Essays about: "Gröbner Bases"

Found 3 essays containing the words Gröbner Bases.

  1. 1. The cosmological polytope of the complete bipartite graph K_{2,n}

    University essay from KTH/Matematik (Avd.)

    Author : Erik Landin; [2023]
    Keywords : Polytopes; Cosmological polytopes; Gröbner bases; Graphs; Polytop; Kosmologiska polytop; Gröbner baser; Grafer;

    Abstract : A cosmological polytope of an undirected connected graph is a lattice polytope which when the graph is interpreted as a feynman diagram can be used to calculate the contribution of that feynman diagram to the wavefunction of some cosmological models. This contribution can be calculated using the canonical form of the cosmological polytope, which can be computed by taking the sum of the canonical forms of the facets of a subdivision of the cosmological polytope. READ MORE

  3. 2. How is Polly? Revisiting the Differential Attack on Polly Cracker after 20 years

    University essay from Lunds universitet/Matematikcentrum

    Author : Christoph Strobl; [2022]
    Keywords : Gröbner Bases; polly cracker; differential attack; asymmetric cryptography; multivariate cryptography; public-key cryptography; Mathematics and Statistics; Technology and Engineering;

    Abstract : För att skapa nya krypteringsalgoritmer är man alltid på jakt efter svårlösta matematiska problem. Men är alla problem lämpliga? Uppsatsen behandlar Gröbnerbaser över ändliga kroppar och visar att de är inte lämpliga för att bygga säkra krypteringsalgoritmer. READ MORE

  4. 3. A Gröbner basis algorithm for fast encoding of Reed-Müller codes

    University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Author : Olle Abrahamsson; [2016]
    Keywords : Gröbner basis; error correcting codes; coding theory; algebra; Reed-Müller; Gröbnerbas; felrättande koder; kodningsteori; algebra; Reed-Müller;

    Abstract : In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. READ MORE