Digital signatures authorize transactions, commands and other requests. Quantum attacks threaten widely used signature schemes, while their post-quantum replacements can be costly to verify inside proofs of execution. Signatureless authorization binds knowledge of an authority secret to a canonical request through a freshly randomized proof capsule. The public statement consists of a request identifier and a 32-byte authority commitment. Application rules enforce context, policy and freshness. The interface supports standalone requests and recursive proof composition. The construction combines a masked degree-ten authority reduction over GF(2^128), embedded in GF(2^256), with a bank-and-companion code proof. Source restoration gives expected polynomial-time public-coin extraction. An adaptive witness-free simulator and a same-experiment source extractor establish a quantum chosen-request authorization reduction in the stated address-compatible random-completion model. The public authority circuit and its address input slice are fixed. One permutation supplies the native transcript and commitments. Finite orbit-profile and resource conditions are explicit. The reduction quantifies simulation and extraction losses alongside authority-preimage hardness and canonical intent binding. For S <= T and T <= 2^24 charged native calls, the combined simulation and extraction loss is below 2^-67, including the uniform-slice setup failure. Parano1d supplies a blockchain implementation and recursive verifier. Canonical capsules are bounded by 92,696 bytes. On four CPU threads, median proving takes 0.81 to 0.89 seconds and verification takes approximately 25.6 milliseconds for two request fixtures. The accompanying reproducibility archive contains the manuscript sources, exact arithmetic and finite operator checks, simulation tests, recorded measurements, Rust reproduction programs and authenticated production source files. Its README provides the reproduction commands. Contact: dev@parano1d.orgLicense information: The paper and accompanying written documentation are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Original software in the reproducibility artifact is licensed under the Apache License, Version 2.0. Third-party dependencies retain their respective licenses.
Digital signatures authorize transactions, commands and other requests. Quantum attacks threaten widely used signature schemes, while their post-quantum replacements can be costly to verify inside proofs of execution. Signatureless authorization binds knowledge of an authority secret to a canonical request through a freshly randomized proof capsule. The public statement consists of a request identifier and a 32-byte authority commitment. Application rules enforce context, policy and freshness. The interface supports standalone requests and recursive proof composition. The construction combines a masked degree-ten authority reduction over GF(2^128), embedded in GF(2^256), with a bank-and-companion code proof. Source restoration gives expected polynomial-time public-coin extraction. An adaptive witness-free simulator and a same-experiment source extractor establish a quantum chosen-request authorization reduction in the stated address-compatible random-completion model. The public authority circuit and its address input slice are fixed. One permutation supplies the native transcript and commitments. Finite orbit-profile and resource conditions are explicit. The reduction quantifies simulation and extraction losses alongside authority-preimage hardness and canonical intent binding. For S <= T and T <= 2^24 charged native calls, the combined simulation and extraction loss is below 2^-67, including the uniform-slice setup failure. Parano1d supplies a blockchain implementation and recursive verifier. Canonical capsules are bounded by 92,696 bytes. On four CPU threads, median proving takes 0.81 to 0.89 seconds and verification takes approximately 25.6 milliseconds for two request fixtures. The accompanying reproducibility archive contains the manuscript sources, exact arithmetic and finite operator checks, simulation tests, recorded measurements, Rust reproduction programs and authenticated production source files. Its README provides the reproduction commands. Contact: dev@parano1d.orgLicense information: The paper and accompanying written documentation are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Original software in the reproducibility artifact is licensed under the Apache License, Version 2.0. Third-party dependencies retain their respective licenses.
Abstract A nonzero real vector can be mapped to a unit vector by taking signed square roots of its normalized absolute coordinates. The associated rank-one projector retains relative magnitudes and signs while forgetting total mass and common sign. We apply this construction to an optimal residual and an optimal dual witness for a finite-dimensional minimum-distance problem in the sum norm. Their trace distance defines an alignment statistic. Complementary slackness gives a strict upper bound below one for every optimal pair, and characterizes the zero-distance case. Successive coordinate minimization selects a unique pair once a coordinate order is fixed. The construction is undefined at a zero residual; a separate convention assigns the statistic the value zero there. We give proofs, an explicit example, and a selection policy that uses the statistic only after primary residual comparisons. The accompanying numerical implementation and discrete Lean results have distinct, stated scopes. Why This Matters The paper distinguishes what its diagnostic inequalities measure from stronger claims that do not follow. Explicit definitions and counterexamples make the selection policy and its limits inspectable. Core Theorems The numbered propositions and proofs in the manuscript state their domains and hypotheses. The revision separates quotient residuals, input norms, discrete formal lemmas and numerical evaluations rather than treating them as equivalent. Formal Verification and Computational Artifacts The package includes source code, tests, a pinned standalone Lean project, an explicit declaration census and source-bound rendered files. The quick start gives commands for replay. Each formal result retains the scope described in the manuscript; test outcomes do not supply a theorem beyond that scope. Scope Boundaries and Non-Claims The real projector construction and strict primal-dual distance bound have prose proofs. Lean checks discrete integer and rational statements. Numerical vector evaluation does not establish optimality or compute the canonical selector. Reproduction See [quick_start.md](quick_start.md) for installation, tests, the Lean census, rendering and independent archive checks. The manuscript and documentation use CC-BY-4.0; reference software and tests use MIT. The renderer, Lua filter and path helperretain Apache-2.0; see the component table in README.md. Related Identifiers and Citations Verified scholarly sources are listed in [references.md](references.md).The new revision has no assigned DOI. The previous record is [10.5281/zenodo.20192297](https://doi.org/10.5281/zenodo.20192297); its verified parent is [10.5281/zenodo.20192296](https://doi.org/10.5281/zenodo.20192296). The metadata records these version relationships.
Signatures post-quantiques à partir de techniques de calcul multipartite Le développement actuel des ordinateurs quantiques pousse la communauté cryptographique à mettre au point de nouveaux cryptosystèmes dont la sécurité se fonde sur la difficulté à résoudre des problèmes cryptographiques résistant au calcul quantique. Dans le cadre de cette thèse, nous nous sommes focalisés sur la conception de schémas de signatures électroniques construits à partir de preuves à divulgation nulle de connaissance (zero-knowledge proofs of knowledge). Plus précisément, nous nous sommes intéressés au paradigme “MPC-in-the-Head” (littéralement, “calcul-multipartite-dans-la-tête”) qui fournit une méthode générique de construire de telles preuves en utilisant des techniques de calcul multipartite sécurisé. Nous proposons plusieurs nouveaux schémas de signatures utilisant le paradigme “MPC-in-the-Head”. La plupart d’entre eux sont compétitifs avec les schémas existants dans l’état de l’art post-quantique. Ils produisent des signatures ayant des tailles entre 5 et 20 kylo-octets (pour un niveau de sécurité de 128 bits) et possèdent de très petites clés (de moins de 200 octets). Les problèmes difficiles sur lesquels la sécurité de ces schémas se fonde sont très variés. Certains schémas s’appuient sur des hypothèses de sécurité issues de la théorie des codes correcteurs d’erreurs, telle que celle sur la difficulté à résoudre le problème de décodage par syndrome pour des codes linéaires aléatoires. Les autres schémas s’appuient sur la difficultés à résoudre un système d’équations quadratiques, le problème de la somme de sous-ensembles ou le problème MinRank. Nous avons également mis au point deux nouvelles techniques de MPC-in-the-Head. La première vise à gérer efficacement les situations où le secret est de petite taille avec un grand modulus. La seconde consiste en une nouvelle méthode pour transformer un protocole de calcul multipartite en preuve de divulgation nulle de connaissance. Cette nouvelle transformation offre des nouveaux compromis entre coût de communication et temps de calcul. En particulier, elle permet de produire des algorithmes de vérification très rapides. Plusieurs soumissions à l’appel du NIST pour des schémas de signatures post-quantiques supplémentaires s'appuient (parfois partiellement) sur des idées développées dans le cadre de cette thèse.
Shor’s quantum factoring algorithm and a few other efficient quantum algorithms break many clas-sical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for quantum computers. However, security of these schemes against quantum attacks is elusive. This is because existing security analysis (almost) only deals with classical attackers and arguing security in the presence of quantum adversaries is challenging due to unique quan-tum features such as no-cloning. This work proposes a general framework to study which classical security proofs can be restored in the quantum setting. Basically, we split a security proof into (a sequence of) classical security reductions, and investigate what security reductions are “quantum-friendly”. We characterize sufficient conditions such that a classical reduction can be “lifted ” to the quantum setting. We then apply our lifting theorems to post-quantum signature schemes. We are able to show that the classical generic construction of hash-tree based signatures from one-way functions and and a more efficient variant proposed in [BDH11] carry over to the quantum setting. Namely, assuming existence of (classical) one-way functions that are resistant to efficient quantum inversion algorithms, there exists a quantum-secure signature scheme. We note that the scheme in [BDH11] is a promising (post-quantum) candidate to be implemented in practice and our result further justifies it. Actually, to obtain these results, we formalize a simple criteria, which is motivated by many classical proofs in the literature and is straightforward to check. This makes our lifting theorem easier to apply, and it should be useful elsewhere to prove quantum security of proposed post-quantum cryptographic schemes. Finally we demonstrate the generality of our framework by showing that several existing works (Full-Domain hash in the quantum random-oracle model [Zha12b] and the simple hybrid arguments framework in [HSS11]) can be reformulated under our unified framework. 1
This is the manuscript and reproducibility package for Quantum Mechanics Without Spooky Action: The Gravacle Theory. The archive includes the paper in PDF, DOCX, Markdown, and TeX formats; proof and scope ledgers; public-data extracts; processed result files; scoring and digitization scripts; source registries; provenance notes; manifest; and SHA-256 checksums. Version v337 clarifies the Single-Run Boundary Closure Theorem so that entangled record closures are explicitly scoped as jointly constrained by one nonseparable registration relation, not independent per-wing selectors. It also preserves the v336 formatting, bibliography, license, data/provenance packet, and reproducibility materials.Locally authored manuscript, reports, scripts, and supporting documentation are released under Creative Commons Attribution 4.0 International (CC BY 4.0), unless otherwise stated. Third-party datasets, source archives, and cited public records retain their original licenses, terms, and citation requirements.
Current solutions to quantum vulnerabilities of widely used cryptographic schemes involve migrating users to post-quantum schemes before quantum attacks become feasible. This work deals with protecting quantum procrastinators: users that failed to migrate to post-quantum cryptography in time. To address this problem in the context of digital signatures, we introduce a technique called signature lifting, that allows us to lift a deployed pre-quantum signature scheme satisfying a certain property to a post-quantum signature scheme that uses the same keys. Informally, the said property is that a post-quantum one-way function is used "somewhere along the way" to derive the public-key from the secret-key. Our constructions of signature lifting relies heavily on the post-quantum digital signature scheme Picnic (Chase et al., CCS'17). Our main case-study is cryptocurrencies, where this property holds in two scenarios: when the public-key is generated via a key-derivation function or when the public-key hash is posted instead of the public-key itself. We propose a modification, based on signature lifting, that can be applied in many cryptocurrencies for securely spending pre-quantum coins in presence of quantum adversaries. Our construction improves upon existing constructions in two major ways: it is not limited to pre-quantum coins whose ECDSA public-key has been kept secret (and in particular, it handles all coins that are stored in addresses generated by HD wallets), and it does not require access to post-quantum coins or using side payments to pay for posting the transaction.
Public photon Bell-test records retain timing structure that is lost in aggregate statistics. This paper tests whether that structure survives quantitative response controls in three experimental archives. In the Weihs data, a rectangular contrast of four channel-pair timing centroids tests whether accepted signal delays can be written as a sum of local channel contributions. For longdist1, the contrast is 1.405 ns and 1.515 ns in disjoint chronological halves, with pointwise 95% block intervals [1.018, 1.791] ns and [1.193, 1.836] ns. Both survive the enumerated centroid scan under the specified 20-block inference at an 8-ns coincidence half-width and remain positive under clock, background, and gate checks. A flexible empirical timing model, however, transfers between chronological halves after clock-drift calibration. In the Christensen archive, the suppressed setting-pair channel is strongly enriched in coincidence tails, but a cross-fitted signal–accidental model predicts 714.6 of 730 counts beyond 300 ns; the residual is 15.4 counts with interval [−54.6, 85.3]. NIST timing-offset records exhibit a terminal-mask excess accompanied by an Alice-side singles-rate change and compatible with a separately calibrated local-setting mixture. The evidence separates reproducible structure, failure of an additive accepted-centroid model, and effects accommodated by explicit response controls. Finite coincidence selection and known switching-related populations prevent the centroid contrast alone from establishing intrinsic polarization–time coupling or a failure of quantum theory. Statistical scope. The analyses are exploratory. Coarser clustering weakens scan-adjusted significance: with ten blocks per half, the highlighted Weihs contrast has adjusted approximate p values of 0.087 and 0.014. The residual is specific to the accepted-centroid model and does not establish a discrepancy beyond all independently calibrated temporal-response models. Files and reproducibility. Bell_manuscript.pdf is the self-contained, 13-page preprint dated 30 October 2026. Bell_Reanalysis_Source.zip contains the editable LaTeX manuscript, numerical figure code, reconstruction and analysis scripts, derived records, source manifests and hashes, full comparison tables, calibration and sensitivity results, and reproduction instructions. The NIST analysis uses 60 prescribed samples of 500,000 trials, rather than complete runs. The full upstream Christensen archive and Weihs time-tag files are retrieved by the supplied fetchers and are not bundled. A clean internal rerun reproduced the checked numerical outputs exactly; external independent reproduction is not claimed. Publication status and assistance. This research preprint has not been peer reviewed. AI tools assisted programming, analysis, and manuscript preparation; responsibility for the work remains with the author. License scope. The manuscript and original figures are licensed under Creative Commons Attribution 4.0 International. Original analysis code is licensed under MIT. Third-party source data and derived excerpts retain applicable source terms and attribution; this deposit does not relicense upstream material.