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.
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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.
Secure, interconnected, and compatible data sharing of Electronic Health Records (EHRs) across healthcare domains is essential for timely patient care and improved adaptability in healthcare infrastructures. Current challenges must be addressed, including centralization threats, fragmented standards, and threats from quantum computing. This paper proposes a blockchain-based EHR framework using post-quantum cryptography and HL7 FHIR standards for secure, interoperable data sharing. It employs smart contracts for patient-centric access control and HotStuff BFT consensus, achieving 928 TPS with 2.1-second finalization. Zero-knowledge proofs enable privacy-preserving authentication, and dynamic accumulators improve revocation storage efficiency by 89%. On a 20-node testbed, the system sustains 620 TPS at 500 ms latency, with under three-second access grants and 95% storage efficiency via cryptographic pointers. Compared to current systems, it offers 20× higher throughput and resists quantum threats. Multi-hop exchange across three hospitals reduced normalization efforts by 40%. Comprehensive assessment on the system outcomes reveals that our framework significantly enhances security, scalability, and interoperability for decentralized healthcare networks.