Related papers: Formal Verification of the Sumcheck Protocol
Formal verification of cyber-physical and robotic systems requires that we can accurately model physical quantities that exist in the real-world. The use of explicit units in such quantities can allow a higher degree of rigour, since we can…
In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
Assurance cases are often required as a means to certify a critical system. Use of formal methods in assurance can improve automation, and overcome problems with ambiguity, faulty reasoning, and inadequate evidentiary support. However,…
We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…
Formal verification of traditional algorithms are of great significance due to their wide application in state-of-the-art software. Timsort is a complicated and hybrid stable sorting algorithm, derived from merge sort and insertion sort.…
The paper examines decentralized cryptocurrency protocols that are based on the use of internal tokens as identity tools. An analysis of security problems with popular Proof-of-stake consensus protocols is provided. A new protocol,…
We present a new sumcheck protocol called Fold-DCS (Fold-Divide-and-Conquer-Sumcheck) for multivariate polynomials based on a divide-and-conquer strategy. Its round complexity and soundness error are logarithmic in the number of variables,…
We propose a new cryptographic task, which we call verifiable quantum secure modulo summation. Secure modulo summation is a calculation of modulo summation $Y_1+\ldots+ Y_m$ when $m$ players have their individual variables $Y_1,\ldots, Y_m$…
An event structure is a mathematical abstraction modeling concepts as causality, conflict and concurrency between events. While many other mathematical structures, including groups, topological spaces, rings, abound with algorithms and…
In this paper, we show a security engineering process based on a formal notion of refinement fully formalized in the proof assistant Isabelle. This Refinement-Risk Cycle focuses on attack analysis and security refinement supported by…
Insurance claims processing involves multi-domain entities and multi-source data, along with a number of human-agent interactions. Use of Blockchain technology-based platform can significantly improve scalability and response time for…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
In this paper we introduce a technique and a tool for formal verification of various quantum information processing protocols. The tool uses stabilizer formalism and is capable of representing concurrent quantum protocol, thus is more…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
We propose to analyse quantum protocols by applying formal verification techniques developed in classical computing for the analysis of communicating concurrent systems. One area of successful application of these techniques is that of…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
Current formal verification of security protocols relies on specialized researchers and complex tools, inaccessible to protocol designers who informally evaluate their work with emulators. This paper addresses this gap by embedding symbolic…