We introduce the first complete formal solution to corrigibility in the off-switch game, with provable guarantees in multi-step, partially observed environments. Our framework consists of five *structurally separate* utility heads -- deference, switch-access preservation, truthfulness, low-impact behavior via a belief-based extension of Attainable Utility Preservation, and bounded task reward -- combined lexicographically by strict weight gaps. Theorem 1 proves exact single-round corrigibility in the partially observable off-switch game; Theorem 3 extends the guarantee to multi-step, self-spawning agents, showing that even if each head is *learned* to mean-squared error $\varepsilon$ and the planner is $\varepsilon$-sub-optimal, the probability of violating *any* safety property is bounded while still ensuring net human benefit. In contrast to Constitutional AI or RLHF/RLAIF, which merge all norms into one learned scalar, our separation makes obedience and impact-limits provably dominate even when incentives conflict. For settings where adversaries can modify the agent, we prove that deciding whether an arbitrary post-hack agent will ever violate corrigibility is undecidable by reduction to the halting problem, then carve out a finite-horizon "decidable island" where safety can be certified in randomized polynomial time and verified with privacy-preserving, constant-round zero-knowledge proofs.
In our research, we propose the first practically deployable construction of a multi-prover zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) protocol specifically tailored for restricted multiplication straight-line (RMS) programs, a computation model widely applicable in evaluating polynomials. Our protocol ensures input privacy, zero-knowledge, and security against fully malicious provers, all while eliminating the need for any inter-prover communication, making it highly suitable for distributed cloud environments. At the core of our approach is the introduction of the Restricted Quadratic Arithmetic Program model, an algebraic structure aligned with RMS semantics that enables provers to independently generate local proofs. We instantiate our framework using the Pinocchio protocol, resulting in a system that requires only 9 group elements per proof and 10 pairings for verification, nearly matching the efficiency of its single-prover counterpart. By leveraging our multi-prover zkSNARK protocol within a multi-server verification computation framework, we enable secure outsourcing of computations to the cloud of fully untrusted cloud servers. Compared to existing works, our protocol uniquely eliminates the need for any inter-server communication while achieving security even against adversaries controlling all servers.
Blockchain provides the opportunity for organizations to execute trustable collaborations through smart contract automations. However, linkability problems exist in blockchain-based collaboration platforms due to privacy leakages, which, when exploited, will result in tracing transaction patterns to users and exposing collaborating organizations and parties. Some privacy-preserving mechanisms have been adopted to reduce linkability problems through the integration of access control systems to smart contracts, off-chain data storage, usage of permissioned blockchain, etc. Still, linkability problems persist in applications deployed in both private and public blockchain networks. Zero-knowledge proof (ZKP) systems provide mechanisms for verifying the correctness of transactions and actions executed on the blockchain without revealing complete information about the transaction. Hence, ZKP systems provide a potential solution to eliminating linkability problems in blockchain-based collaboration systems. The objective of this paper is to identify various linkability problems that exist in blockchain-enabled collaboration systems and understand how ZKP algorithms and smart contract frameworks can be used in addressing the linkability problems. Furthermore, a proof of concept (PoC) is implemented and simulated to demonstrate a ZKP system for a privacy-preserving feedback mechanism that mitigates linkability problems in collaboration systems. The scenario-based results from the PoC evaluation show that a feedback system that includes project participants’ verification through membership proofs, verification of on-time submission of feedback through range proofs, and encrypted calculation of feedback scores through homomorphic arithmetic provides a privacy-aware system for executing collaborations on the blockchain without linking project participants.
Card-based cryptography enables players to compute logical and arithmetic operations securely, such as bitwise AND and addition of integers. Several multiparty computation protocols and zero-knowledge proof protocols utilizing these secure computations have been developed as its applications. However, the realization of an efficient protocol for an arithmetic operation other than addition and subtraction remains an open problem. This paper proposes card-based protocols, based on integer commitment, for multiplication, division, and square root. Compared to general constructions for protocols for these operations based on binary integer commitment, the proposed protocols exhibit superior simplicity and efficiency. Furthermore, these protocols introduce novel applications for card-based cryptography to secure statistical data aggregation.
Assume that, given a sequence of n integers from 1 to n arranged in random order, we want to sort them, provided that the only acceptable operation is a prefix reversal, which means to take any number of integers (sub-sequence) from the left of the sequence, reverse the order of the sub-sequence, and return them to the original sequence. This problem is called “pancake sorting,” and sorting an arbitrary sequence with the minimum number of operations restricted in this way is known to be NP-hard. In this paper, we consider applying the concept of zero-knowledge proofs to the pancake sorting problem. That is, we design card-based zero-knowledge proof protocols in which a user (the prover) who knows how to sort a given sequence with ℓ operations can convince another user (the verifier) that the prover knows this information without divulging it.
IntroductionIn mathematics and theoretical computer science, a fixed point of an operator $F$ is an entity $x$ such that $F(x) = x$. Fixed-point results appear across many domains: for example, Banach’s Fixed-Point Theorem guarantees a unique fixed point for any contraction mapping on a complete metric space, and the Knaster–Tarski Theorem ensures that every monotone function on a complete lattice has a fixed point. These classical theorems establish existence (and sometimes uniqueness) of solutions to $x = F(x)$ under various conditions. In recursive and computational settings, fixed points enable self-referential definitions – a recursive function can be seen as a fixed point of a functional that “unwinds” one step of the recursion. For instance, the Y-combinator in lambda calculus provides a fixed-point combinator $Y$ such that for any function $W$, $Y(W)$ is a term satisfying $Y(W) = W(Y(W))$. This yields recursive definitions (like the factorial function) as solutions to self-referential equations.This article develops a fully formal framework for recursive fixed points – fixed points obtained via an iterative or recursive process. We focus on the convergence of a sequence (possibly transfinite) of transformations to a self-consistent state. Intuitively, we start with an initial approximation and repeatedly apply a transformation $\phi$; if this process approaches a stable state that no longer changes under $\phi$, we have reached a fixed point. Formally, one may consider an iterative sequence $x_0, x_1 = \phi(x_0), x_2 = \phi(x_1), \dots$ and seek a limit $x_{\infty}$ such that $\phi(x_{\infty}) = x_{\infty}$. Such a limit, if it exists, is a recursive fixed point – the result of infinitely (or transfinitely) many applications of $\phi$. This idea can be generalized beyond simple sequences, using the machinery of ordinal-indexed recursion and category theory to rigorously construct $\phi^\infty$, the outcome of transfinitely many iterations of $\phi$.Recent research by Alpay (2025) introduced Alpay Algebra, a category-theoretic framework where transfinite recursive fixed points play a central role. In this framework, an endofunctor $\phi$ (an operator on objects in a category) can be iterated through ordinal numbers to yield a stable initial fixed point denoted $\phi^{\infty}$. The existence of $\phi^{\infty}$ under broad conditions and its universal properties have been proven with mathematical rigor. The fixed point $\phi^{\infty}$ is recursive in that it is obtained as the limit of an ordinal-indexed chain of iterative approximants (often called the initial chain). Notably, this $\phi^{\infty}$ is not just any solution to $X \cong \phi(X)$; it is the smallest or initial solution, meaning it is generated by the recursive process itself and any other fixed point admits a unique morphism from $\phi^{\infty}$. In other words, $\phi^{\infty}$ encapsulates the “ultimate outcome” of the transformation $\phi$ applied repeatedly without end – a self-consistent structure that remains invariant under $\phi$.This manuscript provides a formal exposition of recursive fixed points. We begin by establishing the mathematical preliminaries (category-theoretic foundations and definitions of transfinite iteration). We then prove the existence and uniqueness of the transfinite fixed point $\phi^{\infty}$ under appropriate conditions, drawing on recent developments in Alpay Algebra. We illustrate these concepts with examples ranging from classical structures (natural numbers, infinite streams) to logic (fixed-point semantics of recursive theories) and AI systems (iterative embedding alignment) to demonstrate the ubiquity of recursive fixed points in theory and practice. Throughout, we use a formal style with symbolic notation – emphasizing symbols over prose – to maximize precision and semantic weight. By the end, we will see that recursive fixed points not only exist, but in fact serve as universal invariants in many self-referential systems, providing a rigorous backbone for understanding phenomena like emergent consistency, identity of processes, and convergence of iterative algorithms.Preliminaries: Category-Theoretic FrameworkOur development uses the language of category theory to formalize recursive processes. We briefly summarize the needed notions (for a comprehensive background, see Mac Lane, 1971). We assume a category $\mathcal{A}$ with an initial object $\varnothing$ (an object with a unique morphism from it to any other object). An endofunctor $\phi: \mathcal{A} \to \mathcal{A}$ is an operator that maps objects to objects and morphisms to morphisms within $\mathcal{A}$. Intuitively, $\phi$ represents one step of a generative or transformative process on the structures in $\mathcal{A}$. We are interested in objects $X$ that satisfy an isomorphism $X \cong \phi(X)$ – such objects are fixed points of the functor $\phi$ (also called $\phi$-algebras that are self-consistent).Transfinite Ordinals and Chains: To capture recursive (potentially infinite) iteration, we consider ordinal numbers $0, 1, 2, \dots, \omega, \omega+1, \dots$ which extend the natural numbers into the transfinite. An ordinal-indexed chain(or transfinite sequence) in $\mathcal{A}$ is a family of objects ${X_{\alpha}}{\alpha < \lambda}$ for some ordinal $\lambda$, together with morphisms connecting them, such that $X{0} = \varnothing$ (the initial object), and for each ordinal $\beta < \lambda$:Successor step: If $\beta = \alpha+1$ is a successor, then $X_{\beta} = \phi(X_{\alpha})$. In other words, each step applies the functor $\phi$ to the previous object.Limit step: If $\beta$ is a limit ordinal (zero is the minimal ordinal, any non-zero ordinal with no immediate predecessor is a limit), then $X_{\beta}$ is defined as the colimit (categorical limit of the diagram) of all earlier $X_{\alpha}$ for $\alpha < \beta$. Intuitively, at a limit stage, $X_{\beta}$ is the “union” or limit of the prior approximations $X_{0}, X_{1}, ..., X_{\alpha}, (\alpha<\beta)$.This process yields an initial chain:X0→ X1=ϕ(X0)→ X2=ϕ2(X0)→ ⋯→ Xω=colim{Xn:n<ω}→ Xω+1=ϕ(Xω)→ ⋯Each stage $X_{\alpha}$ is built “recursively” from the previous ones. We say $\phi$ is continuous (or $\kappa$-accessible) if it preserves colimits of chains of length $<\kappa$ for some regular cardinal $\kappa$ (for example, $\omega$-continuous means it preserves countable colimits). Under such conditions, one can show that the initial chain eventually reaches a stage where applying $\phi$ does not produce a new object. Formally, there exists some ordinal $\mu$ (often $\mu = \kappa$ or earlier) such that $X_{\mu} \cong X_{\mu+1} = \phi(X_{\mu})$. When this first occurs, $X_{\mu}$ is a fixed point of $\phi$. By construction, it is the minimal or initial fixed point, since it arose from the smallest starting object by iterative application of $\phi$. We denote this object as $\mu \phi$ or $\phi^{\infty}$ (Alpay’s notation). It is also called the initial $\phi$-algebra in category-theoretic terms.Definition: The recursive fixed point of $\phi$, denoted $\phi^{\infty}$, is the object (if it exists) at which the transfinite iterative chain stabilizes. Concretely, $\phi^{\infty}$ is an object such that $\phi(\phi^{\infty}) \cong \phi^{\infty}$ and for some ordinal $\mu$, $\phi^{\infty} = X_{\mu}$ with $X_{\mu} \cong \phi(X_{\mu})$, where ${X_{\alpha}}$ is the initial chain defined above.Because $\phi^{\infty}$ arises by iterating $\phi$ starting from the smallest object, it intuitively represents the “limit of applying $\phi$ forever.” This aligns with the idea of a recursive process converging to a fixed point. The existence of $\phi^{\infty}$ is not automatic in every category or for every functor $\phi$; it typically requires conditions like completeness of the category or continuity of $\phi$ as mentioned. The Alpay Algebra framework explicitly assumes such conditions (e.g., working in well-behaved categories with transfinite colimits and $\phi$ preserving those colimits). In fact, Alpay Algebra I establishes that $\phi^{\infty}$ exists for every initial object under ZFC set theory assumptions without additional axioms. All proofs are carried out within standard category-theoretic foundations (following Mac Lane’s paradigm).Existence of the Recursive Fixed Point ($\phi^{\infty}$)We now state and prove (in outline) the Existence Theorem for recursive fixed points. This corresponds to the fixed-point existence results found in Alpay’s work and is analogous to the classical results (Knaster-Tarski, etc.) but in a transfinite categorical setting.Theorem 1 (Existence of $\phi^{\infty}$): Let $\phi: \mathcal{A} \to \mathcal{A}$ be an endofunctor on a category $\mathcal{A}$ that admits all colimits of chains of length up to some regular ordinal $\Lambda$, and assume $\phi$ preserves these colimits (i.e. $\phi$ is $\Lambda$-continuous). If $\mathcal{A}$ has an initial object $X_0$, then the initial chain $(X_{\alpha}){\alpha < \Lambda}$ defined by $X{0} = \varnothing$ and $X_{\alpha+1} = \phi(X_{\alpha})$ (with $X_{\lambda} = \mathrm{colim}{\alpha<\lambda} X{\alpha}$ for limit ordinals $\lambda < \Lambda$) will converge to a fixed point. In other words, there exists some ordinal $\mu < \Lambda$ such that $X_{\mu} \cong \phi(X_{\mu})$. This object $X_{\mu}$ is the recursive fixed point $\phi^{\infty}$. Moreover, $\phi^{\infty}$ is an initial algebra for $\phi$: the unique $\phi$-algebra generated by this transfinite iteration.Proof Sketch: Because $\Lambda$ is regular and $\phi$ preserves colimits of chains of length $<\Lambda$, the chain cannot continue to produce strictly larger (non-isomorphic) objects at every stage without end; if it did, one could take the colimit at stage $\Lambda$ (contradicting regularity or continuity). Thus there must be some stage where stabilization occurs. Formally, consider the sequence of inclusions (morphisms) $X_0 \to X_1 \to X_2 \to \cdots$. Either this sequence continues strictly (no stabilization) for all ordinals $<\Lambda$, or else there is a stage $\mu$ where $X_{\mu} \to X_{\mu+1}$ is an isomorphism. The former scenario is ruled out by a cardinality/cumulativity argument: if no stabilization occurs before $\Lambda$, then $X_{\Lambda} = \mathrm{colim}{\alpha<\Lambda} X{\alpha}$ is a fixed point of $\phi$ at stage $\Lambda$, because $\phi(X_{\Lambda}) = \phi(\mathrm{colim}{\alpha<\Lambda} X{\alpha}) \cong \mathrm{colim}{\alpha<\Lambda} \phi(X{\alpha}) = \mathrm{colim}{\alpha<\Lambda} X{\alpha+1} = \mathrm{colim}{\alpha<\Lambda} X{\alpha} = X_{\Lambda}$ (using continuity of $\phi$). Thus $X_{\Lambda}$ itself would be a fixed point, effectively $X_{\Lambda} \cong \phi(X_{\Lambda})$, achieving stabilization at $\Lambda`. In either case, we obtain some least ordinal $\mu$ (possibly $\mu=\Lambda$ if no earlier stage) such that $X_{\mu} \cong \phi(X_{\mu})$. Define $\phi^{\infty} := X_{\mu}$. By construction, $\phi^{\infty}$ satisfies $\phi(\phi^{\infty}) \cong \phi^{\infty}$. Furthermore, for any $\phi$-algebra $(X,\alpha: \phi(X)\to X)$ (any other fixed structure), we have by initiality of the chain that there is a unique homomorphism from each $X_{\alpha}$ into $X$ commuting with the $\phi$-action; at the limit, this yields a homomorphism $h: \phi^{\infty} \to X$. Thus $\phi^{\infty}$ is the initial object among all solutions of $X \cong \phi(X)$. ∎This theorem formalizes the existence of a transfinitely attained fixed point. In plainer terms, if one keeps applying $\phi$ starting from the simplest object, eventually (perhaps after an infinite number of steps) one stops getting new structures and hits a self-consistent one. That endpoint is $\phi^{\infty}$. All the intermediate steps $X_0 \to X_1 \to \cdots \to X_{\mu}=\phi^{\infty}$ are essentially building up a solution to the equation $X = \phi(X)$ piece by piece (like successive approximations). The condition of $\phi$ preserving colimits ensures that no information is lost in the limit process and that $\phi^{\infty}$ truly is a fixed point.In the context of Alpay Algebra (a formal system introduced by Faruk Alpay), Theorem 1 is a central pillar: it guarantees that for the self-referential processes defined in that framework, a stable identity emerges as a fixed point. Specifically, Alpay Algebra treats $\phi^\infty$ as representing the intrinsic identity of a generative process, since it is the unique invariant state that the process converges to. The existence theorem above matches statements in Alpay’s work such as: “We prove that the fixed point $\phi^\infty$ exists for every initial object ... and [that] $\phi$-iterates converge under regular cardinals”. The iterative construction of $\phi^\infty$ is sometimes called an ordinal-indexed fold or transfinite induction on the functor.It is worth noting that this categorical result generalizes classical fixed-point constructions. For example, in domain theory (a branch of theoretical computer science and math), a special case of this theorem states that any continuous endofunction on a complete partial order has a least fixed point (by taking the $\omega$-chain of iterates starting from the bottom element). That is essentially the $\omega$-continuous case of the above, corresponding to Kleene’s Fixed-Point Theorem for monotone operators on CPOs (which is itself an instance of Tarski’s theorem for lattices). Our transfinite approach extends this idea: even if $\omega$ steps are not enough, one allows transfinite steps until convergence. The result is a powerful guarantee: if the process can keep going without inconsistency, it will find a fixed point. In practical terms, this means any self-referential or recursive definition, under broad conditions, “bottoms out” at a well-defined semantics or structure that does not further change under the defining transformation.Uniqueness and Universal PropertyHaving established existence, we examine the uniqueness and universal property of the recursive fixed point $\phi^{\infty}$. Uniqueness here means $\phi^{\infty}$ is essentially the only fixed point that can be obtained through the recursive construction – if there were another built in the it would be to $\phi^{\infty}$. $\phi^{\infty}$ is the smallest fixed point, and every other fixed point of $\phi$ out” of $\phi^{\infty}$ in a unique and In the of Theorem 1, the recursive fixed point $\phi^{\infty}$ is unique up to isomorphism. Moreover, $\phi^{\infty}$ has the initiality for any object $X$ with an isomorphism \cong \phi(X)$ (i.e. any other fixed point of there exists a unique morphism \phi^{\infty} \to (a the appropriate In any other fixed-point object $X$ admits a unique from $\phi^{\infty}$, which is an isomorphism if $X$ is also obtained via a iterative Sketch: Uniqueness up to isomorphism is a standard category-theoretic argument: if and are initial $\phi$-algebras fixed then by initiality of there is a unique homomorphism I \to and by initiality of a unique homomorphism \to The I \to must the identity on (by uniqueness of the on and = Thus and are \cong This any solutions of the transfinite recursion are we can of the $\phi^{\infty}$ up to the universal any other fixed point we can $X$ with a $\phi$-algebra structure and to Specifically, \to can serve as the structure on \cong is there is a unique $\phi$-algebra homomorphism \phi^{\infty} \to such that = Intuitively, maps the fixed into any fixed structure $X$ in the only with $\phi$. If $X$ itself built by a iterative limit process (e.g., another chain that also a fixed then will be an isomorphism $\phi^{\infty}$, cannot into a end up the and formal terms, there is only one smallest self-consistent structure generated by $\phi$, and any other self-consistent structure a from this smallest one. This $\phi^{\infty}$ the universal fixed point or the identity of the process $\phi$. other solution of $X \cong \phi(X)$ through $\phi^{\infty}$ in a unique The morphism \phi^{\infty} \to can be seen as the or the fixed point $\phi^{\infty}$ into the fixed point If $X$ is not not be or but it exists and is universal property that $\phi^{\infty}$ the of all of the recursive process. In Alpay’s terms, $\phi^{\infty}$ as the of the a fixed point that every other fixed point in a This is analogous to the least fixed point in a lattice is in (or maps every other fixed point in that of Recursive Fixed illustrate the theory with recursive fixed points in various the functor = 1 on the category is a $\phi$-algebra is \to which provides a point (the of the and a function \to (the on the $X$ $X \cong 1 in yields the result that $X$ must be a infinite set to the natural numbers (with the point corresponding to and the function corresponding to the starting from the initial object and iterating $\phi$: $X_0 = = 1 \cong (a = 1 1 \cong = 1 \cong ... one \cong and the colimit as \to is \cong $\omega$ we have \cong 1 has a point and the is to is a fixed point of $\phi$. 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In one a transfinite sequence of if the process is but the theory guarantees existence by transfinite The transfinite approach is a powerful – it even if a process as as each stage is built in a there is a fixed point at some ordinal work has even theory with transfinite fixed points Algebra to Banach’s contraction to transfinite In that a of an AI is to have an that is essentially a fixed point of a found via transfinite By Banach’s theorem to transfinite ordinal convergence to a unique semantic which is a recursive fixed point in a have a formal of recursive fixed emphasizing a rigorous By category theory and transfinite we an operator $\phi$ can a unique fixed point $\phi^{\infty}$ reached by an infinite recursive process. This fixed point exists under broad conditions or of and as a universal invariant for the process by $\phi$. We that $\phi^{\infty}$ is the smallest solution to $X = \phi(X)$ and that every other solution through its universal Our examples from mathematics numbers as fixed point, as fixed logic fixed point semantics of recursive and (iterative and semantic to stable In each case, the idea of a self-consistent fixed point of a recursive transformation provides and a on the of recursive fixed points and continuous processes. It a a system can be in of or self-referential one for the fixed point that represents the identity or Alpay’s recent further to that even an identity or a state can be as such a fixed point of its This a within formal mathematics – it that by the chain of transformations and one ensures the existence of a fixed point that encapsulates In practical terms, if every step of or transformation preserves or meaning without then as one iterates one approaches a state that cannot be further That state is the recursive fixed the point that and remains by its defining recursive fixed points are not just are the backbone of in self-referential By them, we that symbolic chains – as as are in a – will into a of This ensures that of symbols can be every is for in the limit, an fixed The mathematical here this in but the is through an recursive process, meaning and structure converge to an invariant fixed point, a on which further can Alpay Universal Alpay Algebra as Fixed-Point in and the of the in Alpay Algebra and the Fixed-Point of Alpay Algebra and Fixed-Point Lane, for the theorem and its of
Zeyad Ghaleb Al-Mekhlaf, Murtaja Ali Saare, Jalal Mohammed Hachim Altmemi, Mahmood A. Al-Shareeda · 9 authors
The rapid adoption of Internet of Medical Things (IoMT) devices enables real-time patient monitoring and remote diagnostics and has revolutionized healthcare delivery. Traditional cryptographic schemes like RSA and ECC, which rely on meaningful mathematical challenges, are under great threat from quantum computing, threatening sensitive medical data confidentiality and integrity. This paper proposes a quantum-resistant healthcare security framework based on lattice-based cryptographic primitives such as Learning With Errors (LWE), Ring-LWE (RLWE), and Short Integer Solution (SIS). To this end, we design a five-phase IoMT-friendly framework—Initialization, Registration, Authentication, Data Exchange, and Treatment—where each phase is backed up by lightweight cryptography primitives that can be easily implemented on the low-resource IoMT devices. Relative to the state-of-the-art lattice- and hash-based constructions, our framework involves 50-75% smaller ciphertext sizes, up to a 50% reduction of the communication overhead, and nearly 60% less in computational cost. Furthermore, the solution relies on zero-knowledge proofs, homomorphic encryption as well and attribute-based access control to guarantee strong security and privacy. Using the AVISPA tool, the framework is formally verified, showing its resistance against classical and quantum adversaries. Focusing on tangible healthcare threats, including data tampering and unlicensed access to patient diagnostics, this research paves the way for scalable, efficient, and quantum-resistant medical data protection. Our results pave the way for future investigations into secure post-quantum healthcare and IoT applications.
Zero-Knowledge Proofs (ZKPs) are critical for privacy-preserving techniques and verifiable computation. Many ZKP protocols rely on key kernels such as the SumCheck protocol and Merkle Tree commitments to enable their key security properties. These kernels exhibit balanced binary tree computational patterns, which enable efficient hardware acceleration. Although prior work has investigated accelerating these kernels as part of an overarching ZKP protocol, exploiting this common tree pattern remains relatively underexplored. We conduct a systematic evaluation of these tree-based workloads under different traversal strategies, analyzing performance on multi-threaded CPUs and the Multifunction Tree Unit (MTU) hardware accelerator. We introduce a hardware-friendly Hybrid Traversal for binary tree that improves parallelism and scalability while significantly reducing memory traffic on hardware. Our results show that MTU achieves up to $1478\times$ speedup over CPU at DDR-level bandwidth and that our hybrid traversal outperforms breadth-first search by up to $3\times$. These findings offer practical guidance for designing efficient hardware accelerators for ZKP workloads with binary tree structures.
Hasib Ahmed Md Khyrul Islam, Huy T. Vo, Aditya Rane
In the era of synthetic media, deepfake manipulations pose a significant threat to information integrity. To address this challenge, we propose TrustDefender, a two-stage framework comprising (i) a lightweight convolutional neural network (CNN) that detects deepfake imagery in real-time extended reality (XR) streams, and (ii) an integrated succinct zero-knowledge proof (ZKP) protocol that validates detection results without disclosing raw user data. Our design addresses both the computational constraints of XR platforms while adhering to the stringent privacy requirements in sensitive settings. Experimental evaluations on multiple benchmark deepfake datasets demonstrate that TrustDefender achieves 95.3% detection accuracy, coupled with efficient proof generation underpinned by rigorous cryptography, ensuring seamless integration with high-performance artificial intelligence (AI) systems. By fusing advanced computer vision models with provable security mechanisms, our work establishes a foundation for reliable AI in immersive and privacy-sensitive applications.
Open access
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Adversarial Robustness in Machine Learning
Digital Media Forensic Detection
Generative Adversarial Networks and Image Synthesis
In educational psychology, emphasizing the situational context is clearly ‘du jour’, becoming arguably most apparent in the renaming of Eccles' Expectancy Value Model to ‘Situated Expectancy-value Model’ (SEVT), outlined in several papers she coauthored (Eccles & Wigfield, 2020, 2024; Gladstone et al., 2022). According to Eccles and Wigfield (2024), the programmatic shift was necessary to reflect the expansion of the theory since its beginnings as a framework to explain gender differences in learning motivation and educational choices of students, to a now full-fledged socio-cognitive developmental theory. As such, the model is explicit about the recursive nature of the underlying processes and acknowledges the idiosyncratic circumstances of each behavioural moment, be it students' decision what classes to take or a teacher's decision about the feedback they give each student. While this makes a lot of sense conceptually, the new framing of the model comes with two challenges. One is of epistemological nature, related to the fact that the emphasis of the ‘situatedness’ weakens the generalizability of empirical finding to other, even very similar contexts. The second challenge lies in the translation of the expanded model to adequate empirical research strategies that reflect the new model complexity or, put more simply: How do we overcome the limitations of questionnaires as the most commonly used tool to collect data in this line of research? It feels inadequate now to pack the ‘situatedness’ in the item stem, for example, ‘When doing your math homework…’ or ‘In general, I love being a science teacher’. This might logically make the response somewhat context-specific, but situation-specific enough in the sense of SEVT. Overcoming this limitation is the common theme throughout the six papers which, each in its unique way, are pushing towards a more convincing empirical approach to illustrate and understand the relevance of the situational context and to identify aspects of it that allow us to carefully generalize findings to a similar class of situations. The latter is important as ‘situatedness’ in the SEVT model is not meant to be merely a new label for otherwise unexplained variance in an analysis that uses stable teacher and student characteristics as predictors. Instead, it suggests characterizing the context in order to integrate relevant features into a predictive model. For example, Stark, Camburn & Kaler (this volume) demonstrate that teacher motivation varies across different but typical work activities. But instead of the ‘classic approach’ to rely on item construction for a cross-sectional study (‘When I teach in the classroom…’, ‘When I interact with colleagues…’, ‘When I grade papers…’, etc.), they use the ‘day reconstruction method’ (DRM) to get not only a more valid measurement of the motivational state of teachers in a given context but also a precise account of how often teachers encounter those qualitatively different, but nevertheless typical, professional situations. It is obvious that a teacher's motivational state during actual teaching is not predictive of their long-term experience of burnout, for example, if this context represents only a small fraction of the professional contexts a teacher navigates on a daily basis. They are able to demonstrate that roughly two thirds of the variance in teacher motivation lies between periods, that is, distinct situations throughout a workday, negligible variance between days (controlling for periods) and roughly a third of the variance resides (stably) between teachers. Wang, Thompson-Lee and Klassen (this volume) combine the emphasis on ‘situatedness’ with the advances made in classroom simulations as a tool for teacher training, which is steadily moving towards the use of virtual reality as a standard tool (see Huang et al., 2023). Wang et al. demonstrate that even in the reduced complexity setting of a simulation in an online training setting, the success in adequately reacting in a set of 15 situations a teacher typically encounters on a daily basis has a consistent impact on student teachers self-efficacy beliefs and their assessment of how good they see themselves aligned with the affordances of the job. Unintentionally, the exposure to the scenarios tends to have a somewhat sobering effect since self-efficacy and career intentions trended down on average. However, one could argue that this is reflective of a more accurate self-assessment of the students regarding their readiness to be a teacher. They can take this either as a call to intensify their learning efforts or as a critical appraisal of their decision to become a teacher. As long as the 15 scenarios authentically reflect the professional life of a teacher, this study implicitly reflects the situational variability of the profession, and one is invited to speculate how this might impact a teacher's motivation in the long run. Similar to Stark, Camburn and Kaler (this volume), Bross, Frenzel and Nett (this volume) consider ‘day’ the key temporal unit of observation for a longitudinal study on teacher motivation or, in this case, the emotion regulation of teachers. Emotion regulation is strongly related to teacher motivation as successful regulation of negative emotions an important predictor of maintained teacher motivation is (Wang et al., 2023). The interesting twist in their study is the use of latent profile analysis that allows them, in addition to identifying coping patterns for two emotions in different situational settings, to reveal flexibility/consistency of teachers' emotion regulation across situations as a trait-like characteristic. Even if the authors do not discuss this explicitly, their approach introduces an interesting expansion of the SEVT model: While it is true that situations matter for the response of teachers, only some teachers actually vary in their response to negative emotions while the majority of teachers show very similar emotion regulation patterns. This could be understood as a situation by person interaction: Only 17.4% of the teacher sample used different combinations of flexibility across situations. The approach also reveals that the remaining three patterns consist of teachers who differ in their coping profiles but not across situations. This opens the door for further investigation beyond the emotion regulation research because it is conceivable that similar ‘meta patterns’, that is, stability of different patterns across situations for some teachers but not for others, exist for other motivational constructs as well. Moving to the papers that focus on the instructional process, we again see the need to resort to more complex statistical tools if ‘situatedness’ is of particular interest. Oschwald, Moeller, Kracke, Viljaranta and Dietrich (this volume) present probably the most fine-grained analysis of ‘situatedness’ in the context of motivational research to date, analysing the ‘micro-cycles’ of instructional quality on college students motivation in 9-min intervals (combining three ratings of 3 min). The basic idea was to illustrate that change/variation in the instructional clarity (detail, variation, consistency) has an immediate/short-term lag effect on student motivation. While the authors are very circumspect in considering methodological and conceptual shortcomings of their Null findings, I am more inclined to take them at face value: Motivational dispositions of students, as conceptualized in the SEVT context, are more inert than the study design implies. If this is true, it is good news for future research in the sense that it is not necessary to choose such a high-resolution (and hence expensive) research design. Most likely, a low-clarity teaching style simply does not dampen college students motivation immediately and maybe not even from 1 day to the next. However, if a teacher consistently over days and weeks teaches with low clarity, students become gradually frustrated, start to question their own competence, etc. The idea that zooming out the time-frame somewhat is corroborated by the Rubach and von Keyserlink paper (this volume) which used 5 weeks within the semester as the elapsed time to investigate longitudinal trends. The consistency of the student assessment of the quality of the instruction dominated observation specificity when the course was held constant. However, at a given time point, students rated different courses differently, suggesting that their assessment reflected substantial differences in their perception of the different courses. Also important is their finding that roughly 30% of variance is a stable difference between students who adds substantial noise to any statistical analysis that aims at identifying causal impact over time. Accordingly, Rubach and von Keyserlink acknowledge that their study is limited as it is a single source study, that is, students rated the instructional quality as well as their interest and expectations. But that consistency of instructional quality throughout the semester is a limiting factor to demonstrate ‘situatedness’ of student motivation comes from other research contexts as well, for example, the research on the often replicated ‘thin-slice-effect’ (Ambady & Rosenthal, 1993): Student evaluations at the end of the semester can be extremely well predicted by the assessment of the first 10 min of the first lecture of the semester. While this is often taken as proof of the importance of the first impression, our own (experimental) research suggests that this high correlation is mainly due to the consistency of teacher behaviour throughout the semester (Samudra et al., 2016). The first impression is a good indicator of the teaching quality for the teacher's behaviour/quality of the rest of the semester. A final course evaluation may well be more or less an accurate average of the experience throughout the semester and therefore a valid measure of instructional quality. With the caveat that student assessment and student motivation are different constructs, this observation would suggest for the Oschwald et al. study that the authors would find more robust effects if the time unit was not 9-min intervals, but daily or weekly aggregates of instructional quality. For both, the Oschwald et al. as well as the Rubach and von Keyserlink study, the measurement of instructional quality becomes a critical issue when we want to avoid artefacts of common-source bias or too short-cycled causal models. Göllner, Lazarides and Stark (this volume) make a foray into new territory by exploring the validity of large language models (LLMs) to assess teaching quality which, in the future, could eliminate the human factor in coding entirely. If a holistic semantic analysis could be able to capture relevant aspects of teaching quality reliably, human coding through expert or student assessment would become obsolete. Quality could even be assessed in real time as the teaching is still happening or shortly thereafter, opening the opportunity to use it as immediate feedback in teacher training. In a more rudimentary fashion, we used the same idea for specific teacher training purposes a decade ago. A voice-recording device (LENA) that distinguished teachers' and students' speaking turns identified in-class discourse segments the teachers were learning to use more frequently in their mathematics classes. Teachers received feedback within 24 h, and for some (not all), it was helpful for improving their teaching (Wang et al., 2014). Göllner et al.'s cutting-edge exploratory study shows that LLMs have potential in this regard, but we have still ways to go. The semantic representations are ‘sensitive enough’ to reflect variation between segments, lessons and teacher. They also were associated with human-coded quality assessment, but a ballpark 20% of shared variance is not even close to the level where the human–AI interrater reliability could reach the level of human–human reliability after efficient coder training. However, they used a zero-shot GPT model which mean that no additional information was provided to guide the semantic analysis, and the PCA-based dimensionality reduction is indicative of the exploratory nature of the approach with its inherent difficulty to interpret the dimensions and questions of replicability. However, the prompted transcript analysis is a first step towards a use of LLMs that is closer aligned with theoretical concepts and hence a promising step to the next level. After all, the LLM can identify the strength of instructional dialogue best when it can use samples of human-identified examples of dialogue that represent the quality dimension in question (multi-shot GPT). There is no doubt that LLMs will in the near future take over a lot of (if not all) coding tasks of texts and video footage. But what and how the AI codes material will always depend on theoretical considerations about student–teacher and student–student interactions and how they facilitate academic learning. The tool does not come with a guiding theory and Göllner et al.'s contribution makes that clear. In her reflections on the situative approach to research in educational psychology, Nolen (2024) points out that the situative view leads to an emphasis on understanding the processes that underlie change. This, in turn, leads to a reflection on what kind of change is to be analysed and what kind of change is considered desirable. Academic learning in educational psychology is, for the most part, conceptualized as a cumulative process, as relatively stable gains over an observed time period, adding to the prior knowledge level. Weeks or months as temporal units of analysis seem appropriate as standard in the learning context of curriculum-based schooling, unless the learning of smaller units is the focus, like learning the content of one particular mathematics lesson. In contrast, the underlying idea in the Stark, Camburn and Kaler contribution on teacher motivation is that high teacher motivation is desirable and a potential goal for interventions. Or it stimulates a teacher's self-directed action by minimizing exposure to situations that are demotivating or to change the quality of the social interactions to avoid the demotivating impact. It is not a cumulative, but rather a protective change model. At least implicitly, the self-efficacy belief of student teachers in Wang, Thompson-Lee and Klassen similarly is a variable one would wish to be and remain high, based on the normative assumption that high self-efficacy beliefs are a characteristic of a good teacher. But different from academic learning, there is a logical ceiling for self-efficacy beliefs. Therefore, it is not a cumulative change model, but an optimization model. The environment should lead teacher to—and keep them at—a ‘5 out of 5’ level of self-efficacy. While those two papers have similar underlying change models, the theory of emotion regulation in Bross, Frenzel and Nett is based on a qualitatively different conceptualization of change: homeostasis. For a teacher, anger is arguably a dysfunctional state and it is desirable to quickly and effectively regulate it down to an emotional set point if the situational trigger cannot be avoided. It is apparent that the logical temporal unit of analysis in this context is probably minutes, if the goal is to investigate the process as such. This, of course, is not the intention of the authors as their focus lies on the coping patterns of teachers across situations encountered throughout the day. The assumption is, in fact, cumulative in the sense that exposure to a lot of anger-inducing situations paired with a suboptimal coping pattern will wear teachers down in the long run and reduce their professional motivation. The intention of the Oschwald et al. study was to demonstrate that instructional clarity has an immediate positive impact on college students learning motivation—again not as a cumulative model but with the normative goal to reach and maintain a high level of learning motivation. At least implicitly, the assumption is that a somewhat consistent lack of clarity over a longer period of time, that is, not 9 min but several weeks of low-clarity instruction, will wear a student's learning motivation down. Even if the short-term lag effect could not be shown, the long-term effect might still—and it is likely to—exist. The measurement used in the Rubach and von Keyserlink study is Likert-scale based, which means that it comes with a maximal value despite the fact that theoretically, at least, interest is logically unlimited and could therefore follow a cumulative model. If the quality of the instruction is extremely high every week I am in class, my interest might continuously grow until the end of the term. I might reach the scale's ceiling, but that would be an artefact of the measurement scale. Why are these considerations important? They identify the epistemological challenge of an overly situation-focused perspective. While it might be relevant in some research contexts to understand features of the situation and not treat it as error variance (Nolen, 2024), we will still need to transcend the insights gained from these analyses to a more general level in order to be of educational relevance. At least for the run-of-the-mill K-12 schooling context, it would be difficult to drop the traditional positivistic rationale when we consider the practical relevance of our research: Once causal mechanisms are identified as tentative truths, they are of practical relevance only if they show long-term impact on academic learning and psychosocial development across a fairly broad class of situational contexts. The more specific the context is defined in the research, the more limited the practical implications. For example, it might be of psychological interest to demonstrate that a student's academic self-concept dips down after 20 instances of unclear instruction. But if the teacher simply was underprepared on that day and otherwise presented the material clearly and accessibly throughout the semester, treating this as a random ‘error’ is probably justified. When long-term development is the main focus of our research (here motivation), the minute-to-minute fluctuations in the clarity of instructions are unlikely to be important. The reason is that, in the back of our heads, we have a model of how motivation affects learning. A student who is—more or less—stably interested in the content of the class will be more likely to work happily on assignments, etc. in the evening and on weekends. As a general rule (non-situative), research has shown that unclear instruction has a negative impact on self-concept and interest in the long run, and we assume that this is true for a broad array of situations, student characteristics, grade levels, etc. This is why it is reasonable that teacher training works with student teachers on instructional clarity as a skill set. If well, across a of situations and contexts a teacher will Even if we that every situation is different and mechanisms are ‘situatedness’ cannot mean that educational psychology, as an of the long-term developmental that are the of educational It means to be more to of the learning environment that are necessary for the impact of on learning means to acknowledge the of but this becomes a only if the goal is to identify situational characteristics that allow The Stark, Camburn and Kaler paper a for this idea because their the teachers themselves to identify situations and their over time and how they in those contexts. While every with other teachers might be different from the they as a features that with other situations in the daily professional for example, actual instruction in the on the situations we on a daily basis to be a good point to ‘situatedness’ into a research that does not of the focus of our process of learning in
Xin Liu, Xinyuan Guo, Dan Luo, Liang Li · 9 authors
Federated learning promotes the development of cross-domain intelligent applications under the premise of protecting data privacy, but there are still problems of sensitive parameter information leakage of multi-party data temporal alignment and resource scheduling process, and traditional symmetric encryption schemes suffer from low efficiency and poor security. To this end, in this paper, based on the modified NTRU-type multi-key fully homomorphic encryption scheme, an asymmetric algorithm, a secure computation scheme of multi-party least common multiple and greatest common divisor without full set under the semi-honest model is proposed. Participants strictly follow the established process. Nevertheless, considering that malicious participants may engage in poisoning attacks such as tampering with or uploading incorrect data to disrupt the protocol process and cause incorrect results, a scheme against malicious spoofing is further proposed, which resists malicious spoofing behaviors and not all malicious attacks, to verify the correctness of input parameters or data through hash functions and zero-knowledge proof, ensuring it can run safely and stably. Experimental results show that our semi-honest model scheme improves the efficiency by 39.5% and 45.6% compared to similar schemes under different parameter conditions, and it is able to efficiently process small and medium-sized data in real time under high bandwidth; although there is an average time increase of 1.39 s, the anti-malicious spoofing scheme takes into account both security and efficiency, achieving the design expectations.
Yao Ma, Wen Yu Kon, J. O. Chu, Kevin Han Yong Loh · 6 authors
Identity verification is the process of confirming an individual's claimed identity, which is essential in sectors like finance, healthcare, and online services to ensure security and prevent fraud. However, current password/PIN-based identity solutions are susceptible to phishing or skimming attacks, where malicious intermediaries attempt to steal credentials using fake identification portals. Alikhani et al. [Nature, 2021] began exploring identity verification through graph coloring-based relativistic zero-knowledge proofs (RZKPs), a key cryptographic primitive that enables a prover to demonstrate knowledge of secret credentials to a verifier without disclosing any information about the secret. Our work advances this field and addresses unresolved issues: From an engineering perspective, we relax further the relativistic constraints from 60m to 30m, and significantly enhance the stability and scalability of the experimental demonstration of the 2-prover graph coloring-based RZKP protocol for near-term use cases. At the same time, for long-term security against entangled malicious provers, we propose a modified protocol with comparable computation and communication costs, we establish an upper bound on the soundness parameter for this modified protocol. On the other hand, we extend the two-prover, two-verifier setup to a three-prover configuration, demonstrating the security of such relativistic protocols against entangled malicious provers.
Ovaj rad istražuje teorijske temelje i praktičnu primjenu dokaza nultog znanja u blockchain sustavima, s fokusom na Polygon zkEVM blockchain. Analiziraju se zk-SNARK i zk-STARK sustavi dokazivanja te njihova implementacija u ZK-rollup rješenjima za poboljšanje skalabilnosti blockchain mreža. Teorijska analiza pokazuje kako dokazi nultog znanja omogućavaju verifikaciju transakcija bez otkrivanja osjetljivih podataka, čime se adresiraju izazovi privatnosti i skalabilnosti. Praktični dio uključuje implementaciju decentralizirane aplikacije za glasovanje na Polygon zkEVM Cardona Testnet mreži, demonstrirajući primjenu tehnologije u realnoj situaciji. Analiza transakcijskih podataka potvrđuje značajne uštede goriva kroz batch procesiranje transakcija u odnosu na direktno izvršavanje na Ethereum glavnom lancu. Rad identificira ključne prednosti i ograničenja trenutnih implementacija te predlaže smjerove za buduća istraživanja u području post-kvantne kriptografije i hardverske akceleracije.
The traditional voting process, whether paper-based or electronic, is often criticized for its lack of transparency, susceptibility to fraud, and dependence on centralized authorities. Blockchain technology, particularly in the Web3 ecosystem, provides a decentralized, secure, and tamper-proof solution for digital voting. This paper explores how blockchain can enhance election integrity by leveraging decentralized applications (DApps), smart contracts, and cryptographic security. The proposed system employs Ethereum-based smart contracts to automate vote casting and tallying while ensuring voter privacy through zero-knowledge proofs. Decentralized Identity (DID) is integrated for secure authentication, preventing double voting and identity fraud. The paper discusses system architecture, security considerations, scalability challenges, and real-world applications of blockchain voting, highlighting how Web3 can transform democratic elections.
Henrique Hepp, Murilo V. G. da Silva, Leandro M. Zatesko
The complexity class of the problems that can be solved by a quantum algorithm in a non-adaptive collapse-free model is called naCQP. This class was introduced in 2016 by Aaronson et al. intended to be a slightly larger class than BQP: larger enough to include important NP-intermediate candidate problems, but likely not to include NP-complete problems. Aaronson et al. (2016) showed that there is an oracle A for which NPA ⊈ naCQPA; and Hepp et al. (2025) showed that relative to an oracle A chosen uniformly at random, (UP ∩ coUP)A ⊈ naCQPA with probability 1, being UP ∩ coUP a subclass of NP. Amongst the NP-intermediate candidate problems in naCQP is the entire class SZK, of the problems that admit a statistical zero-knowledge interactive proof system. The relation between QSZK, which is the class of the problems that admit a quantum zero-knowledge interactive proof system, and naCQP is unknown, with some believing that there is an oracle A for which QSZKA ⊈ naCQPA. A promise problem complete for QSZK is the trace distance distinguishability of mixed quantum states. We show that this problem, when restricted to pure quantum states, is in naCQP.
The breakneck pace of digital transformation in sectors around the world have driven developments in cybersecurity, AI and cloud technology. But with great progress comes great responsibility, and with generating such evolution it gives rise to lots of issues when it comes to data privacy, system to system connectivity, leveraging knowledge and infrastructure scalability. This paper provides an integrated solution that can be harnessed to secure, operate and make digital ecosystems more agile, by amalgamating present day practices and technologies that many organizations face in their current environments across security, operation and agility when it comes to digitalization. It covers proactive cybersecurity approaches like DevSecOps and Zero Trust Architecture, AI based intelligent threat analysis and real-time automation, and cloud-native and edge computing models for scalable and resilient infrastructure. The study at the same time showcases advancements in data processing and encryption, legal compliance, providing enterprises with a roadmap toward safer, AI-infused and cloud supported infrastructure. By bringing these columns together, the research offers strategic recommendations for businesses wishing to future-proof their digital business as they negotiate an ever more volatile and risk-filled technology environment.
Open access
Economic and Technological Systems Analysis
Advanced Research in Systems and Signal Processing
The cryptographic protocol developments are transforming digital trust is the capacity to verify without revealing any underlying information. Traditional authentication and authorization systems are usually prone to leakage of sensitive data, resulting in compromise of privacy and low scalability in distributed systems. The root of these problems is eliminated through the so-called zero-knowledge techniques that allow demonstrating to one party ownership of some information without exposing it. This paper explores the origin and development of zero-knowledge protocols in light of its efficiency, trustless design, and privacy focus to illustrate why the application is worth the hype. Particular attention is paid to such structures as zk-SNARKs, zk-STARKs, and bulletproofs, as well as their application to constructing transparent, scalable systems. Blockchain aptitudes used anywhere in confidentiality of transactions, decentralized identity systems allow a self-sovereign identity without exaggerating personal information, and the healthcare and finance industries enjoy the ability to share information securely without any effect on compliance aspects. The next discussion points are implementations, the scalability issue, cryptographic assumptions, and integration issues. This survey outlines evaluations of deployments from 2021 to 2025 to determine the following top benefits, barriers, and trends in building systems that safeguard privacy without compromising their performance or trust to the client. Future requirement conclusions provide some insights about future requirements in terms of efficient construction of proofs, standardizations, and ease of usability to expand the adoption of infrastructures built on zero-knowledge into a constantly more integrated digital world.
Preet Deepankumar Vyas, Devang Dhorada, Kevin Bhanderi, Akshaybhai J. Patel · 9 authors
In order to protect the ocean ecosystem, the pursuit of sustainable and self-powered photodetectors is critical for revolutionizing underwater optical communication (UOC) used for environmental hazard sensing. This step enables energy-efficient and real-time detection of marine ecosystem threats such as chemical contamination, oil spill, and eutrophication. Although layered metal dichalcogenides (LMDCs) with exceptional optoelectronic properties and chemical stability are the most suitable materials, their integration into UOC technology remains largely unexplored. To address this, the present study demonstrates and evaluates seawater-immersed photoelectrochemical photodetectors (PEC-PDs) based on SnSe<sub>2</sub>, an emerging member from the LMDC family. Direct vapor transport-grown SnSe<sub>2</sub> is well characterized in its thin-film form by X-ray diffraction, X-ray photoelectron spectroscopy, scanning electron microscopy, atomic force microscopy, Raman spectroscopy, and PL spectroscopy, followed by utilization as photoelectrodes in the PEC-PD devices. Fabricated PEC-PDs exhibit a responsivity of 505.74 ± 4.65 μA/W at zero bias and 10.34 ± 0.16 mA/W at 0.4 V bias; they outperform conventional Na<sub>2</sub>SO<sub>4</sub>-based devices by 21-fold and 82-fold, respectively. To the best of our knowledge, this is the first report presenting an SnSe<sub>2</sub>-based PEC-PD utilizing seawater electrolyte and its performance evaluation. A proof-of-concept UOC demonstration of the present study paves the way toward the next-generation green optoelectronic devices for self-sustainable marine technologies.
Существующие типовые модели аутентификации с использованием цифровых удостоверений носят абстрактный характер. Для конкретизации модели аутентификации с использованием цифровых удостоверений предлагаются: алгоритм эмиссии цифровых удостоверений; алгоритм аутентификации на основе доказательства с нулевым разглашением. Производится количественная оценка раскрытых данных удостоверений в результате: предложенного алгоритма аутентификации на основе доказательства с нулевым разглашением; аутентификации с полным раскрытием атрибутов; аутентификации с частичным раскрытием атрибутов. Полученные результаты оценок анализируются и делаются соответствующие выводы. Existing standard authentication models using digital credentials tend to be abstract. To refine the authentication model using digital credentials, the following are proposed: a digital credential issuance algorithm and an authentication algorithm based on zero-knowledge proof. A quantitative assessment is conducted on the amount of disclosed credential data resulting from the proposed zero-knowledge proof-based authentication algorithm, authentication with full attribute disclosure, and authentication with partial attribute disclosure. The assessment results are analyzed, and relevant conclusions are drawn.
Account-based anonymous blockchain systems can provide robust privacy protection for users. However, they become highly inefficient when handling high-frequency micro-payment scenarios. This paper presents systematic optimizations for batch processing and micro-payment transactions in account-based anonymous blockchain systems to enhance both privacy and efficiency. Building on BlockMaze, the first account-based anonymous blockchain system fully protecting transaction privacy, we propose innovations in batch transfers, batch receipts, and micro-payment handling. By reducing redundant data, improving circuit design, and optimizing zk-SNARK proof generation, we achieve up to 55.90% and 23.02% reductions in overall time consumption for batch transfers and receipts, respectively, significantly cutting computational cost and memory use. For micro-payments, a solution encapsulating the payment deadline reduces transaction delays and fund freezing. Experimental results show only slight increases in proof generation time—1.41 seconds for transfers and 1.02 seconds for payments—while maintaining privacy protection. This research lays a foundation for practical applications of account-based anonymous blockchain systems, enhancing privacy, processing efficiency, and transferability to other systems. • Optimized batch processing and improve transaction efficiency in account-based anonymous blockchain systems. • Optimized circuit design reduces redundant data and shortens zero-knowledge proof times. • Time consumption decreased by up to 55.90% in batch transfer function and 23.02% in batch receipt function. • Highly transferable to other account-based anonymous blockchain systems, offering strong flexibility and application potential. • Offers future research directions to improve blockchain efficiency and privacy protection.
Open access
Blockchain Technology Applications and Security
Advanced Steganography and Watermarking Techniques
Daniel Commey, Benjamin Appiah, Griffith Selorm Klogo, Garth V. Crosby
Federated Learning (FL) enables collaborative model training on decentralized data without exposing raw data. However, the evaluation phase in FL may leak sensitive information through shared performance metrics. In this paper, we propose a novel protocol that incorporates Zero-Knowledge Proofs (ZKPs) to enable privacy-preserving and verifiable evaluation for FL. Instead of revealing raw loss values, clients generate a succinct proof asserting that their local loss is below a predefined threshold. Our approach is implemented without reliance on external APIs, using self-contained modules for federated learning simulation, ZKP circuit design, and experimental evaluation on both the MNIST and Human Activity Recognition (HAR) datasets. We focus on a threshold-based proof for a simple Convolutional Neural Network (CNN) model (for MNIST) and a multi-layer perceptron (MLP) model (for HAR), and evaluate the approach in terms of computational overhead, communication cost, and verifiability.
Abstract: This research paper explores the design and implementation of scalable blockchain protocols to enable a trustless digital society through decentralized finance (DeFi), governance, and secure digital identity frameworks. Motivated by the growing demand for transparency, autonomy, and data sovereignty in digital systems, this research introduces a hybrid protocol combining Proof of Stake (PoS) consensus with Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs). The study develops a theoretical mathematical framework and conducts extensive simulation-based evaluations using standardized metrics such as transaction throughput, AUC-ROC, RMSE, and nDCG. Comparative analysis against baseline architectures—Ethereum 1.0, Hyperledger, and Polkadot—demonstrates that the proposed zk-PoS protocol significantly improves throughput, reduces latency, and enhances identity verification accuracy. Regression and predictive modeling further confirm the system's scalability and reliability under varied network conditions. Forecasting models predict an increase in secure identity match rates over time, underscoring the protocol’s adaptability to real-world decentralized applications. The implications of this work are multifold: it advances blockchain scalability theories, lays a foundation for decentralized identity systems, and provides practical insights for deploying trustless governance and financial platforms. These contributions are pivotal for transitioning toward a decentralized, inclusive, and tamper-resistant digital ecosystem. Keywords: blockchain scalability, decentralized finance, trustless systems, zk-SNARKs, Proof of Stake, secure digital identity, decentralized governance, identity verification, blockchain protocols, cryptographic consensus
The digitization of democratic processes promises greater accessibility but presents challenges in terms of security, privacy, and verifiability. Existing electronic voting systems often rely on centralized architectures, creating single points of failure and forcing too much trust in authorities, which contradicts democratic principles. This research addresses the challenge of creating a secure, private e-voting system with minimized trust dependencies designed for the most versatile personal device: the smartphone. We introduce SmartphoneDemocracy, a novel e-voting protocol that combines three key technologies: the emerging European Digital Identity (EUDI) Wallet for Sybil-resistant identity verification, Zero-Knowledge Proofs for privacy-preserving validation, and a peer-to-peer blockchain (TrustChain) for a resilient, serverless public bulletin board. Our protocol enables voters to register and cast ballots anonymously and verifiably directly from their smartphones. We provide a detailed protocol design, a security analysis against a defined threat model, and a performance evaluation demonstrating that the computational and network overhead is feasible for medium- to large-scale elections. By developing and prototyping this system, we demonstrate a viable path to empower citizens with a trustworthy, accessible, and user-controlled digital voting experience.