Proof System Research Articles

A proof system of the CaIT calculus

A proof system of the CaIT calculus

Simulation extractable versions of Groth’s zk-SNARK revisited

Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are the most efficient proof systems in terms of proof size and verification. Currently, Groth’s scheme from EUROCRYPT 2016, Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}, is the state-of-the-art and is widely deployed in practice. Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} is originally proven to achieve knowledge soundness, which does not guarantee the non-malleability of proofs. There has been considerable progress in presenting new zk-SNARKs or modifying Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} to efficiently achieve strong Simulation extractability, which is shown to be a necessary requirement in some applications. In this paper, we revise the Random oracle based variant of Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} proposed by Bowe and Gabizon, BG18, the most efficient one in terms of prover efficiency and CRS size among the candidates, and present a more efficient variant that saves 2 pairings in the verification and 1 group element in the proof. This supersedes our preliminary construction, presented in CANS 2020 (Baghery et al. in CANS 20, volume 12579 of LNCS, Springer, Heidelberg. pp 453-461, 2020), which saved 1 pairing in the verification, and was proven in the generic group model. Our new construction also improves on BG18 in that our proofs are in the algebraic group model with Random Oracles and reduces security to standard computational assumptions in bilinear groups (as opposed to using the full power of the generic group model (GGM)). We implement our proposed simulation extractable zk-SNARK (SE zk-SNARK) along with BG18 in the Arkworks library, and compare the efficiency of our scheme with some related works. Our empirical experiences confirm that our SE zk-SNARK is more efficient than all previous simulation extractable (SE) schemes in most dimensions and it has very close efficiency to the original Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}.

PROOF SYSTEMS FOR TWO-WAY MODAL MU-CALCULUS

Abstract We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-wellfounded proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations.

Preprocessing of Propagation Redundant Clauses

The propagation redundant (PR) proof system generalizes the resolution and resolution asymmetric tautology proof systems used by conflict-driven clause learning (CDCL) solvers. PR allows short proofs of unsatisfiability for some problems that are difficult for CDCL solvers. Previous attempts to automate PR clause learning used hand-crafted heuristics that work well on some highly-structured problems. For example, the solver SaDiCaL incorporates PR clause learning into the CDCL loop, but it cannot compete with modern CDCL solvers due to its fragile heuristics. We present PReLearn, a preprocessing technique that learns short PR clauses. Adding these clauses to a formula reduces the search space that the solver must explore. By performing PR clause learning as a preprocessing stage, PR clauses can be found efficiently without sacrificing the robustness of modern CDCL solvers. On a large portion of SAT competition benchmarks we found that preprocessing with PReLearn improves solver performance. In addition, there were several satisfiable and unsatisfiable formulas that could only be solved after preprocessing with PReLearn. PReLearn supports proof logging, giving a high level of confidence in the results. Lastly, we tested the robustness of PReLearn by applying other forms of preprocessing as well as by randomly permuting variable names in the formula before running PReLearn, and we found PReLearn performed similarly with and without the changes to the formula.

Mjolnir: Breaking the Glass in a Publicly Verifiable Yet Private Manner

This paper formally investigates the problem of unauthorized yet required access to electronically protected information, a.k.a. Break-the-Glass (BtG) access. Reflecting on the rising deployment of such protocols in the current digitized healthcare system, we present Mjolnir1, a blockchain-based BtG framework that offers accountability of unauthorized accesses by healthcare practitioners, dependable right of notification to patients, and privacy of healthcare records accesses. Mjolnir is a smart contract-based protocol which provides undisputed public verifiability of the identity of BtG access entities while maintaining their anonymity except from concerned individual patients, hence protecting the patients’ privacy. We employ an application specific non-interactive cryptographic zero knowledge proof system which ensures that the signing entity (healthcare practitioner) belongs to a given authorized group and that the anonymity of their identity is only revocable by a given opening entity (patient). The security of our system relies on the hardness of the discrete logarithm and decisional Diffie-Hellman problems in elliptic curve groups, and the utilized proof system requires no trusted setup. We formally define and prove the security goals of Mjolnir, provide a proof of concept blockchain implementation on Ethereum, and report on performance experiments and comparisons with other generic zero knowledge proof systems.

Aggregated Zero-Knowledge Proof and Blockchain-Empowered Authentication for Autonomous Truck Platooning

Platooning technologies enable trucks to drive cooperatively and automatically, providing benefits including less fuel consumption, greater road capacity, and safety. To establish trust during dynamic platooning formation, ensure vehicular data integrity, and guard platoons against potential attackers in mixed fleet environments, verifying any given vehicle’s identity information before granting it access to join a platoon is pivotal. Besides, due to privacy concerns, truck owners may be reluctant to disclose private vehicular information, which can reveal their business data to untrusted third parties. To address these issues, this is the first study to propose an aggregated zero-knowledge proof and blockchain-empowered system for privacy-preserving identity verification in truck platooning. We provide the correctness proof and the security analysis of our proposed authentication scheme, highlighting its increased security and fast performance. The platooning formation procedure is re-designed to seamlessly incorporate the proposed authentication scheme, including the 1st catch-up and cooperative driving steps. The blockchain performs the role of verifier within the authentication scheme and stores platooning records on its digital ledger to guarantee data immutability and integrity. In addition, the proposed programmable access control policies enable truck companies to define who is allowed to access their platoon records. We implement the proposed system and perform extensive experiments on the Hyperledger platform. The results show that the blockchain can provide low latency and high throughput, the aggregated approach can offer a constant verification time of 500 milliseconds regardless of the number of proofs, and the platooning formation only takes seconds under different strategies. The experimental results demonstrate the feasibility of our design for use in real-world truck platooning.

Core Type Theory

Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is.

Certified Dominance and Symmetry Breaking for Combinatorial Optimisation

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

Compact Structure-Preserving Signatures with Almost Tight Security

In structure-preserving cryptography, every building block shares the same bilinear groups. These groups must be generated for a specific, a priori fixed security level, and thus, it is vital that the security reduction in all involved building blocks is as tight as possible. In this work, we present the first generic construction of structure-preserving signature schemes whose reduction cost is independent of the number of signing queries. Its chosen-message security is almost tightly reduced to the chosen-plaintext security of a structure-preserving public-key encryption scheme and the security of Groth–Sahai proof system. Technically, we adapt the adaptive partitioning technique by Hofheinz (Eurocrypt 2017) to the setting of structure-preserving signature schemes. To achieve a structure-preserving scheme, our new variant of the adaptive partitioning technique relies only on generic group operations in the scheme itself. Interestingly, however, we will use non-generic operations during our security analysis. Instantiated over asymmetric bilinear groups, the security of our concrete scheme is reduced to the external Diffie–Hellman assumption with linear reduction cost in the security parameter, independently of the number of signing queries. The signatures in our schemes consist of a larger number of group elements than those in other non-tight schemes, but can be verified faster, assuming their security reduction loss is compensated by increasing the security parameter to the next standard level.

MaxSAT resolution for regular propositional logic

Proof systems for SAT are unsound for MaxSAT because they preserve satisfiability but fail to preserve the minimum number of unsatisfied clauses. Consequently, there has been a need to define cost-preserving resolution-style proof systems for MaxSAT. In this paper, we present the first MaxSAT resolution proof system specifically defined for regular propositional clausal forms and prove its soundness and completeness. The defined proof system provides an exact approach to solving Regular MaxSAT and Weighted Regular MaxSAT with variable elimination algorithms.

Morpho-logic from a topos perspective – application to symbolic AI

Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis of structures, that was widely developed and applied in image analysis. Its mathematical bases rely on algebra, complete lattices, topology. Strong links have been established between MM and mathematical logics, mostly modal logics. In this paper, we propose to further develop and generalize this link between mathematical morphology and modal logic from a topos perspective, i.e. categorial structures generalizing space, and connecting logics, sets and topology. Furthermore, we rely on the internal language and logic of a topos. We define structuring elements, dilations and erosions as morphisms. Then we introduce the notion of structuring neighborhoods, and show that the dilations and erosions based on them lead to a constructive modal logic, for which a sound and complete proof system is proposed. We then show that the modal logic thus defined (called morpho-logic here), is well adapted to define concrete and efficient operators for revision, merging, and abduction of new knowledge, or even spatial reasoning.

Pembuktian Kepemilikan Tanah Adat Minahasa Pasini Dalam Praktik Penyelesaian Sengketa Tanah Di Sulawesi Utara

The aim of the research is to find out the use of Pasini land by the Minahasa people. Pasini land ownership proof system in the settlement of land disputes in court at this time. By using normative legal research methods supported by empirical studies as legal facts about pasini soil, the following results are obtained. Pasini Land as a customary right still exists today. Pasini rights as original unwritten Indonesian law affect the use of limited pasini land which cannot be used as collateral for credit loans at the Bank. in proving ownership of pasini land is still very weak compared to land that has been certified as SHM because in principle customary law is an unwritten custom that does not yet have certainty law even though there has been an amendment to the 1945 Constitution Article 18 the position of customary rights Customary law is the same as the field of positive law that exists in this country. Conclusion The existence of pasini land as customary rights is still recognized especially with the amendment to Article 18 of the 1945 Constitution.

Juridical Analysis of The Spread of Hate Speech Conducted by Responsible Parties Through Social Media

Convenience freedom argues with dependence on technology brings the development of new types of crime that as appearance speech hatred or hate speech that is done on social media either from typing as well as videos. such things, if not arranged more continue so, would be very worrying, society will not be off bounds and will raise inconvenience or feeling offended at someone or a group certain. The article will discuss How law criminals looked at criminal speech hatred or this hate speech and will also discuss what is the proof system in following criminal speech hatred. The method used to study which normative law is enforced with the method of researching material libraries and approaches used is approach related legislation with follow criminal speech hate. Results and discussion obtained If We see in the Criminal Code and regulations other legislation already explained several articles that can be imposed on someone who does speech hatred or hate speech. Articles that regulate action about Speech Hatred to a person, a group, or institution based on a Circular Letter National Police Chief No: SE/06/X/2015 contained inside Article 156, Article 157, Article 310, Article 311, then Article 28jis. Article 45 paragraph (2) of Law Number 19 of 2016 concerning information and transactions electronics and Article 16 of Law No. 40 of 2016 concerning deletion of Racial and Ethnic Discrimination. and proof that was made For inspect follow criminal speech hatred This is still based on with tools arranged evidence in the Criminal Code.

Reducing non-occurrence of specified runtime errors to all-path reachability problems of constrained rewriting

A concurrent program with semaphore-based exclusive control can be modeled by a logically constrained term rewrite system. In this paper, we first propose a framework to reduce the non-occurrence of a specified runtime error in the program to an all-path reachability problem of the transformed logically constrained term rewrite system. Here, an all-path reachability problem of the system is a pair of state sets and is demonically valid if every finite execution path starting with a state in the first set and ending with a terminating state includes a state in the second set. Then, we propose a weakened but easily-implementable variant of an existing proof system for all-path reachability problems. As a case study, we deal with the race freedom of concurrent programs with semaphore-based exclusive control.

A Resolution Proof System for Dependency Stochastic Boolean Satisfiability

A Resolution Proof System for Dependency Stochastic Boolean Satisfiability

Reverse Evidentiary Analysis in Article 12 B Paragraph (1) A and B of Law Number 20 of 2001 Amendments to Law Number 31 of 1999 Concerning The Eradication of Corruption

The purpose of this study is to analyze the philosophical basis of the reverse proof system for future Gratification corruption crimes and the formulation of norms for the reverse proof system for future Gratification corruption crimes. The research method used in this study is normative juridical with qualitative descriptive data analysis techniques. The results of the study are the philosophical basis of the reverse proof system for the crime of graft corruption related to bribery Article 12 B, namely that both the public prosecutor and the defendant are obliged to prove but the public prosecutor alone proves the gift received by the recipient of the gratuity while the defendant proves that the gratuity is not a bribe, has nothing to do with position and does not conflict with their duties or obligations. The construction of legal substance, which directs the formulation of reverse evidentiary norms with an emphasis on legislative policies according to the 2003 CAC as a characteristic of the combination of the hukum umum and hukum sipil legal systems as a legal system.

Towards logical foundations for probabilistic computation

The overall purpose of the present work is to lay the foundations for a new approach to bridge logic and probabilistic computation. To this aim we introduce extensions of classical and intuitionistic propositional logic with counting quantifiers, that is, quantifiers that measure to which extent a formula is true. The resulting systems, called cCPL and iCPL, respectively, admit a natural semantics, based on the Borel σ-algebra of the Cantor space, together with a sound and complete proof system. Our main results consist in relating cCPL and iCPL with some central concepts in the study of probabilistic computation. On the one hand, the validity of cCPL-formulae in prenex form characterizes the corresponding level of Wagner's hierarchy of counting complexity classes, closely related to probabilistic complexity. On the other hand, proofs in iCPL correspond, in the sense of Curry and Howard, to typing derivations for a randomized extension of the λ-calculus, so that counting quantifiers reveal the probability of termination of the underlying probabilistic programs.

A Coinductive Reformulation of Milner's Proof System for Regular Expressions Modulo Bisimilarity

Milner (1984) defined an operational semantics for regular expressions as finite-state processes. In order to axiomatize bisimilarity of regular expressions under this process semantics, he adapted Salomaa's proof system that is complete for equality of regular expressions under the language semantics. Apart from most equational axioms, Milner's system Mil inherits from Salomaa's system a non-algebraic rule for solving single fixed-point equations. Recognizing distinctive properties of the process semantics that render Salomaa's proof strategy inapplicable, Milner posed completeness of the system Mil as an open question. As a proof-theoretic approach to this problem we characterize the derivational power that the fixed-point rule adds to the purely equational part Mil$^-$ of Mil. We do so by means of a coinductive rule that permits cyclic derivations that consist of a finite process graph with empty steps that satisfies the layered loop existence and elimination property LLEE, and two of its Mil$^{-}$-provable solutions. With this rule as replacement for the fixed-point rule in Mil, we define the coinductive reformulation cMil as an extension of Mil$^{-}$. In order to show that cMil and Mil are theorem equivalent we develop effective proof transformations from Mil to cMil, and vice versa. Since it is located half-way in between bisimulations and proofs in Milner's system Mil, cMil may become a beachhead for a completeness proof of Mil. This article extends our contribution to the CALCO 2022 proceedings. Here we refine the proof transformations by framing them as eliminations of derivable and admissible rules, and we link coinductive proofs to a coalgebraic formulation of solutions of process graphs.

Robust Subgroup Multisignature with One-Time Public Keys in Order

Robust subgroup multisignature allows any subgroup of signers from a global set to sign a given message on behalf of the whole group, and the individual signatures should be verified before the combination process, which resists poison signature attacks. An emerging application of robust subgroup multisignatures in blockchain is that a qualified subgroup of a global set of users has reached agreement. In the integrated blockchain and edge computing system, the edge server can naturally act as a combiner in multisignatures and help other end devices produce the final aggregate signature. In this paper, we propose a robust subgroup multisignature with one-time public keys in order that has two advantages for solving the signers ordering problem and one-time public key problem simultaneously. Our scheme is a nontrivial extension of Galindo et al.’s robust subgroup multisignature scheme and can be proven unforgeable, robust and chronological in random oracles. Our scheme can also be suitable for the consortium blockchain by adding a noninteractive zero-knowledge (NIZK) proof system for certifying the one-time public keys.

Structural Rules in Natural Deduction with Alternatives

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction.