Topic
Computer-assisted proof
About: Computer-assisted proof is a research topic. Over the lifetime, 913 publications have been published within this topic receiving 22819 citations.
Papers published on a yearly basis
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Papers
TL;DR: A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.
Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.
4,261 citations
TL;DR: The first is constructed according to a simple rule; it consists of the number 01 repeated ten times as mentioned in this paper, and if one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1.
Abstract: The first is obviously constructed according to a simple rule; it consists of the number 01 repeated ten times. If one were asked to speculate on how the series might continue, one could predict with considerable confidence that the next two digits would be 0 and 1. Inspection of the second series of digits yields no such comprehensive pattern. There is no obvious rule governing the formation of the number, and there is no rational way to guess the succeeding digits. The arrangement seems haphazard; in other words, the sequence appears to be a random assortment of 0's and 1's.
691 citations
22 Jul 2013
TL;DR: This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant, using a comprehensive set of reusable libraries of formalized mathematics.
Abstract: This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries of formalized mathematics, including results in finite group theory, linear algebra, Galois theory, and the theories of the real and complex algebraic numbers.
411 citations
14 Aug 2011
TL;DR: It is argued that EasyCrypt is a plausible candidate for adoption by working cryptographers and its application to security proofs of the Cramer-Shoup and Hashed ElGamal cryptosystems is illustrated.
Abstract: We present EasyCrypt, an automated tool for elaborating security proofs of cryptographic systems from proof sketches-compact, formal representations of the essence of a proof as a sequence of games and hints. Proof sketches are checked automatically using off-the-shelf SMT solvers and automated theorem provers, and then compiled into verifiable proofs in the CertiCrypt framework. The tool supports most common reasoning patterns and is significantly easier to use than its predecessors. We argue that EasyCrypt is a plausible candidate for adoption by working cryptographers and illustrate its application to security proofs of the Cramer-Shoup and Hashed ElGamal cryptosystems.
331 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 3 |
| 2023 | 11 |
| 2022 | 23 |
| 2021 | 13 |
| 2020 | 7 |