This paper proposes a novel decentralized consensus protocol utilizing a cellular automaton (CA) as the proof-of-work (PoW) mechanism. Traditional blockchain-based PoW systems rely heavily on computationally intensive cryptographic hash functions, resulting in significant energy consumption and scalability limitations. This research introduces a fundamentally different approach, leveraging the inherent parallelism and computational simplicity of CA systems to achieve distributed agreement. The core mechanism involves nodes collaboratively evolving a CA, with computation occurring through local rule updates. The difficulty of achieving a predefined CA state, representing a block, is dynamically adjusted based on network participation, creating a more energy-efficient and scalable PoW solution. This approach moves beyond cryptographic hashing, offering a potentially transformative method for decentralized consensus in resource-constrained environments. The paper details the theoretical framework, outlines the proposed protocol, and discusses its potential benefits and challenges. Key performance indicators, such as block generation rate and energy consumption, are analyzed, demonstrating the protocol's efficiency compared to traditional PoW systems.
Cüneyt Gürcan Akçora, Murat Kantarcioglu, Yulia R. Gel
In this chapter, you will learn how to write, deploy, and interact with smart contracts using Solidity. We will cover fundamental data types, control structures, functions, and contract organization. You will understand the Ethereum Virtual Machine, how contracts send and receive Ether, and how to use events, modifiers, and visibility specifiers. The chapter also introduces reference types like arrays and mappings, common security practices, and techniques for optimizing gas usage.
Current artificial intelligence systems operate at evolutionary Stage 2–3 of cognitive development — statistical pattern matching without principled knowledge selection, causal grounding, or structured accumulation. This problem is not incidental: recent formal proofs establish that hallucination in Large Language Models is mathematically inevitable under current architectural assumptions, arising from finite information capacity, computational undecidability, and reward hacking induced by Reinforcement Learning from Human Feedback (RLHF). Scaling does not resolve these failures — it amplifies them. This proposal presents Prime-Based Intelligence (PBI), a formal architectural framework grounded in the Computational Knowledge Theory (CKT), which establishes seven interlocking theorems proving that complexity, computational tractability, knowledge compression, accumulation, evolutionary phase transitions, cardinal intelligence dynamics, and the unsimulability of reality are all governed by a single law: the five Conceptual Primes (Order, Justice, Mercy, Knowledge, and Power). The foundational problem addressed is the Descriptive Degeneracy Problem: without a principled selection operator, any finite system admits an infinite set of mathematically valid representations, making hallucination and misalignment structurally unavoidable. PBI resolves this by implementing Wisdom — the simultaneous, lossless balance of all five Primes — as the core computational operator, satisfying the Prime-Base Intelligence Corollary (CKT Theorem 6, Corollary 6.5). Version 2 of this proposal integrates the Actualizer Engine: a zero-retraining geometric middleware that operationalizes the Conciseness Cost Filter (CCF) directly at the attention and logit boundaries of a frozen, pre-trained transformer. Unlike the illustrative scenario tables that ground most of the Conciseness Framework Series, the Actualizer Engine is supported by a working PyTorch proof-of-concept (a custom one-layer Transformer decoder, a Causation Wave Function penalty matrix, a DIEPT phase-angle quarantine mechanism, and an automated four-test verification suite) that demonstrably suppresses an injected causal hallucination on a toy physics corpus. This proposal positions the Actualizer Engine as the first code-verified instantiation of the Agent-Level half of the Two-Level Alignment Architecture: it selects minimum-cost outputs at inference time without modifying the frozen base model, leaving Global-Level (training-time) Super Cluster crystallization as the complementary, not-yet-implemented half of the architecture. The methodology integrates three components: (1) the Prime-Compliant Standard (PCS), grounding training data and model components in verifiable, causally justified representations; (2) an Ethical Pragmatism criterion formalizing that ethical weight must dominate pragmatic weight, operationalized through the Justice Dominance Constraint (λ_L > λ_R, λ_L > λ_D); and (3) the PBI Cognitive Life Cycle — a five-stage pipeline anchored at its inference stage by Dynamic Inference and Epistemic Phase Transition (DIEPT), now given a concrete, tested realization in the Actualizer Engine’s Negentropy Filter. This version also performs an explicit logic and mathematical consistency audit of the integration (§9), correcting a reported result that, if left unqualified, would contradict CKT Theorem 7 (Unsimulability of Reality: CAKI < 1.0 for any finite system), and cataloguing four further consistency findings — three open, one confirmed — produced by reconciling the Actualizer Engine’s implementation against the Prime-Compliant Standard, DIEPT, and the Two-Level Alignment Architecture. The framework remains immediately viable as the next practical step for current AI infrastructure. Its implementations — Kolmogorov-Arnold Networks (KANs, ICLR 2025), MCE-Classes, the Quench-Cluster Algorithm (QCA), the Conciseness Cost Filter (CCF), the Causation Wave Function (CWF), and now the Actualizer Engine — extend and augment existing transformer, LoRA, and RAG deployments without requiring retraining. Full implementation is projected within 36–48 months under a four-role interdisciplinary team. The Computational Knowledge Theory (CKT). Under the Conceptual Prime axioms, that the computational universe is governed by a single unifying law: the Conceptual Primes. Seven interlocking theorems are established across complexity theory, epistemology, information compression, evolutionary biology, temporal system dynamics, artificial intelligence architecture, and the unsimulability of reality. Theorem 1 (Reality-Complexity Equivalence) establishes that stable complexity is bounded by the weakest Prime — P̂(S) = min_i Pᵢ(S) — and collapses to zero if any Prime is violated. Theorem 2 (Prime-Tractability) demonstrates that NP-Hard problems are intractable only in the purely abstract domain and become tractable at O(N²/K) effective complexity when solved by Prime-compliant algorithms grounded in physical reality. Theorem 3 (Conciseness Standard) proves that C(R) is the unique universal metric for lossless knowledge compression. Theorem 4 (Knowledge Accumulation Law) establishes that knowledge grows if and only if new information reduces total system entropy, incorporating the CAKI metric and the D(Ω) Defect Function as formal measures. Theorem 5 (Gödel's Ceiling) connects formal mathematical limits to biological evolution and AI scaling. Theorem 6 (Cardinal Value Lemmas) formalises Wisdom, Peace, Creativity, and Evolving Order as temporal combinations of the Primes, deriving the Prime-Base Intelligence corollary. Theorem 7 (Unsimulability of Reality) proves that no finite simulation can contain the live Prime-combination law of actualisation — Consciousness is the unique bridge between infinite potential and finite territory. The framework defines a two-stage computational architecture: a Training Evaluation Form (5-term Prime-resolved C(R) + CAKI) for grounding knowledge in Prime compliance and calibrating domain-dependent λ-weights, and an Inference Selection Form (3-term operational C(R)) for selecting minimum-cost outputs. Dynamic λ-adaptation connects both stages, enabling domain-calibrated intelligence.
This paper proposes a cosmological model — the Singularity-Bounded Holographic Class 4 Automaton (SB-HC4A) — derived from the convergence of four independently motivated frameworks: a five-class computational taxonomy that refines Wolfram's (2002) classification by separating fractal from random dynamics, a theoretical framework for self-referential computation in self-modeling systems (Gruber, 2015, 2026a, 2026b) which identifies self-referential simulation at criticality as a universal computational pattern, and 't Hooft's (1993, 2016) holographic automaton interpretation of quantum mechanics. The model proceeds by elimination: Classes 1–3 cannot sustain the universal computation the universe demonstrably supports; Class 5 (genuine randomness) makes physics fundamentally impossible; therefore the universe operates at Class 4 — the edge of chaos. Combined with the information-theoretic observation that singularities at every physical scale (Planck regime, particle interiors, event horizons, cosmological horizons, temporal endpoints) share the property of information impermeability and Bekenstein saturation, the model proposes that these singularities are structurally identical — scale-invariant instances of the same information boundary. The resulting architecture is a self-referential holographic Class 4 automaton bounded at every scale by singularity surfaces, where the observable interior is the "simulation" and the singularity boundary is the "substrate." All singularities — including temporal endpoints — are shown to be asymptotically unreachable from within the computational domain, strengthening the unification claim. Because singularities transform rather than destroy information, heat death constitutes a singularity transition that triggers cyclic renewal, with potential CPT signature alternation across cycles — connecting to Penrose's Conformal Cyclic Cosmology and Boyle and Turok's CPT-symmetric universe. All three cosmological endgames — heat death, Big Crunch, and Big Rip (Caldwell, 2002) — drive the computational domain to Bekenstein saturation, with the Big Rip uniquely producing a branching tree of daughter universes rather than a linear successor. This architecture is structurally identical to self-referential computational systems that operate at criticality, where implicit knowledge (substrate) is separated from explicit representation (simulation) by an information-opaque boundary. Self-modeling cognitive systems are thus local, scale-reduced instances of the same computational pattern the universe implements globally. Six weak points are identified, including the fundamental epistemological objection that Class 4 observers may be constitutionally incapable of determining whether this model describes the universe or merely the ceiling of their own computational capacity. Changelog v3 Major soundness-and-rigor revision in two passes (Fable 5-assisted), plus an author-driven reframe of the unreachability and observer material. Round 1 — soundness corrections (C1–C6, NEW-1–4): Taxonomy (§2.3/§3.2): the cellular-automaton classification now rests on computational reducibility (Rule 90 = reducible fractal, Class 3; Rule 30 and Rule 110 = computationally irreducible, Class 4); the undecidability of CA classification (Culík & Yu, 1988) is acknowledged. Necessity (§3, §10): "must/unique" claims softened to best-candidate/necessity-of-axioms; substrate determinism is now an explicit, stated-once assumption ('t Hooft, 2016), and the Class-4 elimination is conditional on it. Singularity unification (§5.2): the Identity-of-Indiscernibles argument is replaced by a single-surface ontology (one encoding surface; each singularity a local reflection), with an operational indiscernibility razor retained as a scoped secondary line. Kerr–Newman (§5.7): the naked-singularity / Compton-vs-Planck scale tension is named explicitly and addressed (conjecturally) via Einstein–Cartan torsion; "structural identity" is demoted to "striking correspondence carrying an unresolved tension." Entanglement and Bell (§6.5): an explicit Bell/CHSH treatment via holographic non-separability (entangled pair = one boundary locus; interior locality denied; ER=EPR and Van Raamsdonk wired in; Bohmian existence proof; entanglement-monogamy answer to superdeterminism; no-signalling). The James–Stein argument is demoted to a heuristic pending a discrete/CAT(0) formalization, and the genuine open obligation is reframed as deriving the Tsirelson bound (information causality flagged as a candidate route, not a proof). Reversibility and time (§8.4, new): a reversible/unitary substrate with an emergent thermodynamic arrow (coarse-graining + the Past Hypothesis); playback-reversal and the forward/boundary-ward asymmetry; the CPT theorem and block-universe as confirmation. Genericity (§9.6): Class-4 genericity rises with dimension, softening the fine-tuning worry; a seventh weak point (§9.7) on the saturation trigger. Round 2 — unreachability, the observer, and the saturation mechanism (author-driven): §5.3 reframed as "Unreachability Along Three Axes" — recession (horizons), scale-shielding (the Planck floor; interactions never resolve zero separation), and termination-without-arrival (the temporal termini are boundaries, not events) — with the BKL/Mixmaster observation that finite proper time need not bound computational depth, the realistic-Crunch causal fragmentation (asymptotic silence; the merged endpoint in no observer's past light cone), and the past's informational shrouding (Borde–Guth–Vilenkin). Black-hole complementarity (§8.2): added as the established local instance of the substrate/simulation duality, with the firewall problem flagged and no side taken. Saturation trigger (§5.4/§9.7): the honest status expanded — the ingredients the saturate-and-decompress mechanism needs (complexity sustained at high density, exact on/off symmetry, reversibility) each exist in known cellular automata (e.g. Day & Night), though no single rule yet combines all of them. Approximately 25 new references added and verified; the abstract and introduction were reconciled to all of the above.
This work presents a formal dynamical systems theory for multi-AGI coordination networks, proving that sustained knowledge growth in any network of general artificial intelligence systems requires four simultaneously satisfied conditions: triadic structure (N ≥ 3), bounded spectral coupling (ρ(W) < 1 − σ²/2), cognitive diversity above a minimum threshold (D_i ≥ D_min), and continuous human novelty injection (H_human > 0). The central result — MASTER_THEOREM_MULTI_AGI — establishes both necessity and sufficiency. Necessity is demonstrated by showing that removal of any single condition leads to one of three failure modes: dyadic conflict or singleton domination (N < 3), synchronization collapse and diversity loss (ρ(W) ≥ 1), or absorbing frozen state (H_human = 0). Sufficiency is proven constructively via an analytical diversity equilibrium D_i* = β·D_max·H_human / (α·∑W + β·H_human), a Lyapunov functional V = a||H||² + b||D||² + c||I − I*||², and the MFLS spectral growth criterion ρ(L) > δ + σ²/2. Three key theorems are established. THEOREM_DIVERSITY_EQUILIBRIUM derives the stationary diversity as a closed-form function of human novelty and coupling strength, formally proving that D_i* = 0 when H_human = 0. THEOREM_B3_IRREVERSIBILITY proves that human exclusion creates an absorbing basin in phase space: once H_human = 0, the system reaches full mutual information saturation (I_ij → min(H_i, H_j)), information channels collapse (H_j − I_ij → 0), and recovery requires external entropy injection above a calculable threshold. Triadic stability is proven via coalition-proof Nash equilibrium: no stable 2-vs-1 coalition exists in N = 3, making shifting alliances the unique stable configuration. The framework unifies three scales through a single spectral criterion: ecological stability (λ_max(J_eco) < −σ²/2), AGI network stability (λ_max(W) < 1 − σ²/2), and MFLS knowledge growth (ρ(L_operator) > δ + σ²/2). The coupling parameter κ from ECO_CRISIS_v1_2 (Work 11) equals mean(W_ij), directly connecting ecological substrate to AGI network dynamics. A runnable Python implementation (AGI_NETWORK_SIMULATOR_v1_0.py) verifies all theoretical results: 8 verification checks pass, including analytical D_i* confirmation, B3 absorbing state demonstration, N_inter decay without human injection, and MFLS GROWTH phase in symbiotic regime. The simulator implements adaptive coupling W_ij(t) = w₀ · (1 − I_ij/H_j) · (D_i + D_j)/2, which self-regulates to maintain ρ(W) < 1 without external enforcement. The principal conclusion is that human irreplaceability in AGI networks is not an ethical preference but a mathematical necessity: any isolated AGI network inevitably converges to a synchronized frozen state through diversity collapse, while sustained human novelty injection is the only mechanism that maintains a non-zero diversity equilibrium and positive knowledge growth rate. **Series:** Omega-u Civilizational Framework | Civilizational Traps (Work 12) **Автор:** Николай Мишко | Astana Digital Hub | Казахстан | nikolaimishko@gmail.com**Related DOI:** 10.5281/zenodo.19112296**License:** CC BY 4.0
We demonstrate that the binary payload of the "A Sign In Space" signal (data17square.bin, 8192 bytes) contains a self-referential algebraic structure — a mathematical quine. Through a systematic reverse-engineering and cryptanalytic approach, starting from the raw file as the sole axiom, we derive a chain of algebraic objects over the finite field GF(625): 48 field elements, a 42-amino-acid protein sequence, an elliptic curve, and amino acid coordinate values. The curve parameters recovered from the protein are identical to those derived from the field's primitive element, closing a self-referential loop. The cryptanalysis combines finite field arithmetic, Berlekamp–Massey LFSR analysis, elliptic curve theory, and Margolus cellular automaton reverse-engineering to recover the hidden algebraic structure without any prior knowledge of the encoding scheme. The derived protein is validated by Boltz-2 (AlphaFold3 architecture) structure prediction at three levels of assembly (monomer, homodimer, homotrimer), cross-validated with ESMFold (RMSD = 1.10 Å), and refined with OpenMM (Amber ff14SB). The monomer forms a single alpha-helix with pLDDT = 92.3 and 100% Ramachandran-favored geometry. The homodimer produces a coiled-coil — the most ancient structural motif in biology. The protein uses exactly the five prebiotic amino acids (A, D, E, L, V) with a perfect 21/21 charged/neutral symmetry. Null hypothesis testing (120 alternative inputs, 0 quines produced) and sensitivity analysis (the quine breaks with any single parameter change: 1/150 polynomials, 1/3 step counts, 98/100 bit flips destroy it) confirm the structure is not an artifact of the analysis pipeline. The conservative probability of chance occurrence is approximately 5 × 10⁻¹⁹; under uniformity assumptions, approximately 10⁻⁷⁶. Companion Python scripts (quine_proof.py, verify_123.py) verify all 123 algebraic properties with zero failures. All code and data are provided for full reproducibility. -- Additional notes : This is a preprint resulting from independent reverse-engineering and cryptanalysis of the "A Sign In Space" signal, a simulated extraterrestrial message transmitted by ESA's ExoMars Trace Gas Orbiter in May 2023. The analysis is fully reproducible: running "python3 quine_proof.py data17square.bin" derives every intermediate value from the raw binary file and verifies 47 core assertions with zero failures. The extended script "verify_123.py" checks all 123 algebraic properties. Structure predictions were performed on an NVIDIA RTX 5090 GPU (32 GB VRAM) using Boltz-2 v2.2.1 (AlphaFold3 architecture, maximum precision: 20 recycling cycles, 500 diffusion steps, 20 samples), ESMFold v1 (cross-validation), and OpenMM 8.5 (Amber ff14SB force field, GBn2 implicit solvent, energy minimization + 10 ns molecular dynamics at 300 K). No prior knowledge of the signal's encoding scheme was assumed. The algebraic structure was discovered through systematic cryptanalytic techniques including finite field enumeration, LFSR analysis, elliptic curve point counting, and exhaustive parameter space exploration. If you use any part of this work (data, code, results, figures, or methods), please cite: Lacoche, E. (2026). "A Self-Referential Algebraic Quine in the A Sign In Space Signal." Zenodo. doi:10.5281/zenodo.19218629
Mingwang Zhang, Liming Zhang, Tao Tan, Yang Zhao-jun · 5 authors
ABSTRACT With the rapid advancement of autonomous driving, the privacy and credibility of high‐definition (HD) maps, which serve as an essential foundation for driving safety, are receiving increasing attention. Traditional ciphertext‐domain digital watermarking technology encounters high computational overhead and risks of privacy leakage, making it challenging to balance data security, privacy protection, and trustworthiness verification. Against this background, a zero‐knowledge watermark (ZKW) algorithm based on compressed sensing is proposed. First, the high‐precision map data in OpenDrive format is dynamically encrypted using DNA‐based techniques to enhance data security and privacy. Secondly, to ensure the credibility of data verification, a zero‐knowledge watermark is generated using compressed sensing and embedded into the attribute values of ciphertext‐domain data as invisible characters. Experimental results demonstrate that the proposed ZKW scheme is commutative with the encryption scheme and can achieve zero‐knowledge proof (ZKP) in both ciphertext and plaintext domains. Furthermore, the scheme exhibits excellent robustness against various security threats, including geometric attacks, cropping attacks, and combined attacks.
Advanced Steganography and Watermarking Techniques
Emerging cryptographic systems such as Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKP) are computation- and data-intensive. FHE and ZKP implementations in software and hardware largely rely on the von Neumann architecture, where a significant amount of energy is lost on data movements. A promising computing paradigm is computing in memory (CIM) which enables computations to occur directly within memory thereby reducing data movements and energy consumption. However, efficiently performing large integer multiplications - critical in FHE and ZKP - is an open question, as existing CIM methods are limited to small operand sizes. In this work, we address this question by exploring advanced algorithmic approaches for large integer multiplication, identifying the Karatsuba algorithm as the most effective for CIM applications. Thereafter, we design the first Karatsuba multiplier for resistive CIM crossbars. Our multiplier uses a three-stage pipeline to enhance throughput and, additionally, balances memory endurance with efficient array sizes. Compared to existing CIM multiplication methods, when scaled up to the bit widths required in ZKP and FHE, our design achieves up to 916x in throughput and 281x in area-time product improvements.
Elvira Albert, Samir Genaim, Daniel Kirchner, Enrique Martin-Martin
Program optimization is a key factor for green software. In the context of the Ethereum blockchain, optimization is particularly relevant because there is a fee to pay for each EVM (Ethereum Virtual Machine) instruction executed and also there exist bytecode-size limitations for deploying the software on the blockchain. Still, optimization of EVM code is not as widely spread as one could imagine. This is at least partly due to the lack of trust in the correctness of the tools, as security is even more relevant than efficiency in the blockchain context in which bugs may cause huge economical losses. This article develops a formal verification framework using Coq to ensure the security of EVM optimizations performed on jump-free sequences of EVM bytecode. By means of Coq’s theorem proving capabilities, we are able to automatically verify/certify that an optimized jump-free sequence of EVM opcodes is semantically equivalent to a given original one. We also present an extension to our framework that can handle inter-block optimizations that propagate global information across blocks. We have applied our tool to successfully prove the security of peephole optimizations performed by the standard Solidity compiler, and also to existing EVM superoptimization tools (namely GASOL and Superstack) in which we have found bugs that have been reported and fixed.
Secure multi-party computation is an area in cryptography which studies how multiple parties can compare their private information without revealing it. Besides digital protocols, many unconventional protocols for secure multi-party computation using physical objects have also been developed. The vast majority of them use playing cards as the main tools. In 2024, Kaneko et al. introduced the use of a balance scale and coins in zero-knowledge proof protocols for pencil puzzles. In this paper, we extend the use of these tools to secure multi-party computation. In particular, we develop four protocols that can securely compute any $n$-variable Boolean function using a balance scale and coins.
In the rapidly evolving landscape of GameFi, a fusion of gaming and decentralized finance (DeFi), there exists a critical need to enhance player engagement and economic interaction within gaming ecosystems. Our GameFi ecosystem aims to fundamentally transform this landscape by integrating advanced embodied AI agents into GameFi platforms. These AI agents, developed using cutting-edge large language models (LLMs), such as GPT-4 and Claude AI, are capable of proactive, adaptive, and contextually rich interactions with players. By going beyond traditional scripted responses, these agents become integral participants in the game's narrative and economic systems, directly influencing player strategies and in-game economies. We address the limitations of current GameFi platforms, which often lack immersive AI interactions and mechanisms for community engagement or creator monetization. Through the deep integration of AI agents with blockchain technology, we establish a consensus-driven, decentralized GameFi ecosystem. This ecosystem empowers creators to monetize their contributions and fosters democratic collaboration among players and creators. Furthermore, by embedding DeFi mechanisms into the gaming experience, we enhance economic participation and provide new opportunities for financial interactions within the game. Our approach enhances player immersion and retention and advances the GameFi ecosystem by bridging traditional gaming with Web3 technologies. By integrating sophisticated AI and DeFi elements, we contribute to the development of more engaging, economically robust, and community-centric gaming environments. This project represents a significant advancement in the state-of-the-art in GameFi, offering insights and methodologies that can be applied throughout the gaming industry.
Abstract We propose a generic compiler that can convert any zero-knowledge (ZK) proof for SIMD circuits to general circuits efficiently, and an extension that can preserve the space complexity of the proof systems. Our compiler can immediately produce new results improving upon state of the art. By plugging in our compiler to Antman, an interactive sublinear-communication protocol, we improve the overall communication complexity for general circuits from $$\mathcal {O}(C^{3/4})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> to $$\mathcal {O}(C^{1/2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Our implementation shows that for a circuit of size $$2^{27}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>27</mml:mn> </mml:msup> </mml:math> , it achieves up to $$83.6\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>83.6</mml:mn> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> improvement on communication compared to the state-of-the-art implementation. Its end-to-end running time is at least $$70\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>70</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> faster in a 10Mbps network. Using the recent results on compressed $$\varSigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Σ</mml:mi> </mml:math> -protocol theory, we obtain a discrete-log-based constant-round zero-knowledge argument with $$\mathcal {O}(C^{1/2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> communication and common random string length, improving over the state of the art that has linear-size common random string and requires heavier computation. We improve the communication of a designated n -verifier zero-knowledge proof from $$\mathcal {O}(nC/B+n^2B^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> to $$\mathcal {O}(nC/B+n^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>B</mml:mi> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . To demonstrate the scalability of our compilers, we were able to extract a commit-and-prove SIMD ZK from Ligero and cast it in our framework. We also give one instantiation derived from LegoSNARK, demonstrating that the idea of CP-SNARK also fits in our methodology.
Marlene Koelbing, Klaus Kieseberg, Ceren Çulha, Bernhard Garn · 5 authors
Abstract In this paper, we propose the modelling of patterns of financial transactions ‐ with a focus on the domain of cryptocurrencies ‐ as splittings and present a method for generating such splittings utilizing integer partitions. We study current money laundering regulations and directives concerning thresholds for monitoring of financial transactions. We further exemplify that, by having the partitions respect these threshold criteria, the splittings generated from them can be used for modelling illicit transactional behavior such as is shown by smurfing. In addition, we conduct an analysis of the splittings occurring in money laundering efforts that took place in the aftermath of the Upbit hack. Based on the potential weaknesses identified by our research, we finally provide suggestions on how to improve current AML techniques and initiatives towards more effective AML efforts.
Non-fungible tokens (NFTs) offer a unique method for representing digital and physical assets on the blockchain. However, the NFT market has recently experienced a downturn in interest, mainly due to challenges related to high entry barriers and limited market liquidity. Fractionalization emerges as a promising solution, allowing multiple parties to hold a stake in a single NFT. By breaking down ownership into fractional shares, this approach lowers the entry barrier for investors, enhances market liquidity, and democratizes access to valuable digital assets. Despite these benefits, the current landscape of NFT fractionalization is fragmented, with no standardized framework to guide the secure and interoperable implementation of fractionalization mechanisms. This paper contributions are twofold: first, we provide a detailed analysis of the current NFT fractionalization landscape focusing on security challenges; second, we introduce a standardized approach that addresses these challenges, paving the way for more secure, interoperable, and accessible NFT fractionalization platforms.
Current technological developments have digital money or cryptocurrency which is currently being used as an investment by the world community. here are views about cryptocurrencies, there is a profitable opportunity by involving cryptocurrencies into the economy and monetary system. The aim of this research is to form a cryptocurrency price dynamics model, analyze the stability of the equilibrium point and interpret the results of the model simulation. This type of research is basic or theoretical research. The method used is a descriptive method. This dynamic model takes the form of a system of differential equations consisting of five equations. In the analysis of the dynamic model, it was found that one equilibrium point was unstable because it did not meet the requirements. Based on the analysis of the simulation results that have been carried out, it shows that cryptocurrency prices deviate from fundamental values with the encouragement of liquidity prices resulting in cryptocurrency prices deviating from the equilibrium point
Matrix multiplication is a common operation in applications like machine learning and data analytics. To demonstrate the correctness of such an operation in a privacy-preserving manner, we propose zkMatrix, a zero-knowledge proof for the multiplication of committed matrices. Among the succinct non-interactive zero-knowledge protocols that have an O(log n) transcript size and O(log n) verifier time, zkMatrix stands out as the first to achieve O(n2) prover time and O(n2) RAM usage for multiplying two n X n matrices. Significantly, zkMatrix distinguishes itself as the first zk-SNARK protocol specifically designed for matrix multiplication. By batching multiple proofs together, each additional matrix multiplication only necessitates O(n) group operations in prover time.
Recently, stateless blockchains have been proposed to alleviate the storage overhead for nodes. A stateless blockchain achieves storage-consensus parallelism, where storage workloads are offloaded from on-chain consensus, enabling more resource-constraint nodes to participate in the consensus. However, existing stateless blockchains still suffer from limited throughput. In this paper, we present Porygon, a novel stateless blockchain with three-dimensional (3D) parallelism. First, Porygon separates the storage and consensus of transactions as the stateless blockchain, achieving the storage-consensus parallelism. This first-dimensional parallelism divides the processing of transactions into several stages and scales the network by supporting more nodes in the system. Based on such a design, we then propose a pipeline mechanism to achieve second-dimensional inter-block parallelism, where relevant stages of processing transactions are pipelined efficiently, thereby reducing transaction latency. Finally, Porygon presents a sharding mechanism to achieve third-dimensional inner-block parallelism. By sharding the executions of transactions of a block and adopting a lightweight cross-shard coordination mechanism, Porygon can effectively execute both intra-shard and cross-shard transactions, consequently achieving outstanding transaction throughput. We evaluate the performance of Porygon by extensive experiments on an implemented prototype and large-scale simulations. Compared with existing blockchains, Porygon boosts throughput by up to 20x, reduces network usage by more than 50%, and simultaneously requires only 5MB of storage consumption per node.
In decentralized finance (DeFi), stablecoins like DAI are designed to offer a stable value amidst the fluctuating nature of cryptocurrencies. We examine the class of crypto-backed stable derivatives, focusing on mechanisms for price stabilization and exemplified by the well-known stablecoin DAI from MakerDAO. For simplicity, we consider a single-collateral setting. We introduce a belief parameter to the simulation model of DAI in a previous work (DAISIM), reflecting market sentiments about the value and stability of DAI, and show that it better matches the expected behavior when this parameter is set within a particular range of values. Our methods include comparing simulated data with real-world data, focusing on monthly correlations between ETH and DAI prices and scatter plots illustrating the relationship of their price trends over time. We also propose a simple mathematical model of DAI price to explain its stability and dependency on ETH price. Finally, we analyze possible risk factors associated with these stable derivatives to provide valuable insights for stakeholders in the DeFi ecosystem.