This paper presents a novel zero-knowledge proof scheme constructed upon polynomial multi-variable rings. The core claim is to design a scheme that significantly enhances proof efficiency and security while addressing the computational complexity bottlenecks prevalent in existing approaches. The proposed mechanism leverages the unique properties of multi-variable polynomial rings to establish a streamlined proof and verification process, minimizing the risk of information leakage. Unlike traditional zero-knowledge proofs that often rely heavily on large number arithmetic, this scheme utilizes polynomial operations, leading to potentially improved performance. This work contributes to the field of cryptographic primitives by offering a new design paradigm rooted in algebraic structures, potentially unlocking avenues for more efficient and practical zero-knowledge proofs. The key contributions are a novel construction and a theoretical analysis demonstrating the security and efficiency gains. The scheme operates by encoding the statement to be proven as a polynomial equation in a multi-variable ring, and the prover generates a proof that allows the verifier to confirm the equation's validity without learning any information beyond the proof itself. This design aims to provide a more scalable and practical solution for zero-knowledge proof applications.
The ubiquity of lightweight resource-constrained Internet-of-Things (IoT) devices in 5G smart environments necessitates authentication protocols with the conflicting goals of being lightweight, highly secure, and having a decentralised credential management structure. Existing schemes use trusted third-party key distributors or heavyweight cryptographic primitives infeasible to IoT embedded hardware; they also fail to anchor device credentials on a permissioned blockchain ledger for tamper-evident credential revocation. In this work, we introduce BLAP-IoT: a Blockchain-Assisted Lightweight Authentication Protocol over live Hyperledger Fabric 2.5.9 that leverages elliptic-curve Diffie–Hellman over P-256 curve, keyed MACs, and a three-message challenge-response protocol to provide injective mutual authentication with device key confirmation. Device credential commitments are stored on-chain to facilitate decentralised and efficient device revocation without revealing secrets on-chain. A formal security verification of the protocol in ProVerif 2.05 shows session-key secrecy, injective mutual authentication, and perfect forward secrecy in the presence of the Dolev-Yao attacker. The empirical evaluation of BLAP-IoT on measured P-256 primitives reports that the scheme achieves a total computation cost of 0.303 ms on constrained devices — up to 52% less than compared schemes, 1920-bit two-way communication overhead, and 0.218 mJ device energy consumption. The underlying blockchain layer sustains up to 277 transactions per second (TPS) in peak throughput, with end-to-end authentication latency less than 13 ms at 1000 concurrent devices.
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.
Open access
2 source records
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Stateful cryptographic schemes—exemplified by the hash-based signatures XMSS (RFC 8391) and LMS (RFC 8554)—require the signer to advance a local state monotonically; any rollback is catastrophic, yet a verifier has no way to check it. IETF guidance on state and backup management for hash-based signatures states explicitly that the verifier must simply trust the signer not to have reused state. We define verifiable monotone chains (VMC), a primitive that makes such state discipline cryptographically verifiable: state evolves along a finite poset (S, ⪯) under inflationary monotone operators, every transition carries a zero-knowledge proof, and a public commitment to the state provides an audit trail. We formalize two security notions: monotone-unforgeability (MU), which captures that an external adversary cannot certify an illegal or rolled-back transition, and auditability (AUD), which captures that signer rollback cannot be hidden from a public root history. Both notions reduce, with explicit advantage bounds, to position binding of the underlying vector commitment and knowledge soundness of the proof system. We instantiate VMC as RSEP-XMSS, in which each XMSS signature carries a proof that the signed leaf advanced along the chain FRESH ≺ USED ≺ SPENT in a Poseidon-based state Merkle tree, and we give a complete algorithmic specification with a concrete circuit design (~6041 R1CS constraints estimated, Groth16 proving time estimated at 5–15 ms, signature overhead of about 1–3 KB). RSEP-XMSS is one-way compatible with standard XMSS: legacy verifiers verify the core signature, while enhanced verifiers reject unprotected signatures, preventing downgrade attacks.
The subject matter of the article is the cryptographic integrity of digital authentication systems facing quantum computing threats, specifically focusing on post-quantum alternatives and efficient authenticated data structures. The goal is to design and formally analyze VERKLE-FRI—a hybrid architecture synthesizing Verkle tree proof-size reduction with FRI-based quantum-resistant commitments, establishing a scalable, stateless, and quantum-secure framework. The tasks are: analyze limitations of hash-based signatures and Merkle trees; evaluate polynomial commitment schemes (KZG, Bulletproofs, FRI, lattice-based); propose a hybrid Verkle-FRI design; develop a formal security proof against classical and quantum adversaries; execute complexity analysis with concrete implementation parameters. The methods used are: theoretical cryptographic analysis, formal security modeling via reductionist proofs, algebraic methods over finite fields, polynomial interpolation, random oracle model, FRI protocol with DEEP-FRI optimization, Merkle trees, vector commitments, and asymptotic complexity analysis. The following results were achieved: a novel architecture where Verkle node vectors are polynomial-encoded, committed via Merkle trees over FRI codewords, and verified through FRI with out-of-domain sampling. A formal proof establishes λ-bit quantum security using 2λ-bit hash functions. Complexity yields proof size O(λ log² N), prover time O(λ N log N), and verifier time O(λ log N). Concrete 128-bit quantum parameters include SHA3-512, field size ≈2²⁵⁵, branching factor 256, and 128 FRI rounds, achieving soundness error ≤2⁻¹²⁷. For a concrete benchmark authenticating 2²⁶ elements, a traditional Merkle proof requires ≈0.8 KB, whereas our VERKLE-FRI proof requires ≈180 KB. While larger, this provides quantum resistance and eliminates the trusted setup, a critical trade-off for long-term security. Conclusions. Scientific novelty consists in: 1) the first hybrid Verkle-FRI architecture replacing pairing-based assumptions with hash-based proximity testing; 2) a formal security proof reducing security to hash collision resistance and FRI soundness; 3) quantified efficiency-security trade-offs; 4) a viable pathway for quantum-resistant infrastructure in blockchains, software distribution, and government communications.
Open access
Cryptographic Implementations and Security
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Murugeshwari B., Kayalvizhi S, Daya Florance D, Saranya S
To deploy deep learning-based diagnostic systems in a clinical setting, they need to have not only a high degree of predictive accuracy, but also an unbroken cryptographic chain to prove that the model parameters have not been changed from one inference to the next. This incompatibility arises because softmax, GELU activation, and layer normalization involve transcendental operations to produce the final output. Transcendental operations cannot be represented over the prime finite fields that are necessary when utilizing Rank-1 Constraint Systems (R1CS). The work here provides a mathematically sound approach to resolving the incompatibility by providing three formally defined polynomial approximations: a degree-3 Taylor series softmax approximation (ε ≤ 2.47E-03 per weight); a degree-5 composite polynomial GELU (ε ≤ 1.80E-03); and a squared witness hint reformulation of layer normalization that results in exact constraint satisfaction. The accumulating polynomial approximation errors across 12 transformer encoder blocks have a total approximation error defined as (ε total ≤ 0.0512) and results in a loss of less than one-fifth of a percent in accuracy (94.1% vs. 94.3%) on the RSNA Pneumonia Detection benchmark. The entire ViT-B/16 inference model was compiled into an R1CS form of approximately 2.3×10⁸ R1CS constraints and instantiated as a Groth 16 zk-SNARK. The integrity of the model is confirmed by hashing the parameters using SHA-256 onto an immutable Polygon zkEVM smart contract, allowing for on-chain verification of inference without revealing any of the proprietary model weights. Additionally, this system produces an area under the receiver operating characteristic curve (AUC-ROC) of 0.961, a mean latency for proof generation of 2.84 seconds, an end-to-end verification time of 5.07 seconds, and an average cost for on-chain verification of 0.012ETH, all within the operational constraints of typical radiology workflows.
Shahla Atapoor, Cyprien Delpech de Saint Guilhem, Al Kindi
This work describes a digital signature scheme constructed from a zero-knowledge proof of knowledge of a pre-image of the Rescue Prime Optimized (RPO) permutation. The proof of knowledge is instantiated using the DEEP-ALI interactive oracle proof and made non-interactive via the Ben-Sasson–Chiesa–Spooner (BCS) transformation in the random oracle model. The resulting construction yields a signature scheme with transparent setup. Our design is motivated by recursive zero-knowledge applications, in which signature verification must itself be efficiently provable inside larger proof systems. To this end, the choice of the RPO permutation, the use of a simple algebraic intermediate representation (AIR), and working over the Goldilocks field are made with the goal of enabling efficient recursive verification and aggregation. The implementation of the scheme computes signatures in 4.6–7.2 ms and verifies them in 0.46–0.52 ms when the BCS transform is implemented with Blake3. When the BCS transform is instead instantiated with the RPO permutation itself, the configuration required when signature verification is to be proven recursively inside a proof system, signing takes 20.9–30.4 ms with Metal acceleration and 59.2–229.2 ms on CPU, while verification takes 5.09–5.79 ms. We validate the recursion-friendliness claim end to end by proving one signature verification inside the Miden zkVM and reporting the recursive prover time and proof size. These speeds are obtained with parameters achieving 113 or 122 bits of average-case security, depending on the chosen preset, against adversaries that can obtain up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>64</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> signatures.
Zero-knowledge proofs (ZKPs) are a fundamental building block in cryptography, enabling powerful privacy-preserving and verifiable computations. In the post-quantum era, hash-based ZKPs have emerged as a promising direction due to their conjectured resistance to quantum attacks, along with their simplicity and efficiency. In this work, we introduce SmallWood, a hash-based polynomial commitment scheme (PCS) and zero-knowledge argument system optimized for relatively small instances. Building on the recent degree-enforcing commitment scheme (DECS) from the Threshold-Computation-in-the-Head (TCitH) framework, we refine its formalization and combine it with techniques from Brakedown. This results in a new hash-based PCS that is particularly efficient for polynomials of relatively small degree –typically up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> – outperforming existing approaches in this range. Leveraging this new PCS, we design a hash-based zero-knowledge argument system that outperforms the state-of-the-art in terms of proof sizes for witness sizes ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Additionally, we present exact zero-knowledge arguments for lattice-based problems using SmallWood, demonstrating highly competitive performance: our scheme yields proof sizes under 25 KB across a wide range of lattice parameters, including Kyber and Dilithium instances.
ABSTRACT TRSP — The Temporal Security Architecture: The Consolidated Record. Three documents, one DOI: the Security Record, the Economic Record, and a general-audience companion. Every cryptographic system in production today rests on one assumption: that a mathematical problem is too hard to solve in practical time. Quantum computing places an expiry date on that assumption, and adversaries are already recording encrypted traffic and public ledgers at scale — harvest now, decrypt later. This record consolidates the Temporal Rotation Security Protocol (TRSP) series into its canonical form. TRSP closes the attack surface that post-quantum mathematics leaves open: cryptographic keys are generated from physical hardware entropy at the moment of use, exist for a rotation window measured in milliseconds, and are destroyed by hardware-enforced destructive readout. Between operations, no persistent credential exists anywhere in the system. This record comprises three documents under one DOI: Document 1 — The Security Record (TRSP — The Temporal Security Architecture: Time as the Fundamental Security Parameter). The consolidated technical reference of the series. It states the security doctrine with precision as a division of labour across three attack mechanics: temporal rotation eliminates the stored-credential surface (endpoint extraction by malware, insiders, hardware probing, or coercion); NIST-standardised post-quantum mathematics (ML-KEM, ML-DSA) eliminates the recorded-transcript surface; single-use protocol rules eliminate the public-record surface, since a retroactively derived key finds its one permitted action already complete and refused for reuse. Each threat is assigned to the layer that closes it structurally — the combination this architecture defines as quantum permanence. The architecture is organised in three layers named for the Norse Norns of time: URDHR (the irrecoverable past — hardware commitment and Landauer-anchored destruction, with optional macroscopic optical entropy), VERÐANDI (the witnessed present — geographically distributed quorum validation bounded by light-speed, with a canonical rotation-window definition of 10–100 ms default and adaptive extension to 500 ms for global quorums), and SKULD (the anchored future — LEO satellite quorums contributing unpredictable physical state measurements under relativistic timestamp validation). Further parts document the four-layer temporal-quantum hybrid (LTQS), the formal ephemeral verification pipeline with zero-knowledge enrollment binding and an explicit statement of the minimised persistent root, application domains ordered by strategic value (AI-to-AI authentication and micropayment, cloud access immune to credential breaches, interbank settlement finality across multi-decade ledgers, critical infrastructure command authorisation, interplanetary autonomous verification, and the consumer expression documented in the TRSP Citadel record), a compliance architecture reconciling maximum personal privacy with institutional regulatory obligations through enrollment tiers, and nine engineering considerations with documented solution pathways. Document 2 — The Economic Record (TDC — The Temporal Digital Coin: Value Anchored in Verified Moments). The corrected canonical economic layer of the series (NC-TDC-26 through NC-TDC-32). It opens with an explicit correction: earlier records simultaneously asserted fungibility of all units, no re-pricing across phases, and rising per-phase value ranges — three statements that are jointly impossible, since a fungible asset trades at exactly one price. This record resolves the contradiction in favour of the principles and formally retracts the per-phase value ranges. The canonical doctrine: one coin, one price, stability by coupled expansion — supply is admitted only against verified, settled growth of the anchored economies under the quantity-theory identity M·V = P·Q, with governance-bounded elasticity, so that price-level stability becomes an accounting consequence of the issuance rule rather than a promise, and early holders gain no phase windfall by construction. Further parts document Proof of Physical Presence consensus economics (validation democratised to enrolled devices; the attack currency is human recruitment), the corrected role of temporal uniqueness (events anchor authenticity, never scarcity — scarcity derives from governance, value from anchor-economy demand), supply and issuance rules, the multi-anchor demand architecture (machine, institutional, and sovereign economies as demand sources, never price classes), consortium governance defined primarily by its prohibitions, the phased rollout in corrected form, and economic engineering considerations including velocity management, demand shocks, exchange-rate regime, bootstrap liquidity, and measurement integrity. Document 3 — The Companion Article (The Key That Even a Time Machine Cannot Steal). A general-audience presentation of the complete architecture — protocol, secure personal computer, and coin — written for readers outside the field, including the time-traveler thought experiment, the three guards (sortition, light-speed, multilateration) in plain language, and the estate architecture. It introduces no claims beyond the technical records. Newly registered contributions. In addition to consolidating and re-registering all prior novel contributions of the series (NC-TDC-1 through NC-TDC-41, NC-URDHR-1, NC-TRSP-Hybrid-1), this record places the following on the public record of prior art as of its publication date, each with a full enabling defensive specification (Security Record, Part 10a): NC-TDC-42 — Optical Air-Gap Content Transfer (formally registered herein, first described in the Citadel record): content crosses a security boundary as rendered light captured by a hardware-switched sensor and locally reconstructed via optical character recognition — the meaning crosses, the file never does; enumerated elements include the security inversion (the receiver harvests, the sender has no channel), the hardware-gated exception to device-level optical silence, and throughput asymmetry as a security property; registered embodiments include matrix-barcode, audio-channel (synthesised speech to local speech-to-text), and enterprise domain-transfer variants. NC-TDC-43 — Chained Presence Verification (newly documented): a unified three-link defence against device-farm collusion — sortition (per-transaction quorum draw via verifiable random function, unpredictable in advance, verifiable after), light-speed (adaptation between draw revelation and window close physically impossible), and multilateration (propagation-delay fingerprints against a relativistically validated time base expose any participant absent from its claimed position) — with the explicit answer to the position-based-cryptography impossibility result (Chandran–Goyal–Moriarty–Ostrovsky 2009): the architecture proves the position of an attested hardware module under an unpredictable draw, removing the pre-positioned-collusion premise the impossibility proof requires. NC-TDC-44 — Ephemeral Witness Relations (newly documented): the formal security model of time-bounded credentials — keys as functions of bounded temporal support with the derived metric of temporal attack surface; erasure completeness as a zero-mutual-information condition I(sk_eph; S(t)) = 0 with Landauer's bound identified as the realisation floor of erasure and explicitly not as a barrier to mathematical re-derivation; the composite adversarial bound over orthogonal domains (computational hardness, temporal measure, combinatorics of presence) with the binomial sortition term; the spacetime-local physical oracle O(D, t) with destructive-readout consumption; and ownership as a time-indexed capability predicate over uncopyable events, including the transient-witness class, the notion of proof of transient knowledge, and the no-retroactive-forgery bound. NC-TDC-45 — Disturbance-Elevated Alpha-Quorum Time Reference. Binding authorisation to short time windows places the local clock in the trusted computing base. This contribution redistributes time-validation authority at the moment of attack rather than fixing it in advance: under normal conditions all nodes validate equally; on detection of a time-source anomaly (cross-source divergence, or a multilateration residual beyond threshold), the system elevates a small set of hardened, atomic-clock-bearing nodes to a median-of-five reference — which tolerates two outliers, so shifting it requires corrupting at least three of five. Membership is fixed by short-lived sortition at the moment of elevation, so the set cannot be pre-targeted. Every coordinated time attack thereby degrades to denial, never forgery: it can interrupt authorisation, not manufacture one. Additionally placed on record in the Economic Record: the coupled-expansion issuance doctrine (corrected canonical form of NC-TDC-29), the corrected scope of NC-TDC-27 (temporal anchoring of authenticity, with uniqueness explicitly disclaimed as a source of value), and the formal retraction recorded in NC-TDC-31 — the corrections themselves are part of the prior-art registration. Consolidation and continuity. This record consolidates and supersedes as canonical reference: TRSP v3 (10.5281/zenodo.20324081), TRSP Digital Coin (10.5281/zenodo.20346658; v2: 20332811; v1: 20288860), TRSP: The Authorization Protocol for Everything (10.5281/zenodo.20402892), and TRSP Citadel (10.5281/zenodo.20481331). The four source records remain in force as prior art; where formulations differ, this record is authoritative. The CRATON designation in prior records and the URDHR designation in this and future records refer to architecturally identical concepts; prior-art continuity is complete and uninterrupted. The economic layer and the security layer are maintained as separate documents within this record by design: each addres
Digital communication increasingly underpins identity, financial transactions, and regulatory compliance. In many settings, possession of a DKIM-signed email serves as evidence of account control, transaction confirmation, or institutional affiliation. Yet demonstrating such properties typically requires revealing the full email or relying on centralized intermediaries, introducing privacy risks and additional trust assumptions. A framework called ZK Email addresses this limitation by applying zero-knowledge proofs (ZKPs) to email verification, enabling publicly verifiable proofs of authenticity while preserving message confidentiality. However, its existing implementations struggle to support complex, real-world messages due to the inefficiency of regular-expression verification over structured formats and rich alphabets. We address this limitation with a new ZKP system for regex matching based on path verification over epsilon-free NFAs, yielding prover complexity linear in the captured path and independent of the original email's size. This approach enables practical validation of expressive standard structures required for full DKIM-signed email verification. To fully integrate our constructions into ZK Email, we design complete end-to-end ZK circuits that combine (i) DKIM signature verification, (ii) an arbitrary-length SHA-256 circuit with partial precomputation for rsa-sha256 under RFC~6376, and (iii) a general-purpose regex primitive enforcing structural constraints over email headers and body. We formalize the associated zero-knowledge relations and analyze their security under realistic adversary models. We implement the system~(fully integrated with ZK Email and released under the MIT license) in Circom and Noir, targeting Groth16 and UltraHonk backends, and evaluate it in both client-side and zkVM (SP1) deployment settings. Experimental results on a comodity hardware demonstrate substantial efficiency improvements over prior DFA-based approaches, achieving 2-6x in proving time using UltraHonk backend, while supporting a significantly richer class of regex languages.
Modular exponentiation is among the most demanding computational operations in cryptographic systems. Effective computation of modular exponentiation is most beneficial for public-key cryptography. The computational complexity and the growing number of bits of the key size, as required by increasingly stringent security demands in the RSA, the Diffie–Hellman key exchange and the Zero-Knowledge Proof (ZKP) protocols, have become a top research priority in terms of algorithmic efficiency. This study proposes a novel triple modular exponentiation algorithm based on the Improved Common-Multiplicand-Multiplication (ICMM) framework. The exact complexity formula was obtained through systematic probabilistic analysis of eight mutually exclusive bit-level states. The efficiency of modular exponentiation is primarily determined by the number of modular multiplications and exponentiation squares required. It is observed that improved common-multiplicand multiplication efficiently minimizes the computational complexity of the triple modular exponentiation by reducing the number of modular multiplications. The overall computational complexity of triple modular exponentiation is 1.875j, where j is the bit length of the exponent. This represents a reduction of approximately 16.7% in total multiplication count relative to double modular exponentiation, corresponding to a 44.4% reduction on a per-exponent basis, and a reduction of 58.3% relative to three independent binary exponentiations. This study concludes that the proposed decomposition reduces the average-case computational complexity of triple modular exponentiation to 1.875j modular multiplications for a j-bit exponent. The proposed triple modular exponentiation algorithm is shown to have lower number of multiplications per bit length of exponent as compared to double modular exponentiation. This result demonstrates the potential of proposed algorithm to reduce the computational cost of triple modular exponentiation in cryptographic protocols where it is a recurring operation, such as interactive ZKP identification schemes.
Arithmetization-oriented (AO) hash functions are the dominant cost in zero-knowledge proof systems, and their security against the strongest known attacks rests on the hardness of the constrained-input constrained-output (CICO) problem, solved by Gröbner-basis techniques. Raising the nominal algebraic degree of a design is known not to suffice, as recent attacks (FreeLunch, CheapLunch, resultant methods) have repeatedly shown. This work identifies a positional design lever for AO substitution-permutation networks over the Goldilocks field with the power-map S-box x^7: folding a low-degree quadratic coupling into the input of the S-box adds one bit of CICO ideal degree per round, whereas the same coupling placed in the linear layer or after the S-box adds nothing. The ideal degree follows the measured law D_I = 7^(R·m) · m · 2^(R−1) against a baseline of 7^(R·m), where R is the number of rounds and m the number of free input branches. Measurements in the msolve Gröbner engine indicate that the added degree is genuine rather than a nominal inflation (the F4 solving degree rises; an auxiliary-variable-free model reproduces the ideal degree; a resolved large instance rules out competing laws), that it is generic across four unrelated coupling patterns, that it is independent of the coupling density (one term per round suffices), and that it carries no differential/linear cost. The principle is instantiated as Alaniz-AO, a Goldilocks sponge whose HADES partial-round schedule reaches 0.74x the constraint cost of Poseidon2 at a 128-bit target under an explicit ω=2 cost model. A secondary result: the branch number of the linear layer does not govern algebraic CICO security. Measurements are reproducible and use proxy primes sharing the exponent structure of Goldilocks. Round counts and cost figures are extrapolations from the measured degree law under the stated cost model; instances beyond three rounds exceed the solver on commodity hardware and are reported as gaps. A reference implementation and reproduction scripts accompany the paper.
Open access
2 source records
Cryptographic Implementations and Security
Cryptography and Residue Arithmetic
Physical Unclonable Functions (PUFs) and Hardware Security
The automotive industry is transitioning to Zonal-oriented Architectures (ZoA) for Software-Defined Vehicles (SDVs), enabling frequent over-the-air (OTA) updates for 100+ Electronic Control Units (ECUs). While OTA updates improve efficiency, they introduce safety-critical security risks. Current standards like Uptane and AUTOSAR Adaptive rely on Public-Key Infrastructure (PKI). However, PKI-based authentication creates bandwidth bottlenecks in in-vehicle and vehicle-to-cloud (V2I) communication as ECU density increases. It also risks exposing sensitive vehicle configurations and passenger privacy due to centralized architectures. Next-generation Zonal SDVs require decentralized, scalable authentication with data privacy. To address this, we propose zk-ScalHard, a hardware-rooted, privacy-preserving authentication protocol. We introduce a decentralized, hierarchical trust-promotion model utilizing Silicon Physical Unclonable Functions (PUFs) and two novel Zero-Knowledge Proof (ZKP) circuits: (1) Zonal Identity and Integrity (ZIDI) and (2) High-Performance Computing Aggregation (HPCA). These circuits employ multi-party computation (MPC) and recursive aggregation to achieve decentralization and scalability. The integration of ZKPs and PUFs ensures 100% vehicle-level data sovereignty. Benchmarked against Uptane, zk-ScalHard achieves constant O(1) communication and verification complexity, improving upon the linear O(n) complexity of current systems. Evaluation shows a 99.2% reduction in authentication bandwidth and a 99.9% reduction in the temporal attack surface. Our results demonstrate that zk-ScalHard provides a scalable, secure, and GDPR-compliant architecture for future Zonal SDVs.
Open access
3 source records
cs.CR
Physical Unclonable Functions (PUFs) and Hardware Security
Numerous reports and studies indicate that the lack of effective regulation in cryptocurrencies has not only led to substantial financial losses but also eroded the traditional ”central bank-commercial bank” framework, thereby destabilizing financial systems. To address these issues, a growing body of research has focused on developing regulatory mechanisms for cryptocurrencies. However, existing regulatory proposals face a persistent trilemma: they fail to simultaneously achieve three critical properties—(i) one‑time registration with self‑updating addresses, (ii) completeness (including a lost‑coin retrieval mechanism), and (iii) fine‑grained access control that respects the ”central bank‑commercial bank” framework. This study bridges this gap by proposing TCoin, the first regulatory cryptocurrency that fulfills all three requirements. We first introduce TSFG, a traceable scheme built on SkyEye, which employs cryptographic techniques to achieve one‑time registration with self‑updating addresses and fine‑grained access control for tracing. By integrating TSFG into the RSCoin framework, we construct TCoin—a regulatory cryptocurrency that achieves one‑time registration with self‑updating addresses, ensures completeness through a novel coin recovery mechanism, and enforces fine‑grained access control. Compared to prior work (CB, DAP, PDC, RSCoin, e‑CNY, and RECoin), TCoin is the first to resolve the regulatory trilemma, offering a comprehensive solution that reconciles the disruptive potential of cryptocurrencies with the stability requirements of the traditional monetary system.
Abstract When resource-constrained Internet of Things (IoT) terminals connect to industrial control, sensing, and edge systems, it is necessary to balance low-overhead authentication, credential privacy protection, and cross-platform deployment. Traditional password and USBKEY authentication methods rely on static credentials and certificate mechanisms, which are vulnerable to eavesdropping, replay, and forgery attacks, while simultaneously suffering from privacy leakage and high platform adaptation costs. To address these issues, this paper proposes a hardware-assisted zero-knowledge authentication scheme for resource-constrained terminals. It utilizes a USBKEY as the local trusted hardware carrier and introduces a quadratic constrained zero-knowledge proof protocol under the Generalized Subspace Vector Oblivious Linear Evaluation framework (GSVOLE-2DLC) to construct a session-bound dynamic authentication process. In the registration phase, the scheme binds protocol parameters with user credentials and writes them into the USBKEY. In the authentication phase, the server (acting as the verifier \((\mathcal{V})\)) generates a random challenge, and the USBKEY (acting as the prover \((\mathcal{P})\)) generates temporary proof parameters based on local witness information. Subsequently, the verifier \((\mathcal{V})\) completes the verification through constraint consistency and GSVOLE consistency, thereby avoiding the transmission of original identity credentials over the network. To adapt to terminals with varying computational capabilities, this paper further designs configurable finite field parameters and cross-platform modular arithmetic interfaces, which are implemented in a PowerPC-architecture USBKEY prototype and a host-side verification environment. Experimental results demonstrate that under the parameter configuration of a 64-bit prime field, \((n_C=4)\), \((k_C=3)\), \((d_C=3)\), \((\ell=2)\), and \((t=7)\), the total system authentication time is approximately 0.5476 s, and the verification time for the verifier \((\mathcal{V})\) is 0.0031 s. Protocol performance and functional tests indicate that the proposed scheme can correctly execute identity authentication under the assumed threat model, making it suitable for IoT edge scenarios requiring privacy protection and lightweight authentication.
The convergence of Smart Grids and the Internet of Medical Things (IoMT), termed Grid-IoMT, represents an emerging paradigm where healthcare facilities dynamically interact with energy grids to optimize both clinical operations and power consumption.Real-time medical data streams (e.g., continuous vital signs from wearable monitors, infusion pump logs, ventilatory parameters) traverse network infrastructure shared with grid telemetry, creating unprecedented attack surfaces where energy-demand manipulation can indirectly compromise patient safety, and conversely, medical data injection can destabilize grid frequency regulation.This paper presents BlockAuth-GridMed, a novel blockchain-anchored adaptive authentication framework specifically designed for real-time medical data streams in AI-driven Smart Grid-IoMT converged networks.The framework integrates three synergistic innovations:(1) A hierarchical blockchain architecture (local permissioned chains for clinical domains interconnected via a main chain for cross-domain trust) that anchors authentication proofs without introducing latency prohibitive for real-time medical applications (median latency 187ms),(2) An adaptive authentication engine powered by deep reinforcement learning (DRL) that dynamically adjusts authentication strength based on real-time risk assessment-escalating to multi-factor requirements during grid instability events or cyber-threat alerts while maintaining low-friction single-factor authentication during quiescent periods,(3) A zero-knowledge proof (ZKP) layer enabling mutual authentication between medical devices and grid nodes without revealing sensitive patient identifiers or clinical data patterns to energy system operators.We evaluate BlockAuth-GridMed using a realistic testbed emulating a 200-bed smart hospital integrated with an IEEE 13-bus distribution grid model, processing 15,000 real-time medical data streams per second across 6,500 IoMT devices and 12 grid sensors.The framework achieves 99.97% authentication success rate for latency-sensitive medical alerts (critical events requiring <100ms end-to-end latency) and maintains an average authentication overhead of 28ms, well within clinical requirements.Under adversarial conditions (simulated man-in-the-middle, replay, and grid-state injection attacks), BlockAuth-GridMed demonstrates 96.8% attack detection and 99.1% attack prevention rates, outperforming baseline certificate-based (83.4%/87.2%)and token-based (71.3%/74.6%)schemes.The DRL-driven adaptive authentication reduces unnecessary multi-factor challenges by 73% compared to static high-security policies, significantly improving clinical workflow efficiency.We also analyze blockchain gas costs (approx.\$0.012 per authentication), scalability under IoMT device churn (up to 15% daily device joins/leaves), and regulatory alignment with HIPAA, NERC CIP, and FDA pre-market guidance for medical device security.This work provides the first integrated authentication framework specifically tailored to the Grid-IoMT convergence, enabling secure, real-time, and adaptive protection for medical data streams in energy-aware healthcare infrastructures.
This paper presents a rigorous analysis of the hash chain auditability mechanism implemented within the MF+SO sovereign identity vault, specifically the `.aioss` hash chain data structure. The hash chain links successive vault state commitments through SHA3-256 cryptographic hashes, creating an immutable, tamper-evident log of all state transitions. Each link in the chain incorporates a parent_hash invariant that binds the current state to the entire prior history, a canonical JSON serialization of the vault state to ensure deterministic hashing across platforms, and an Ed25519 signature providing cryptographic proof of authenticity. We demonstrate that this construction achieves the forensic auditability properties first described by Haber and Stornetta (1991) for digital timestamping, extended to the identity management domain. The paper provides a formal mathematical model of the chain construction, analyzes the computational and storage costs of chain verification, presents a security proof for the tamper-detection properties under the random oracle model, and compares the MF+SO approach against alternative audit log constructions including Merkle trees, Certificate Transparency logs, and blockchain-based registries. The implementation leverages SHA3-256's sponge construction to eliminate length extension vulnerabilities that would compromise naive hash chain implementations. Empirical measurements demonstrate that chain verification for a typical user with 10,000 state transitions completes in under 200 milliseconds on modern mobile hardware. The paper concludes with an analysis of forward secrecy guarantees, key rotation impacts on chain continuity, and proposed extensions for zero-knowledge proofs of chain membership. Part of The Anticloud research corpus by Lois-Kleinner Alpasan (ORCID: 0009-0009-2233-6107). This work explores cryptography, key management in the context of sovereign AI infrastructure, post-cloud computing architectures, and transparent, blackbox-free systems.
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.
You Wu, XinFeng Dong, Yongqiang Li, F Liu · 8 authors
Abstract With the development and practical application of technologies such as Fully Homomorphic Encryption (FHE), Secure Multi-Party Computation (MPC), and Zero-Knowledge Proof (ZK), it has become crucial to research the design and analysis of symmetric cryptographic primitives with low multiplicative complexity and depth. First, by using multiplication and addition over the finite field $$\mathbb {F}_{q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> , where $$q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> is either a prime number $$p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> or $$2^{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , we proposed a non-linear function over $$\mathbb {F}_{q}^{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> based on the generalized Feistel structure. This function features a multiplicative complexity of 4, a multiplicative depth of 2 and 8 additions, and its maximum differential/linear probability of the function is bounded by $$q^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Then, we designed a family of HE-friendly block ciphers called DuX. We conduct a comprehensive security analysis of DuX within certain parameters against various cryptanalysis methods, including differential cryptanalysis, linear cryptanalysis, impossible differential cryptanalysis, zero-correlation linear cryptanalysis, integral analysis, related-key differential cryptanalysis, algebraic attacks, slide attacks, reflection attacks, and boomerang attacks. Our research indicates that DuX maintains a robust security margin against those attacks. Finally, based on the BGV scheme in HElib, we present a detailed homomorphic decryption implementation of the DuX instantiated with $$q = 2^{8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>8</mml:mn> </mml:msup> </mml:mrow> </mml:math> , $$2^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>16</mml:mn> </mml:msup> </mml:math> and $$65537$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>65537</mml:mn> </mml:mrow> </mml:math> , respectively. The results show that, for the same block size, the throughput of the DuX-128 over $$\mathbb {F}_{2^{8}}^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>8</mml:mn> </mml:msup> </mml:mrow> <mml:mn>16</mml:mn> </mml:msubsup> </mml:math> can reach approximately 14.95 times, 7.85 times and 20.76 times that of the AES-128, Low MC-128 and CHAGHRI, respectively. Compared with YuX-128, its throughput has increased approximately by 21.59%.
In the ZKP community, it has long been discussed that the SumCheck protocol is asymptotically more efficient than the Number Theoretic Transform (NTT), requiring only $O(N)$ arithmetic versus $O(N \log N)$. At the same time, hardware accelerator designers propose that NTT is more hardware-friendly, benefiting from locality and data reuse, while SumCheck suffers from sequential, dependent rounds. Despite these competing intuitions, the hardware-system-level trade-offs between NTT- and SumCheck-based proving primitives remain insufficiently understood. Beyond individual accelerator design, this work presents, to our knowledge, the first hardware-system-level direct comparison of NTT- and SumCheck-based proving primitives under a unified architectural framework. We study them in the context of the ZeroCheck protocol, a common building block in zkSNARKs. We implement optimized systems for both primitives. Both are evaluated under the same level on-chip SRAM and off-chip bandwidth budgets. Our results show that there is no universal winner. Generally, SumCheck outperforms NTT for high-degree polynomials. For low-degree polynomials, performance depends on memory availability: under given SRAM budgets, NTT might deliver better performance for medium-sized workloads by exploiting data reuse. These findings, bridging cryptographic protocol design and hardware architecture, offer practical guidance for understanding the proving cost of NTT- and SumCheck-based zero-knowledge proof systems.
PYCO is the native token of the Lindblad Protocol, emerging as a direct consequence of a network that measures and rewards physical coherence. This paper describes the mechanism by which PYCO is generated, distributed, and consumed within the Spectral Ledger, and establishes the economic properties that result from anchoring token issuance in physical hardware validation. Every PYCO in existence was produced by a physical node running the Lindblad Cryptography Protocol (LCP) stack on real hardware. As of June 2026, over 1,512,000 PYCO have been mined across 35,842+ epochs by physical hardware nodes deployed on mainnet on Arbitrum One.
Abstract Ethereum's transaction validity model is currently anchored in ECDSA over secp256k1, whose security assumptions weaken in the presence of large-scale quantum adversaries. While NIST-standardized post-quantum signature schemes such as ML-DSA, SLH-DSA, and FALCON provide resistance against quantum attacks, integrating these schemes into Ethereum introduces significant systems-level challenges involving bounded execution, gas determinism, and adversarial verification complexity. This paper introduces PQSigAbstract, a modular post-quantum signature verification architecture for Ethereum that separates validation into a stateless pre-validation phase and a deferred cryptographic verification phase linked through commitment binding. The design defines typed Verification Modules with explicit gas estimation, a versioned Scheme Registry with quarantine-based deployment safety, and a probabilistic aggregation mechanism for non-aggregatable post-quantum schemes. The proposed architecture preserves EU-CMA security while maintaining compatibility with ERC-4337 and RIP-7560 account abstraction models. Formal gas cost models are derived for ML-DSA-44, FALCON-512, and SLH-DSA-128f, and empirical evaluation demonstrates practical deployment feasibility for high-value Ethereum accounts despite substantially higher verification costs relative to ECDSA. Status: Technical Report / Working Paper Author: Ankita Virani Affiliation: University of Colorado Boulder