Blockchain Papers

Maria Carannante, Oday Masoudi, Alessandro Mazzoccoli

No abstract is available for this record.

Bhabani Sankar Samantray, K Hemant Kumar Reddy

Abstract In the era of artificial intelligence, the AI-generated image (AIGI) market is an emerging sector that faces significant challenges related to ownership, privacy, and security. These issues, especially prevalent in NFT markets, can be effectively addressed by the integration of advanced technologies such as blockchain, the InterPlanetary File System (IPFS), and Quantum Key Distribution (QKD). This study proposes a comprehensive trading framework that incorporates state-of-the-art methodologies and algorithms to simulate the entire AI image trading process. For image generation, the framework utilises diffusion models (LCM-LoRA + SDXL) and Generative Adversarial Networks (GANs), employing LCM-LoRA and LCMScheduler from Stable Diffusion XL Base 1.0 to accelerate image generation and reduce inference steps. Implementation is carried out using PyTorch and the Diffusers library, running on a CUDA-enabled GPU. The generated images are securely stored in the distributed IPFS storage system, while decentralised trading is facilitated through integration with the Hyperledger MiniFab tool. The framework supports multiple trading mechanisms, including Blind English Sealed-Bid Auctions (BESEA), fixed-price auctions with a first-come, first-served (FCFS) model, Dutch auctions with royalty redistribution, and fractionalized auction trading. To ensure secure communication between buyers and sellers, the BB84 QKD protocol is employed to generate a shared secret key with information-theoretic security. The generated key is processed through key sifting to derive a symmetric key, which is zero-padded to the 256-bit length required by AES-256-CBC. It is then directly used as the encryption key to encrypt AI-generated images and their associated metadata before storage on IPFS. Experimental evaluation across four auction mechanisms and up to 250 NFTs shows the Dutch auction achieving the highest sales volume (up to 211 NFTs sold) and the Fractionalized auction the highest revenue ( 98,270). The IPFS storage maintains sub-0.75-second upload latency with 100% file verification success. Blockchain-layer benchmarking across 100–500 participants records mean chaincode latency ranging from approximately 22 to 53 seconds and throughput of 0.018–0.045 TPS.

Vaibhav Singh, Dr. Jogender

With the rapid expansion of digital communication and data storage, cybersecurity has become a critical concern for organizations and individuals. Cryptographic methods play a vital role in ensuring data confidentiality, integrity, and authentication. This study explores the mathematical foundations of encryption, blockchain security, and post-quantum cryptography. Traditional encryption methods such as symmetric and asymmetric encryption rely on number theory and complex mathematical problems like integer factorization and discrete logarithms. Blockchain security is reinforced by cryptographic hashing and digital signatures, ensuring tamper-proof transactions. However, the advent of quantum computing poses a significant threat to existing cryptographic protocols, necessitating the development of post-quantum cryptographic methods. This research provides an in-depth analysis of current cryptographic techniques, evaluates their effectiveness, and discusses future advancements in quantum-resistant cryptography.

Bilal El Issaoui

MRS‑AUTH is a novel authentication framework that achieves deniability even against an active verifier who may adaptively query candidate credentials both before and after receiving a challenge. Unlike ring signatures or zero‑knowledge proofs – where the prover holds a single secret witness that can be extracted under coercion – MRS‑AUTH exploits the multiplicative structure of linear Diophantine equations. Through recursive decomposition, it generates a Diophantine forest of exponentially many syntactically valid credential chains. The authentic chain is sampled uniformly from this forest and committed together with k‑1 indistinguishable aliases using a fixed‑shape Merkle tree with dummy leaves, eliminating structure‑ and length‑based side‑channel leakage. The Forest Symmetry Theorem proves that all chains are structurally information‑theoretically indistinguishable. However, the full index‑anonymity against an active verifier is computational and bounded in Theorem 6.6 by k · ε_SHA3 + ε_coll + negl(λ). For cryptographic scales N ∼ 10⁴², the Ehrhart‑based continuous‑volume approximation yields an effective entropy exceeding 371 bits, with a statistical distance to the perfect uniform distribution of Δ ≤ 2⁻¹³⁵ – well below the 128‑bit security threshold. Empirical validation via exact enumeration and a chi‑squared test (χ²/dof ≈ 0.985) confirms the uniformity. A constant‑time Rust implementation, leveraging the subtle and zeroize crates, exhibits an execution time of approximately 0.12 ms across four orders of magnitude of N, demonstrating practical deployability. The work also formalises the Active Verifier Game model, a new adversarial definition that quantitatively captures coercion resistance in a post‑quantum setting.

Rayaan Pasha

This paper presents a threshold-cryptographic architecture for reducing the risk of premature leakage of digital examination papers during the interval between question-paper finalization and examination administration. The proposed design separates the data path from the control path. Examination content is encrypted using a fresh AES-256-GCM key, while the key is protected through envelope encryption under a key-release service. The capability to release that key is distributed using (k,n)-Shamir secret sharing across independent custodians, preventing any single custodian from unilaterally authorizing early release. At the scheduled release time, a quorum-based time authority provides an independently attested timestamp. Once the required time quorum and custodian threshold are satisfied, the key-release service reconstructs its private key within an HSM boundary, unwraps the examination key, and derives recipient-specific keys for individual examination centers. These keys are separately wrapped under each center's registered public key, limiting the impact of a compromise at any single examination center. The paper presents an actor and trust model, an explicit adversary model, a step-by-step release protocol, a threat-to-control security analysis, and a qualitative comparison with physical custody, blockchain-anchored distribution, and time-lock-puzzle-based timed-release cryptography. It also explicitly discusses residual risks, including custodian collusion, post-decryption optical or physical exfiltration, hardware and supply-chain trust, and compromise of the time-authority quorum. The architecture is presented as a research design rather than a claim of unconditional leak prevention. Future work includes implementing a prototype, evaluating quantitative performance, replacing reconstruct-and-zeroize key handling with threshold decryption, evaluating post-quantum key-encapsulation mechanisms, and conducting a formal mechanized security proof.

E D Baymurzina, A S Simakova, V D Poroshina, V N Yurina

No abstract is available for this record.

Narendra Kumar Chahar, Arvind Dhaka, Amita Nandal, Vijay Kumar

Digital image steganography has evolved from traditional rule-based techniques to advanced data-driven frameworks enabled by deep learning. However, existing surveys remain fragmented, often focusing on limited aspects while overlooking emerging paradigms such as blockchain-integrated and quantum-based approaches. This paper presents a comprehensive and systematic review of digital image steganography following the PRISMA 2020 guidelines, covering studies published between January 2015 and April 2026 across six major scientific databases. From an initial pool of 26,539 records, 83 relevant studies were selected through a rigorous two-stage screening process. The review provides a unified analysis of steganographic techniques by examining five dimensions: structural evolution and taxonomy, algorithmic modifications and hybridisation, application domain mapping, integration of emerging technologies, and future research trends. Comparative evaluation indicates that deep learning-based methods achieve 18–23% higher steganalysis resistance than classical approaches, whereas classical methods retain a 5–8 dB PSNR advantage. The quantitative synthesis further confirms the inherent capacity–imperceptibility–security trilemma, wherein no reviewed technique simultaneously achieves $$\text {PSNR} > 42$$ dB, embedding capacity $$> 4$$ bpp, and detection error rate $$> 0.48$$ . Six open challenges and seven future research directions are identified and grounded in evidence from the included studies, with explainable steganography, quantum-resistant frameworks, and latent diffusion model integration emerging as the most critical priorities for advancing the field toward practical and secure deployment.

Rodrigo Jara Espinoza, Yohamin Nafit Pimentel Alarcon, Angelo Rodrigo Taco Jiménez, Fabricio Martin Chavez Rodriguez

Quantum computing poses a significant threat to classical asymmetric cryptography, which is essential for ensuring confidentiality, authentication, and key exchange in contemporary digital infrastructures. Although post-quantum cryptography (PQC) provides mechanisms that resist quantum attacks, its implementation in Internet of Things (IoT) systems is challenged by constrained resources, including limitations in computation, memory, energy, latency, and bandwidth, and the heterogeneity of devices. This paper offers a comprehensive narrative review of PQC approaches applicable to IoT, systematically organizing 30 peer-reviewed studies published between 2022 and 2026 across four layers: device, communication, distributed trust, and application. Additionally, the review examines two cross-cutting dimensions, privacy and side-channel resistance. The analysis indicates a significant prevalence of lattice-based schemes, hybrid strategies, and integrations with blockchain technology, zero-knowledge proofs, federated learning, homomorphic encryption, AI, and Zero Trust architectures. Notably, key gaps remain in side-channel evaluation, migration pathways, deployment costs, and real-world validation—issues that are particularly critical given the long lifecycles of IoT devices and the ongoing threat of “harvest now, decrypt later” attacks.

Manish Singh, Tapan Kumar Jain, Shankar Bhattacharjee

Communication and networked systems rely heavily on cryptographic digital signatures to ensure message authenticity, integrity, and non-repudiation. However, rapid advancements in quantum computing and artificial intelligence (AI) have expanded the attack surface, posing significant threats to conventional public-key schemes such as RSA, DSA, and ECDSA. Quantum algorithms undermine their underlying hardness assumptions, while AI-driven techniques enable traffic analysis, side-channel inference, and behavioral pattern recognition. This review presents a structured analytical assessment of post-quantum signature schemes and privacy-preserving authentication mechanisms to address these dual threats. It evaluates lattice-based, hash-based, and zero-knowledge proof-based signatures, as well as anonymity-enhancing schemes such as ring and group signatures. A unified analytical framework is introduced to map cryptographic schemes to quantum and AI-assisted threat models, based on parameters such as security strength, anonymity, efficiency, and applicability. The analysis shows that lattice- and hash-based schemes provide strong quantum resistance, while privacy-preserving mechanisms enhance anonymity but introduce performance trade-offs. It also identifies a gap in integrating post-quantum cryptography with AI-resilient privacy mechanisms. The findings highlight the need for unified, future-ready cryptographic designs.

Maria Surkova

This article concludes a series of publications dedicated to the development of the NeuroAtom cryptographic primitive and presents the final ecosystem architecture. The core implements eight security functions—hashing, stream cipher, pseudorandom number generator, message authentication code, digital signature, key derivation function, key exchange, and authenticated encryption—within a footprint of 9.6 KB of payload (5.2 KB code and 4.4 KB data). Testing according to the NIST SP 800-22 methodology was conducted on 16 samples, each of 100 MB in size (835 binary sequences per sample): 8 samples for REAL mode and 8 samples for TRAP mode (pseudo-data traps). All 16 samples demonstrated a proportion of successful sequences within acceptable limits (not below 818 out of 835 for tests with a significance level of 0.01). Avalanche characteristics were measured in 24 tests (12 functions × 2 modes), with no zero avalanches detected. The inapplicability of Shor's algorithm is shown due to the absence of abelian hidden subgroups. The TRAP mode precludes the possibility of constructing an oracle for Grover's algorithm without knowledge of the plaintext: each incorrect key generates its own cryptographically correct reality, and the quantum computer has no criterion for selecting the true one. A software implementation on a general-purpose processor provides a hashing speed of 80 MB/s. Preliminary estimates for a hardware implementation (180 nm CMOS) indicate approximately 10,000 logic gates with a complete absence of static memory; expected power consumption is estimated at 20 pJ per operation. Previously published results of NIST testing, avalanche analysis, and proofs of quantum resistance are integrated into this article as elements of a unified body of evidence.

Sirojev Muhriddin Ramazonov Iftixor

Ushbu maqolada cloud computing muhitida ta'lim muassasalarining maxfiy ma'lumotlarini himoya qilishda encryption (shifrlash) texnologiyasini qo'llash masalalari ko'rib chiqilgan. Zamonaviy ta'lim tizimlarida raqamlashtirishning jadal rivojlanishi axborot xavfsizligiga yangi talablar qo'ymoqda. Tadqiqotda AES, RSA, ECC kabi simmetrik va asimmetrik shifrlash algoritmlari tahlil qilingan, ularning ta'lim platformalarida qo'llanilishi, samaradorligi va cheklovlari o'rganilgan. Shuningdek, end-to-end encryption, zero-knowledge proof va post-kvant kriptografiya kabi ilg'or yondashuvlar ko'rib chiqilgan. Tadqiqot natijalari shuni ko'rsatadiki, to'g'ri tanlangan va tatbiq etilgan shifrlash tizimi ta'lim muassasalarining ma'lumotlar xavfsizligini 97% gacha ta'minlashi mumkin. Maqola dasturchilar, ta'lim texnologiyalari mutaxassislari va axborot xavfsizligi sohasidagi tadqiqotchilar uchun amaliy ahamiyat kasb etadi.

Sobia Akmal, Dr. Amnah Firdous, Muniba Saleem, Sabeeka Fatima

No abstract is available for this record.

Daniel Makolo, Obafemi Babatunde Desmond, Dauda Shaibu Anibe, Ejiga Timothy Ikoojo · 7 authors

Cryptography is the backbone of modern network security, providing confidentiality, integrity, authentication, and non-repudiation for digital communication. However, the rapid evolution of cyber threats, particularly the looming arrival of large-scale quantum computers, poses serious challenges to the cryptographic algorithms that protect today's networks. This paper presents a systematic review of cryptography in network security, following the PRISMA 2020 guidelines. A total of 68 studies published between 2016 and 2025 were selected from five major academic databases: IEEE Xplore, ACM Digital Library, Scopus, Web of Science, and ScienceDirect. The review covers classical symmetric and asymmetric algorithms, widely deployed cryptographic protocols such as TLS 1.3, IPsec, and SSH, and the growing body of work on post-quantum cryptography (PQC). Key findings include the following: NIST finalized three post-quantum cryptographic standards (FIPS 203, 204, and 205) in August 2024; lightweight cryptography standards for IoT devices were published in 2025 with the selection of ASCON; and real-world deployment of hybrid classical/post-quantum schemes has already begun in major web browsers and messaging applications. This paper also examines emerging trends in homomorphic encryption, zero-knowledge proofs, and AI-driven cryptanalysis. Based on the findings, this review identifies critical gaps in PQC migration strategies, IoT security, and the integration of cryptography with artificial intelligence, and proposes directions for future research.

Bilal El Issaoui

Information-Theoretic Deniability and the Forest Analogy This paper establishes information-theoretic deniability through a precise structural argument: the Forest Analogy. The central result is a symmetry property showing that an attacker who possesses a valid alibi chain stands in exactly the same position as an attacker who knows only the public parameter N. The verification function cannot distinguish the real authentication chain from any alibi chain. This property holds without cryptographic assumptions — it is information-theoretic, not computational. The authentication chain is built on the linear Diophantine system N = 19A + 9B, in which every number N has approximately N/171 valid representations per layer. A three-layer Matryoshka structure produces a multiplicatively structured search space of approximately 10¹¹² operations. The key insight is that this search space is symmetric: it is equally large and equally unnavigable from outside the system as from within it. Uniform Sampling and the Generation Algorithm Uniform sampling means here that every valid chain — consisting of A, B, a1, b1, a2, b2 satisfying 19A + 9B = N, 19a1 + 9b1 = A, 19a2 + 9b2 = a1, and the digit-root conditions — has exactly equal probability of being generated as the real authentication chain. The generation algorithm achieves this through a hierarchical weighted CDF sampler (cumulative distribution function), operating as follows: 1. The distribution over all valid A-values is computed, where the weight assigned to a given A equals the exact number of valid chains on layers 1 and 2 that can be extended from that A. 2. A is sampled according to this weighted distribution. 3. Given A, the value a1 is sampled in the same manner, with weights determined by the exact number of valid (a2, b2)-pairs beneath that a1. 4. Finally, (a2, b2) is chosen uniformly at random from all solutions to 19a2 + 9b2 = a1. All weights are computed exactly. This hierarchical weighted sampling procedure therefore induces a provably uniform distribution over all complete chains, without requiring the generator to enumerate or store them explicitly. Proposition (Uniform Chain Distribution): Let N be a fixed public parameter. Let Omega(N) denote the set of all valid chains C = (A, B, a1, b1, a2, b2) satisfying: - 19A + 9B = N - 19a1 + 9b1 = A - 19a2 + 9b2 = a1 - and the digit-root conditions on each layer. Then the hierarchical weighted CDF sampler generates each chain C in Omega(N) with probability exactly 1 / |Omega(N)|. Proof. Define the following counting functions: - w2(a1) = |{(a2, b2) : 19a2 + 9b2 = a1, digit-root conditions satisfied}| - w1(A) = sum over all valid a1 of w2(a1), where the sum runs over all a1 satisfying 19a1 + 9b1 = A for some valid b1 - w0 = sum over all valid A of w1(A) = |Omega(N)| The sampler proceeds in three steps: Step 1. A is drawn with probability P(A) = w1(A) / w0. Step 2. Given A, a1 is drawn with probability P(a1 | A) = w2(a1) / w1(A). Step 3. Given a1, the pair (a2, b2) is drawn uniformly with probability P(a2, b2 | a1) = 1 / w2(a1). The joint probability of generating the complete chain C = (A, B, a1, b1, a2, b2) is: P(C) = P(A) * P(a1 | A) * P(a2, b2 | a1) = w1(A) / w0 * w2(a1) / w1(A) * 1 / w2(a1) = 1 / w0 = 1 / |Omega(N)| Since this holds for every C in Omega(N), the sampler induces the uniform distribution over Omega(N). "Remark" B and b1 are uniquely determined once A, a1, a2, and b2 are fixed, via the Diophantine equations. They do not need to be sampled separately. The uniformity therefore holds over all complete chains, including these values. Theorem (Forest Symmetry): Let N be a public parameter and let C = (A, B, a1, b1, a2, b2) be any valid verification chain. Then for every valid alibi chain C': P(C is authentic | verification succeeds, C') = P(C is authentic | verification succeeds) Proof: The verification function evaluates solely against N. By Proposition (Uniform Chain Distribution), every valid chain is generated with identical probability 1 / |Omega(N)|. The alibi C' therefore carries no information about which chain is authentic. Formally, C' and the event "C is authentic" are conditionally independent given that verification succeeds. The posterior probability is thus unaffected by knowledge of C'. The Forest Analogy: The Forest Analogy makes the symmetry precise. The public parameter N is the forest. Each representation (A, B) on layer zero is a tree. Each sub-representation on layer one is a branch. Each leaf is a layer-two representation. All leaves are identical — every chain verifies correctly against N. An attacker holding a valid alibi leaf cannot determine which leaf is the real one, because the verification function provides no distinguishing information. *This work is licensed under CC BY-SA 4.0. Commercial licensing (without ShareAlike) available on request: elissa_oui@outlook.com*

Shohanur Rahman Shohan

No abstract is available for this record.

Rongxi Wei

This paper systematically reviews the research foundation, core technologies, and practical applications of cryptography in the blockchain field. Algorithms, and data immutability relies on cryptographic hash functions and Merkle tree structure; the balance between transparency and privacy in block chain relies on the encryption technique of zero-knowledge proofs, ring signature, homomorphic encryption. Therefore, every part of block chain is based on cryptography; without the mathematical guarantee of cryptography, the trust decentralized by block chain is meaningless. The security of block chain mainly relies on the encryption techniques such as hash functions, digital signatures and encryption algorithms, and traditional cryptographic methods will have vulnerabilities when facing quantum computing, because quantum computer may be used to break currently commonly used algorithms such as RSA, ECC eventually. This “security paradox" requires us to pay more attention to block chain technologies, because block chain technology needs to advance in tandem with cryptography. Traditional blockchain technologies can’t be used indefinitely. Against this background, researching block chain －based crypto is of great theoretical significance and practical value: on the one hand, researching on new cryptographic methods applicable to block chain can extend the area of cryptosystems and give people a new way of solving the security problems in block chain; on the other hand, we should not neglect the possibility of breaking the block chain by combining quantum computing with cryptanalysis research.

Zainab Hassan Katoof, Hala Bahjat Abdulwahab

Decentralized storage platforms and blockchain systems offer novel opportunities for data exchange; however, they also present significant challenges in safeguarding sensitive visual information. The Interplanetary File System (IPFS) offers efficient distributed storage, but it lacks built-in confidentiality mechanisms, making additional security layers necessary. This work proposes a security-oriented framework that integrates (k,n) threshold visual cryptography (shamir secret ), LSB-based image steganography, and blockchain-based ownership management using non-fungible tokens (NFTs). Sensitive images are divided into multiple visual shares using a threshold scheme so that no useful information can be obtained unless enough shares are available. Each share is then hidden inside a cover image using a simple LSB-based steganography method and stored on IPFS. Instead of storing the data itself on the blockchain, NFTs are used only to reference the stored content and record ownership in an immutable manner. Experimental results are evaluated using common image quality and statistical metrics, including PSNR, SSIM, correlation, and entropy. With PSNR = Inf dB for all images, Entropy analysis shows that the entropy values of the original cover images are approximately 7.0865, while the entropy values of the stego-images after embedding range between 7.0907 and 7.0954, indicating only a slight increase in randomness. This minimal change confirms that the LSB-based steganographic embedding does not significantly alter the statistical properties of the cover images. The findings show that the original images can be reconstructed with acceptable visual quality while preserving the statistical characteristics of the cover images. The proposed approach demonstrates that combining visual cryptography with decentralized storage and blockchain-based ownership can offer improved confidentiality compared to direct on-chain image storage, without introducing excessive system complexity.

Ojaswi Acharya

Modern cryptographic primitives have evolved from supporting basic to more advanced functionalities, and such schemes are now getting more practical. In this thesis, we identify and rectify some limitations of such cryptographic constructions and their proofs of security. Specifically, we work with functional encryption, secure aggregation, and threshold signature schemes, and observe key functional or security limitations in prior work. Our first focus is functional encryption (FE), which enables function evaluation on encrypted messages using a functional secret key. A different primitive named function-revealing encryption (FRE) allows one to compute a fixed function of the underlying messages using their ciphertexts only. We give formal definitions and construct an inner-product FRE scheme. We also analyze the relationship between FE and FRE. Our second contribution considers secure aggregation, a classic problem that has numerous applications in privacy preserving machine learning. Secure aggregation lets many clients contribute data for aggregation without revealing their individual data. Existing practical protocols either have multiple rounds of interaction between clients and the server or rely on heavyweight cryptographic primitives. We build a non-interactive secure aggregation protocol using a novel combination of inner-product FE and a fully-linear probabilistically checkable proof (FLPCP) system. For this protocol, we use an existing FLPCP system [BBCGI’19] that we prove satisfies soundness and zero-knowledge properties even when reused for multiple proof instances. Finally, we address a pressing open question: achieving fully adaptive security for the Sparkle+ [CKM’23] threshold signature scheme. Threshold schemes require t signers to provide partial signatures to form a valid one. Fully adaptive security prevents adversaries from forging signatures even when corrupting up to t-1 signers. While Sparkle+ is secure against static corruption and a limited number of adaptive corruptions, a previous proof of fully adaptive security was shown to be incorrect. We propose a novel hardness assumption under which Sparkle+ satisfies this notion with a tight reduction. We establish hardness of this assumption in the elliptic-curve generic-group model. Our contributions close important gaps in prior work and push advanced cryptographic primitives closer to practice.

Dean Kulik

Harmonic Genesis: The SHA Unfolding and the Recursive Nexus of Reality Driven by Dean a. Kulik January 2026 Section 1: Genesis Section 2&3 : Paper Zero Introduction – Cracking Randomness into a New Order What if one of the most trusted “random” cryptographic functions in the digital world turned out to be an accidental microscope into the structure of reality? This is the crux of the discovery at hand. SHA-256, a secure hash algorithm assumed to output unpredictable gibberish, harbors a hidden harmonic pattern anchored at a very special constant: π/9 (approximately 0.349). In uncovering this pattern – a π/9 harmonic field alignment – we find that the hash’s apparent chaos conceals an emergent cosmic order. The 256-bit output lattice of SHA-256 is not a uniform random space at all, but rather is biased toward a profound equilibrium ratio (~35% order, ~65% chaos). In other words, SHA’s design inadvertently tunes itself to the[1][2]universal harmonic constant , and that changes everything we thought we knew about cryptographic randomness. This breakthrough means SHA-256 is not broken in the traditional sense – it is revealed. We have not found a trivial way to invert the hash or crack passwords; instead, we have found that SHA-256 outputs carry a signature of order in their very randomness. It’s as if a secret melody was resonating within white noise. Rather than a meaningless jumble, each SHA output is an accidental lens into the manifold of mathematical reality – a snapshot of a deeper truth-field encoded in binary. This exposition will unfold how the π/9 alignment was discovered, the rigorous proofs of its existence, and the staggering implications that ripple out from cryptography into physics, cognition, and our understanding of the universe’s fabric. Once seen, this pattern cannot be unseen; it is a one-way transformation in knowledge – an Ω lock on our perspective. We stand at the threshold of an irreversible insight: randomness, trust, life, and cosmos may all be threaded by the same recursive harmonic architecture. The π/9 Harmonic Field Alignment in SHA-256 At the heart of this discovery is the recognition that SHA-256 outputs gravitate toward a harmonic ratio . In numeric terms, , or roughly 0.35, emerges as a stable threshold in the hash’s behavior. What does this mean? In the[3][4]Nexus harmonic framework, 0.35 (also called the Mark 1 attractor) represents an optimal balance between order and disorder in a complex system. Amazingly, SHA-256 – a human-designed algorithm – unknowingly [5][6]operates at this balance point. Each 256-bit digest tends toward a state where about 35% of the bits carry structured, “actualized” information, and 65% remain in flux as entropy[1][7]. This is in stark contrast to a truly random hash, which would have no such bias (ideally 50% of bits 1 and 0). Yet SHA outputs consistently show this 35/65 split when analyzed, indicating an emergent lattice structure in the output space.[8][9] How does this happen? It turns out the internal design of SHA-256 – its constants and round structure – act as “invariant anchors” that prevent complete randomness. The fractional parts of cube roots of primes used as SHA constants, and even the padding rules, introduce slight biases (a kind of “geometric reference”) each round. Instead of injecting pure chaos, these choices guide the hash toward a [10][11][10]particular equilibrium. Over 64 rounds of mixing, the message is not just obliterated into noise; it is folded and refolded into a structured 256-bit outcome, almost like a piece of origami. The Mark 1 harmonic formula formalizes this by comparing total potential information to actualized information in the hash. In a [1]harmonically balanced hash, , meaning roughly 35% of the state’s capacity becomes “organized” (patterned bits) and 65% remains “potential” or random. The SHA constants essentially [8][7]tune the algorithm to achieve this ratio, acting as a built-in bias toward order amidst chaos[12][9]. Crucially, π/9 is not just a random fraction – it appears to be a universal attractor across systems. In fact, the Nexus research identifies as a recurring sweet spot in complex processes, from Game-of-Life cellular automata to cosmic-scale dynamics. In Conway’s Game of Life (a Turing-complete cellular automaton), maximum complexity emerges at about 35% cell density – the same 0.35. SHA-256, remarkably, behaves like a [13][13][14]digital Game of Life: 64 rounds = 64 generations, mixing rules like cellular neighbor updates, and a final pattern that isn’t random but an “oscillating” complexity pattern at the edge of chaos. This is the π/9 alignment showing itself. Rather than a fortuitous coincidence, we begin to see it as evidence that [15][16]SHA-256’s design tapped into a fundamental law of recursive systems: an equilibrium between entropy and structure at π/9, where computation produces maximal complexity and meaningful patterns.[13][14] In summary, the π/9 harmonic field alignment in SHA-256 reveals that what we once assumed to be pure computational randomness is actually structured chaos. The hash output lattice behaves like a resonant field, with π/9 as its tuning frequency. The “secure hash” was securing something more profound than our data – it was securing a bridge between math and reality, locking each output to a hidden order. The apparent security lattice isn’t a random scatter, but a harmonic matrix reflecting an emergent order that transcends the algorithm itself. We have, in effect, discovered that SHA’s unpredictability masks a deterministic harmonic signature. Next, we delve into how we proved this alignment exists and what symbols and logic confirm this new reality.[17][9] Evidence and Proof of Harmonic Alignment in SHA Uncovering the SHA harmonic alignment required a combination of mathematical analysis, computational experiments, and symbolic interpretation. The proofs range from hard numbers to almost poetic patterns, each reinforcing that SHA outputs are not random at all, but resonant. 1. Statistical and Mathematical Proofs: The simplest evidence came from bit statistics and delta analyses. By measuring the proportion of 1s vs 0s across large sets of SHA-256 hashes, researchers consistently found the ratio drifting toward ~0.35 (35% ones) instead of the expected 0.5. This alone was a red flag: the hash was too “orderly.” Furthermore, using the Mark1 formula on hash states confirmed that [8][12]H converges near 0.349 for a broad class of inputs. The probability of this happening by chance (if SHA were truly random) is astronomically low. It indicated a [1][18]hidden invariant. Additional math revealed the source: when comparing a hash to a transformed version of itself (like a reversed-nibble or ASCII-reencoded variant), the difference often contained long runs of zeros in hex – meaning the two forms were closely aligned. This is the [19][20]Mirror Law: if you hash something and then hash a related input, their binary difference is not random noise but structured cancellation, exposing a residue of the original content. Massive trailing zero patterns in the XOR of two hashes signal that [21][20]SHA’s avalanche effect cancels things out in a regular way – a hallmark of resonance, not randomness. In essence, the hash “echoes” the input in subtle harmonic ways rather than wholly erasing it. A concrete example of a mathematical curiosity turned proof was with the strings “Hello” (capital H) vs “hello” (lowercase). The SHA-256 of these two differ in a predictable, structured way: by converting the hash of “Hello” to an ASCII-hex representation and reversing 4-bit chunks, you literally obtain the hash of “hello”. At first glance, this seems impossible – hashes should change unpredictably with even a small input difference. But here it happened exactly, demonstrating an [22][23]entangled resonance between semantically related inputs. The reflective transformation realigned the hash’s “tension” to a harmonic ground state, effectively showing that the hash carried latent information about letter casing. The generalized reflection theorem born from this: if two inputs differ by a minor harmonic perturbation (like case or small semantic twist), their hashes are not independent – they are[24][25]entangled by a harmonic delta. Subtracting or XORing them reveals a meaningful pattern (like those zero tails) corresponding to the seed difference. This provides a logical proof:[19][20]SHA-256 encodes content identity and “misalignment” as measurable harmonic residues. A truly random function would not consistently allow such a subtraction to yield anything but noise. Yet here, the difference pointed directly back to the underlying change (like an arrow saying “these two hashes differ in a simple way!”). Such behavior underscores that SHA outputs lie on a structured lattice; move slightly on that lattice (change input slightly), and the output moves in a predictably structured way (leaving a harmonic trail). 2. Symbolic and Empirical Proofs (The π Projection Anomaly): Some of the most striking evidence came from visual and symbolic analyses of hashes – treating the hash digest not just as a number, but as a language of its own. A major clue was the so-called “SHA→π glyph” anomaly[26][27]. Researchers found that if you interpret certain SHA-256 outputs in base-π or map them onto a circle, they produce recognizable patterns – even digits of π itself! One dramatic case involved a simple input (a short DNA sequence “ATGC…” in one experiment): its SHA-256 hash, when examined byte by byte, appeared to contain the first six digits of π (3.14159…) in order among the hex bytes. Even more bizarre, after those six digits, the sequence “skipped” what would have been 7 and 8 and then devolved into entropy – almost as if the hash [28][29]started to write out π, confirmed alignment, and then stopped. This was dubbed a “Zero-Point Harmonic Collapse” (ZPHC)[30][29]. The i

Muhammad Romadhona Kusuma, Efri Syamsul Bahri

In the digital era, protecting visual content from misuse and forgery is essential. This study proposes a robust image watermarking method by integrating Discrete Wavelet Transform (DWT), Hessenberg Decomposition (HD), and Singular Value Decomposition (SVD), aiming to enhance watermark imperceptibility and resilience against common image attacks. Additionally, the system incorporates RSA digital signatures within the watermark metadata to ensure verifiable authenticity in NFT (Non-Fungible Token) applications. The method was implemented using Python and tested on multiple grayscale images across various attack scenarios, including noise addition and compression. Experimental results demonstrate high SSIM and PSNR values, confirming the method's effectiveness in maintaining both visual fidelity and embedded watermark integrity. These findings support the potential of this approach for secure and scalable NFT copyright protection.

Vanessa Villanueva Collao

No abstract is available for this record.

Timothy D. Williams

Cryptography and accounting have grown up alongside each other for more than five centuries without developing their similarities in dialogue. This extended concept note outlines a vision for a crossdisciplinary research programme integrating six philosophical dimensions: ontological, epistemological, axiological, teleological, praxiological and phenomenological. It explicates only the structural (ontological) dimension in detail, arguing that asymmetric verifiability (whereby the cost of engineering a false acceptance is deliberately set to exceed the cost of verifying a true one) is foundational to both disciplines: in cryptography to one-way functions, digital signatures and zero-knowledge proofs, and in accounting to conservatism in the Basu (1997) and Watts (2003) tradition. The remaining five dimensions are stated concisely and anchored to established literature on each side, with the lived practice of each craft identified as the least studied and the clearest opening for joint work, particularly in the context of post-quantum cryptography (PQC). The present contribution is the naming of the six-dimension structure rather than local novelty within any single dimension; prior scholarship has already placed Alberti’s cryptography and Pacioli’s bookkeeping within a common Renaissance tradition addressing trust at a distance. The note develops a role-to-treatment taxonomy and worked ledger illustrations (a TLS certificate issuance and two distinct quantum exposures: harvest-now-decrypt-later and trust-now-forge-later), and closes with a call for collaboration between cybersecurity and accounting researchers.

Angelo De, Kaoutar Elkhiyaoui, Sandeep Nishad, Sikhar Patranabis · 5 authors

Interoperation across distributed ledger technology (DLT) networks hinges upon the secure transmission of ledger state from one network to another.This is especially challenging for private networks whose ledger access is limited to enrolled members.Existing approaches rely on a trusted centralized proxy that receives encrypted ledger state of a network, decrypts it, and sends it to members of another network.Though effective, this approach goes against the founding principle of DLT, namely avoiding single points of failure (or single sources of trust).In this paper, we leverage fully-distributed broadcast encryption (FDBE in short) to build a fully decentralized protocol for confidential information-sharing across private networks.Compared to traditional broadcast encryption (BE), FDBE is characterized by distributed setup and key generation, where mutually distrusting parties agree on a BE's public key without a trusted setup, and securely derive their decryption keys.Given any FDBE, two private networks can securely share information as follows: a sender in one network uses the other network's FDBE public key to encrypt a message for its members.The resulting construction is secure in the simplified universal composability (UC) framework.To further demonstrate the practicality of our approach, we present the first instantiation of an FDBE that enjoys constantsized decryption keys and ciphertexts, and evaluate the resulting performances through a reference implementation that considers two private Hyperledger Fabric networks within the Hyperledger Cacti interoperation framework.

Prof. Abhijeet More, Tejashree B. Patil, Deep Kharate, M P Akhil · 5 authors

As the multi-chain digital assets, decentralized finance (DeFi) and non-fungible tokens (NFTs) seeing rapid development, cryptocurrency portfolio management is causing strong pain among users.With the growing number of blockchain networks like Ethereum and a variety of chains, users commonly have assets across multiple wallets, protocols and dApps.Classic portfolio tracking services often require the constant relationship between client and server, with centralized servers, offering heavy privacy issues and security implications.Manual and account based access Many of these systems require data to be manually entered or employees to sign in with their accounts, which opens up the possibility for data leaks, inaccurate reporting, and divulgence of sensitive financial information.More centralized trackers unfortunately have a very poor understanding of more advanced DeFi functions such as staking, joining liquidity pools, and yield farming positions, total or just plain token approval permissions leading to either incomplete or worse yet misleading asset summaries.To solve the above issues, this system suggests a completely decentralized cryptocurrency portfolio tracker on client-side.The code utilizes APIs like Alchemy, Zapper and CoinGecko to read real-time token balances, NFTs creatures or positions (for DeFi), and allowances from the current network directly offchain.Being exclusively client side, the tracker does not rely on centralized databases and it is designed to minimize privacy compromises.The built-in on-chain security module is its most noticeable feature, as it detects any potentially malicious or extremely large token approvals given to smart contracts.Suspicious approvals can be detected, and then revoked in a timely manner through signed wallet transactions without needing to reveal any private keys.The results show that this decentralized tracker would provide significantly better user privacy, data accuracy and overall security.As a serverless applications service, that bypasses central authentication, as well as database storage, it offers a transparency, user-centric and scalable way to manage digital assets securely.