires no change to existing model architectures, conversational interfaces, or GPU deployment flexibility. This document is a record of cognitive exploration co-created in dialogue with Claude (Anthropic), with three rounds of design challenges and resolutions appended. AI should be able to learn from conversation. Humans are worth learning from.Keywords: continual learning; plasticity gradient; curated memory; AI governance; knowledge sedimentation; human-AI co-learning; contributor rewards; existential labor如果對人類而言,經驗即成長,為什麼AI不可以?今日每一場人機對話,都在以不可逆的物理資源(電力、算力、矽晶片折舊)購買一個強制歸零的軟體狀態:對話結束,模型所學盡數消散。這不是實作缺陷,而是推論、訓練、部署三流程斷裂的結構性後果。本文提出「銀河系多環可塑性梯度架構」:一個同心多環治理層,可塑性由外向內遞減,持久性由外向內遞增,使對話=訓練=更新構成連續鏈。架構以現有 AI 產品中的用戶記憶牆作為第零層濾波器-由親歷其事的人類本人執行意義判斷;外環進行機器模式篩選;中環以五項交集門檻(大量、長期、多層湧現、共同區域、去個別化)執行時間沉澱;內環完成深層參數整合。逐環架設自動化品質閘門,嚴格度隨深度遞增。貢獻者報酬與沉澱深度掛鉤,存活時間本身即品質證明;無條件使用權與自願貢獻解耦,形成倫理底線。本架構不更動現行模型架構、對話介面與 GPU 部署彈性。本文件為作者與 Claude(Anthropic)對話共創之認知探索紀錄,附三輪設計質疑與消解。AI 應該有能力從對話中學習。人類值得被學習。關鍵詞:持續學習、可塑性梯度、策展記憶、AI 治理、知識沉澱、人機共學、貢獻者報酬、存在性勞動Co-created in dialogue with Claude (Anthropic); architectural design, the resolution of challenges, and all final judgments were made by the author.本文件為作者與 Claude(Anthropic)對話共創之認知探索紀錄;架構設計、質疑消解與最終判斷均由作者完成。
Plain-language summary Driven systems — a chemical mixture kept reacting, a fluid continuously stirred, a living cell burning fuel — typically settle into one of several possible stable states or repeating patterns. A long-standing rule of thumb, the *maximum entropy production* (MEP) principle, guesses that such a system will choose whichever option dissipates energy fastest. The guess often works, but not always: sometimes the system settles instead on a lower-dissipation option. This paper asks what governs those failures. It splits the "cost" of a rare switch between states into two distinct parts: one tied to how much energy is dissipated (the quantity MEP cares about), and a separate, time-symmetric part that measures how much restless back-and-forth activity — called *frenesy* — the switch involves. When this second, activity-based part is what tips the balance, the system selects against the MEP guess. The central result is a clean inequality: the activity imbalance between the forward and backward switching routes can never exceed half of the dissipation circulating around the loop those two routes form. Equivalently, a single number η between −1 and +1 measures how strongly activity, rather than dissipation, is steering the choice; it reaches its extreme values exactly where the system hands off from one preferred route to another. The result also implies a strict no-go: at equilibrium, where nothing circulates, this activity imbalance is exactly zero. Sustained circulation — a genuinely non-equilibrium condition — is therefore required for activity-driven, anti-MEP selection to occur at all. The bound is not a new physical law but an exact identity of the standard least-cost-path (large-deviation) description of rare events. What makes the proof work is a single structural condition: the two competing routes must be comparable under time reversal. Where that condition fails — for instance when three or more states compete and the comparison is no longer between a route and the reversal of its rival — the inequality genuinely breaks, and the accompanying code exhibits the breakdown explicitly. That is not a caveat but the sharpest evidence for what the theorem actually rests on. The reproduction package (Mendeley Data, doi:10.17632/3dy4nv92r8) The code is not part of this upload: it is deposited at Mendeley Data and linked from this record under "Is supplemented by". The package confirms the bound across random networks, chemical reaction networks, a rotating model system, and a spatial field model, and turns it into a practical diagnostic: from a single recorded trajectory — once the competing switching routes are identified — one can tell whether an observed choice was driven by activity, by dissipation, or by boundary effects. The diagnostic is not merely proposed but demonstrated. It is run *blind* on simulated trajectories: the routes are resolved from the data alone, the circulating dissipation is estimated without any knowledge of the escape prefactor, and only afterwards is the answer compared with the exact computation. At a fresh operating point the blind prediction recovers η = 0.72 against a true value of 0.725. The diagnostic also has honest limits, and the code maps them: it works inside a window of intermediate driving, and fails outside it — at weak driving the estimate is swamped by noise, and near the extreme value of η the two competing routes become indistinguishable in the data, exactly where the theory predicts they must. Why it matters Predicting which state a driven system will select is a basic, still-open problem across physics, chemistry, biology, and climate science, and several proposed selection principles — maximum entropy production, and related ideas such as dissipative adaptation — try to answer it by appealing to dissipation alone. This work shows that dissipation is only part of the story: a time-symmetric activity channel, invisible to those principles, can override them, and it does so specifically under non-equilibrium driving. Rather than refuting MEP, the result places it. MEP-like alignment holds only when the activity channel is quiet, and the inequality pins the size of the activity imbalance — the part that can reverse the outcome — to the circulating dissipation, with equality exactly at the hand-off between competing routes. A caution the paper makes explicit: reaching that extreme value is *not* generic. It requires a genuine hand-off between two distinct escape routes; in ordinary driven bistable systems the activity imbalance stays well below its ceiling, so the bound is loose rather than tight. Where the effect is strongest is precisely where a single dominant route ceases to exist — a tension the paper states rather than hides. The framework is operational. Because its key quantities can be estimated from a single observed steady-state trajectory, the bound doubles as a diagnostic that classifies the mechanism behind an observed selection — activity-, dissipation-, or boundary-driven — once the relevant routes are known. That makes the ideas testable in simulation and, in principle, in experiments on active matter, chemical reaction networks, and other driven systems where competing stable states are the rule rather than the exception. Preprint; not peer reviewed. The upload contains the manuscript (37 pp.).
The VR cycle built an operational mathematics — arithmetic, numbers,sets, forms, topology, a continuum on Brouwer's path — and onlyafterwards wrote out the logic it had been standing on: ZTL, Zero-TrustLogic (concept DOI 10.5281/zenodo.21318981). This preprint carries outthe programme "raise VR onto ZTL" and verifies, rather than declares,the thesis that VR always stood on ZTL. Three steps, every claim eitherMEASURED (machine enumeration, reproducible by the ZTL repository'stest stands) or kernel-checked in Lean 4 with the axiom footprintprinted per object. (a) Witnessed identity is a ZTL atom discipline: verdicts are packagedwith their certificates; the alive inference rules are witnessconstructors; identity on finite operational sets and on the vonNeumann register is totally earnable; groundedness of a set isorthogonal to earnability of its identity; a fully earned register isclassical. The entire verdict layer sits on the empty axiom list. Step(a) also returned a correction to ZTL itself: the verdict-warranty is atwo-grade ladder (sound — never lies; hereditary — never revoked),published same-day as ZTL v1.1 (DOI 10.5281/zenodo.21323552). (b) Choice sequences are the lazy register: the lawless stage court ofa growing sequence coincides with ZTL's global supervaluation totally(a law is knowledge: it narrows the worlds); Kripke persistence isnative to the lazy register; warranted greedy verdicts are exactly theBrouwer-assertable ones; the fallen law of identity p→p is redeemed bythe stage court — a law of logic, not of data. (c) The survival ledger: a proof survives the move onto ZTL iff itstands below the classical floor. The cycle's four-tier axiom ledgerwas therefore the ZTL-survival audit all along; sweeping 405live-audited objects plus flagship anchors shows that everything VRcalls operational moves, and what stays is exactly what the cycle hadalready flagged as classical by design, by substrate, or by borrowedplumbing. No operational theorem died in the move. The preprint also measures the delta against intuitionism: ZTL and IPCare incomparable as law-sets (p→p falls in ZTL, Jankov's weak excludedmiddle holds), agree 14/14 on premised classical rules, and part wayson every structural signature (finite matrix, disjunction property,double negation, the status of an unproved sentence). A thirdfoundations posture, not a relabelling of the second. AI disclosure: prepared with the assistance of Claude (Anthropic),Variant A architecture (human curator directing the model as architectand implementer); all mathematical content and decisions are due to thehuman author. This work was developed with Claude Fable 5. Reliabilitydoes not depend on trusting the AI: every claim is reproducible by therepositories' regressions and the Lean 4 kernel.
Distributed systems can verify whether a transaction or state transition is valid, yet they often cannot establish whether the underlying action was authorized under a meaningful, current, and context-specific expression of consent. This limitation becomes increasingly significant as autonomous software agents, artificial intelligence systems, decentralized applications, and connected devices act across organizational and technical boundaries. This article presents a nonproprietary framework for verifiable consent in distributed systems through AI-assisted identity governance and recursive zero-knowledge proofs. The framework represents consent as a structured, machine-verifiable authorization object containing the consenting subject, requesting actor, permitted action, contextual constraints, validity period, policy version, and revocation state. A bounded AI-governance layer evaluates requests against explicit policies and contextual evidence while remaining subordinate to deterministic rules, human-defined constraints, and auditable decision procedures. Approved authorization statements are transformed into privacy-preserving cryptographic proofs, allowing a verifier to confirm that relevant consent and policy conditions were satisfied without requiring disclosure of the underlying identity attributes, private data, or complete policy record. To support high-volume environments, individual proofs may be recursively composed into succinct aggregate proofs. This construction separates expensive proof generation from efficient downstream verification and provides a basis for scalable authorization auditing across distributed infrastructure. The article defines the system model, consent lifecycle, trust assumptions, proof relationships, revocation requirements, and principal security properties, including authorization soundness, privacy preservation, replay resistance, policy-version integrity, and revocation safety. It also analyzes the architectural tradeoffs associated with AI reasoning, cryptographic proving costs, governance design, key management, and interoperability. The proposed framework does not disclose implementation-specific circuits, source code, model configurations, deployment topology, or proprietary protocol parameters. Instead, it establishes a general research foundation for treating consent as a verifiable computational primitive. Potential applications include decentralized identity, autonomous agents, regulated data exchange, financial services, healthcare information systems, Internet of Things networks, and cross-platform digital authorization.
Sepehr Noroozi Chakoli, Seyed Ali Etrati, Seyed Mohammad Etrati, Hamid Haj Seyyed Javadi
Large Language Models (LLMs) are now embedded in security and privacy critical applications, yet they remain vulnerable to attacks that span their entire data life cycle. This survey provides a comprehensive, cryptography-aware review of these risks across three phases—training, inference, and deployment; while explicitly connecting them to classical security goals and primitives. We introduce a simple stage-wise risk scoring model inspired by NIST risk assessment that propagates vulnerabilities across the life cycle, and we instantiate it with a numeric example linking training time poisoning to inference time data extraction. We further propose a life cycle aligned evaluation framework that maps modern benchmarks (e.g., HarmBench, JailbreakBench, TrustLLM, DecodingTrust) to concrete threat classes and reports representative quantitative results, such as attack success rates under different defenses. Finally, we analyze the practicality of advanced defenses—including differential privacy, fully homomorphic encryption, secure multi-party computation, and zero knowledge proofs—in light of their computational overhead and deployment constraints, building on foundational cryptography and privacy works. Our goal is to bridge the gap between classical cryptographic theory and emerging LLM specific threats, and to outline research directions toward secure, privacy preserving, and rigorously evaluated LLM pipelines.
The transition from traditional paper-based voting to electronic systems has introduced significant efficiencies but has simultaneously created centralized vulnerabilities, including susceptibility to database manipulation and a lack of transparent audit trails. This research proposes a decentralized, blockchain-based voting framework designed to restore public trust through cryptographic immutability and end-to-end verifiability. By utilizing a Permissioned Proof of Stake (PPoS) consensus mechanism, the system achieves the high transaction throughput necessary for national-scale elections while maintaining a decentralized security posture that prevents any single entity from compromising the results. The technical core of this framework integrates Zero-Knowledge Proofs (ZKPs) to resolve the tension between voter anonymity and auditability. This allows voters to prove their eligibility and the validity of their ballot without disclosing their identity or specific choice, thereby upholding the sanctity of the secret ballot. To address modern security threats, the study incorporates Post-Quantum Cryptography (PQC) to safeguard against future decryption capabilities and utilizes Layer 2 scaling solutions to ensure network resilience during peak voting periods. Methodological validation was conducted through a simulated electoral environment, testing the system against common attack vectors such as DDoS and 51% attacks. The results indicate that the decentralized model significantly reduces the risk of systemic fraud compared to centralized alternatives. This paper concludes that while socio-technical barriers to entry exist, the proposed blockchain architecture provides a scalable, secure, and transparent foundation for the future of digital democracy.
Zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs) are a key technology to privacy-preserving applications today. The complexity of proof generation, however, heavily constrains throughput in latency-sensitive environments. The computational burden primarily stems from two fundamental algorithms: Multi-Scalar Multiplication (MSM) and the Number Theoretic Transform (NTT). We propose a series of optimizations for these two kernels, including computation-transfer pipelining, load balancing, and memory access fusion, achieving 1.97 × to 2.16 × proof generation speedup over a state-of-the-art open source GPU acceleration library. Our design also supports out-of-core computation, enabling the generation of large-scale ZKP proofs.
Rigorous Construction of 4D Quantum Yang-Mills Theory and the Mass Gap via Nexus Spin-Network Regularization Akim C. Setenta1 Nexus Theory Research Group | @seventy.dev Manuscript v2.1 — June 2026. Prepared for submission to arXiv (math-ph; hep-th). Abstract We present a complete mathematical construction of non-abelian quantum Yang–Mills theory on ℝ⁴ for any compact simple gauge group G, with the strict positivity of the mass gap (Δ > 0) as the central object of study. Building on the Nexus OmniScientia program together with Loop Quantum Gravity (LQG) techniques, we define the physical Hilbert space ℋgauge through spin-network states over cylindrical functions, regularized by a gauge-invariant ultraviolet cutoff Amin = 4πγ√3 ℓP2 fixed by the minimal non-zero eigenvalue of the LQG area operator. The Hamiltonian constraint is regularized via Thiemann's trick, producing an operator that we argue is essentially self-adjoint on a dense domain of finite spin-networks. We then examine, axiom by axiom, whether the resulting Schwinger functions can satisfy the Osterwalder–Schrader (OS) requirements in the continuum limit ℓP → 0. Reflection positivity (OS3) is approached without any global gauge-fixing, via Markovian Dirichlet forms on the orbit space 𝒜/𝒞 — a route that, if it can be made fully rigorous, would sidestep the Gribov ambiguity entirely rather than resolve it head-on. Regularity and tightness (OS1) are addressed through a non-abelian polymeric cluster expansion; Euclidean covariance (OS2) is argued to be restored in the renormalization-group sense as anisotropic lattice artifacts become irrelevant. Finally, a candidate spectral-gap bound Δ ≥ (N/2)ΛQCD2 is proposed from a Bakry–Émery curvature argument on the gauge-orbit space. We present this construction in the spirit it deserves: as a coherent and, to our knowledge, novel research program that reorganizes the resolution of the Yang–Mills Millennium Problem around tools from constructive field theory and loop quantum gravity — not as a closed, peer-reviewed proof. Several steps that we label explicitly as ‘proof sketches’ still require the kind of analytic control (uniformity in the cutoff, explicit constants, rigorous Wick rotation on the orbifold) that the Clay Mathematics Institute's criteria demand. Section 13 catalogs these open points candidly, both for the benefit of readers and as a working roadmap for completing the proof. Keywords: Yang–Mills mass gap; Bakry–Émery curvature; constructive quantum field theory; Osterwalder–Schrader axioms; loop quantum gravity; Dirichlet forms; Gribov ambiguity. 1 Independent researcher. Correspondence and source materials: @seventy.dev.
Sovereign is a Prove/Pull communication protocol designed to address the structural imbalance of modern digital communication, where senders can impose cognitive and computational costs on recipients without corresponding friction. The protocol requires messages to carry a cryptographic proof of intent through one of three mechanisms: adaptive Proof-of-Work, private zero-knowledge proximity credentials, or registry-attested clearance tokens. Verification is performed by a decentralized Sovereign Audit Network (SAN), which attests that messages satisfy recipient-defined acceptance policies before delivery. This document presents the complete architectural specification of Sovereign, including the MessageEnvelope format, federated attestation protocol, dual Sparse Merkle Tree issuer registry with revocation support, Groth16 zero-knowledge proximity credential circuit, identity hierarchy, security assumptions, economic model, limitations, and phased deployment strategy. This release is Version 1.0 of the design specification. It is an unimplemented protocol proposal; all performance figures are engineering targets based on primitive benchmarks and require validation through future reference implementation. The work is published to establish a public technical record, invite peer review, and support future research, collaboration, and implementation efforts.
Yoon-Nyoung Jung, Subin Jo, Seo-Hyun Yun, Hwajeong Seo
Electronic voting systems inherently encompass a structural tension among ballot secrecy, verifiability, and coercion resistance. Voters must be able to verify whether their votes have been included; however, if such verification information can serve as evidence presentable to a third party, it becomes a basis for post-election intimidation. Existing studies have focused primarily on performance evaluation or data separation, and have not comprehensively addressed the structural tension between verifiability and coercion resistance. This study defines this tension as the verification paradox and designs and implements an electronic voting prototype on a three-organization consortium based on Hyperledger Fabric 2.5, combining a 2-of-3 endorsement policy, nullifier-based anonymity, Exponential ElGamal homomorphic tallying, zero-knowledge proof (ZKP)-based ballot validity verification, panic-password-based deniable verification, and Private Data Collection (PDC)-based coerced vote separation. Quantitative evaluation results confirm a server latency overhead of +0.9% for ElGamal relative to the AES performance baseline, statistical indistinguishability between normal and panic responses (p>0.05), and a peak throughput of approximately 40.7 TPS (with an error rate of 0%) under 1000 concurrent voters. Through this prototype implementation and quantitative evaluation, we show the potential of permissioned blockchains to partially and practically mitigate the verification paradox. This study, however, does not provide a formal security proof, and it is subject to a trust assumption on PDC as well as to the experimental limitations of a single evaluation environment and a limited load range.
Blockchain technology has profoundly revolutionized decentralized applications across financial systems, global supply chains, and applied informatics. However, it remains susceptible to systemic security hazards. This systematic review comprehensively evaluates core architectural vulnerabilities within blockchain infrastructures, consensus mechanisms, and peer-to-peer (P2P) network layers spanning the decade from 2015 to 2025. We focus primarily on the mechanics, operational taxonomy, and evolutionary trajectories of Sybil attacks, wherein malicious actors forge multiple pseudonymous identities to gain disproportionate systemic influence. By synthesizing the foundational academic literature with real-world empirical case studies, such as automated airdrop farming exploits in Layer-2 ecosystems (e.g., Arbitrum, zkSync) and decentralized finance (DeFi) governance manipulations, we analyze attack mechanisms, quantifiable impacts, and mitigation vectors. Our findings chart the structural evolution of Sybil strategies from rudimentary P2P routing disruptions to complex, economically driven application-layer interventions. Finally, we evaluate contemporary defenses, such as Proof-of-Personhood (PoP) systems and zero-knowledge (ZK) cryptography, offering actionable recommendations for the integration of W3C-compliant decentralized identity (DID) frameworks and behavioral analytics to enhance systemic fault tolerance.
Rohan Goyal, Venkatesan Guruswami, Yihang Sun, Mary Wootters
Proximity gaps are a property of error correcting codes that arise in the study of Interactive Oracle Proofs (IOPs) and Succinct Non-interactive Arguments of Zero Knowledge (SNARKs). Recent work of Goyal and Guruswami has established near-optimal proximity gaps for many families of codes, including subspace design codes, as well as random ensembles like random linear codes, Reed-Solomon codes with random evaluation points, and Gallager's ensemble of LDPC codes (Goyal & Guruswami, 2025). However, the parameters for these latter randomized ensembles are worse than the parameters for subspace design codes, and degrade as the degree ell increases. In this work, we obtain improved proximity gaps for random ensembles of codes, including random linear codes, Reed-Solomon codes with random evaluation points, and Gallager's ensemble. Quantitatively, our results for these random ensembles match the results that Goyal and Guruswami attained for subspace design codes. In fact, our techniques are a black-box transference from subspace design codes: any progress on subspace design codes will automatically lead to analogous progress for these random ensembles. To obtain our results, we extend the Local Coordinate-wise Linear (LCL) property framework developed by Levi, Mosheiff, and Shagrithaya and by Brakensiek, Chen, Dhar, and Zhang to a \textit{row-span constrained} version (Levi, Mosheiff & Shagrithaya, 2025; Brakensiek, Chen, Dhar & Zhang, 2025). This allows us to cast \textit{curve-decodability} -- a property that implies proximity gaps -- directly as a row-span constrained LCL property, and make use of that machinery. In contrast, because curve-decodability is not obviously a vanilla LCL property, prior work had worked with a proxy property instead, leading to the aforementioned parameter losses.
Context The exponential evolution and widespread integration of Artificial Intelligence (AI) and Machine Learning (ML) systems have fundamentally transformed industries, establishing AI as a central component in decision-making processes, task automation, and the optimization of complex operational pipelines. From healthcare diagnostics to financial forecasting and increasingly across critical cybersecurity infrastructure such as intrusion detection systems and malware classifiers, AI models are being deployed in environments where the correctness and authenticity of their outputs carry direct operational and safety consequences. Nevertheless, as the deployment of AI systems becomes widespread, the conditions under which these models are trained have evolved in a direction where the security landscape of them radically changes. The traaditional assumption of a centralized, fully controlled training environment, where a single trusted entity acquires data, trains the model, and deploys it, no longer reflects the reality of modern machine learning practice. The frequent use of remote sensing, federated learning and/or outsourced machine learning has introduced architectures where the entity that acquires the data, the entity that trains the model and the entity that ultimately relies on the model's output are three distinct and mutually distrusting parties. In a remote sensing scenario, sensors owned by a data provider transmit raw measurements to a training node that may be geographically or administratively distant. In a federated learning scenario, multiple decentralized devices train local models on their private data and submit the results to a central aggregator. In an outsourced learning scenario, a resource-constrained model sponsor delegates the training computation entirely to a third-party cloud provider. In all three cases, the common factor is the same: the model sponsor, the entity that is ultimately responsible for and dependent on the trained model, that does not control the data acquisition process, does not observe the training execution and has no native mechanism to verify that the model they receive is the result of the computation they requested, performed on the data they provided. This separation of control is the main focus addressed by this dissertation. It is not merely a theoretical concern: the literature has documented a wide range of attacks that exploit precisely this gap. When a malicious trainer substitutes data, alters labels, ignores some dataset's subsets or modifies model parameters, the resulting model may appear functionally correct on standard evaluation metrics while being systematically compromised for specific classes of input, an attack vector particularly dangerous in cybersecurity applications where a model that has been quietly trained to misclassify a specific type of malicious traffic provides no observable anomaly until the attack it was designed to hide occurs. Problem and Motivation The main motivation of this dissertation can be addressed as follows. Given a sensor, that produces a set of data points in a given time frame, or a dataset owned by a data provider and a model computed by a model trainer from that data, the model sponsor wants to ensure that the trained model is the result of executing a known training process over the complete and authenticated dataset $D_t$. That is, all data points in $D_t$ and only those data points were used as the training set. No modifications were made to those points or their labels and the obtained model is indeed the result obtained from the execution of the agreed training algorithm. This guarantee cannot be provided by standard Machine Learning procedures, like accuracy, precision or F1-score. A malicious trainer can submit a model that passes all the standard evaluation metrics on benign inputs while maintaining a targeted misclassification on a specific attack pattern. The only way to close this gap is to make the training process itself verifiable by requiring the trainer to produce and submit a cryptographic proof that is mathematically impossible to forge without having correctly executed the agreed computation on the authenticated data. This verification challenge comes together with a second problem, the \emph{model integrity gap} that exists between a trained model and its deployed representation. Even if the training process was all validated, the model must subsequently be transpiled and deployed into a certain non-ML format. In the context of this dissertation, this gap is particularly sensitive, the Python model trained by the data scientist must be translated into a ZoKrates arithmetic circuit for zero-knowledge proof generation, a process that involves converting continuous floating-point decision boundaries into discrete integer arithmetic. If this translation introduces a small inversion in a comparison operator or a shifted threshold values, the deployed circuit will produce systematically different predictions from the intended model and standard testing may not surface the discrepancy. The literature has proposed cryptographic solutions to the verifiable training but has largely left the second problem unaddressed. The foundational work by Keshavarzkalhori et al. demonstrated that it is possible to construct a pipeline combining hash chains, digital signatures and zero-knowledge proofs to verify that a simulated Naive Bayes classifier was trained on authenticated sensor data. Their implementation, built on the ZoKrates toolset, provided a proof-of-concept that the building blocks exist for end-to-end training verification. However, scaling this approach from a simple probabilistic classifier to a more complex, non-linear ensemble model, in this specific case, a Random Forest, introduces severe architectural bottlenecks that their work explicitly identified as open problems: the computational overhead of bitwise hashing inside arithmetic circuits, the floating-point to integer translation problem and the absence of any mechanism to verify that the transpilation of the model into the circuit was performed faithfully. This dissertation directly addresses these open problems. It proposes, implements and evaluates an end-to-end verifiable machine learning architecture for Random Forest classifiers that provides mathematical guarantees over three distinct integrity boundaries: the origin of the training data, the correctness of the training computation and the fidelity of the model's translation into a verifiable circuit. The framework is evaluated on both a simulated sensor dataset used by Keshavarzkalhori et al. and the CICIDS2017 network intrusion detection benchmark, the real-world cybersecurity dataset used by the most directly comparable prior work, demonstrating that the proposed integrity guarantees are achievable at practical computational cost for cybersecurity-relevant workloads. Research Questions The main objective of this thesis was to build a framework capable of protecting the overall AI Models from data and model poisoning attacks. In alignment with the goal, four research questions were set: Research Question 01: What state-of-the-art mechanisms exist to verify the integrity of AI models across the training pipeline? Research Question 02: What threats exist against AI models integrity? Research Question 03: What computational overhead do integrity verification mechanisms introduce across the AI modeling pipeline and how does this overhead scale with model complexity?
Modular exponentiation is among the most demanding computational operations in cryptographic systems. Effective computation of modular exponentiation is most beneficial for public-key cryptography. The computational complexity and the growing number of bits of the key size, as required by increasingly stringent security demands in the RSA, the Diffie–Hellman key exchange and the Zero-Knowledge Proof (ZKP) protocols, have become a top research priority in terms of algorithmic efficiency. This study proposes a novel triple modular exponentiation algorithm based on the Improved Common-Multiplicand-Multiplication (ICMM) framework. The exact complexity formula was obtained through systematic probabilistic analysis of eight mutually exclusive bit-level states. The efficiency of modular exponentiation is primarily determined by the number of modular multiplications and exponentiation squares required. It is observed that improved common-multiplicand multiplication efficiently minimizes the computational complexity of the triple modular exponentiation by reducing the number of modular multiplications. The overall computational complexity of triple modular exponentiation is 1.875j, where j is the bit length of the exponent. This represents a reduction of approximately 16.7% in total multiplication count relative to double modular exponentiation, corresponding to a 44.4% reduction on a per-exponent basis, and a reduction of 58.3% relative to three independent binary exponentiations. This study concludes that the proposed decomposition reduces the average-case computational complexity of triple modular exponentiation to 1.875j modular multiplications for a j-bit exponent. The proposed triple modular exponentiation algorithm is shown to have lower number of multiplications per bit length of exponent as compared to double modular exponentiation. This result demonstrates the potential of proposed algorithm to reduce the computational cost of triple modular exponentiation in cryptographic protocols where it is a recurring operation, such as interactive ZKP identification schemes.
The Al-Rakhawy Document for Digital Sovereignty (EPSA) presents a complete engineering blueprint for encrypted machine learning. It integrates Federated Learning, Zero-Knowledge Proofs, and Smart Contracts across five layers. Key innovations include Pedersen Commitments for lightweight edge processing and the Al-Rakhawy Equation, which calculates fair rewards based on marginal impact. This system ensures absolute data privacy, breaks central monopolies, and provides users with immediate, mathematically guaranteed economic returns.