Essays about: "ändliga kroppar"

Found 5 essays containing the words ändliga kroppar.

  1. 1. The Abel-Ruffini Theorem : The insolvability of the general quintic equation by radicals

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Axel Sjöblom; [2024]
    Keywords : ;

    Abstract : This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. 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. Tensor Rank

    University essay from Matematik och tillämpad matematik; Tekniska högskolan

    Author : Elias Erdtman; Carl Jönsson; [2012]
    Keywords : generic rank; symmetric tensor; tensor rank; tensors over finite fields; typical rank; generisk rang; symmetrisk tensor; tensorrang; tensorer över ändliga kroppar; typisk rang;

    Abstract : This master's thesis addresses numerical methods of computing the typical ranks of tensors over the real numbers and explores some properties of tensors over finite fields. We present three numerical methods to compute typical tensor rank. READ MORE

  5. 4. A Design Study of an Arithmetic Unit for Finite Fields

    University essay from Institutionen för systemteknik

    Author : Ivar Tångring; [2003]
    Keywords : Datorteknik; ändliga kroppar; polynombas; aritmetik; aritmetisk enhet; ALU; systolisk; multiplikation; invertering; Datorteknik;

    Abstract : This thesis investigates how systolic architectures can be used in the implementation of an arithmetic unit for small finite fields of characteristic two with polynomial basis representation. Systolic architectures provide very high performance but also consume a lot of chip area. READ MORE

  6. 5. Computational Complexity of Finite Field Multiplication

    University essay from Institutionen för systemteknik

    Author : Nils-Hassan Quttineh; [2003]
    Keywords : Datorteknik; Finite Field; Multiplication; Complexity; Polynomial Bases; Normal Bases; Triangular Bases; Multiples.; Datorteknik;

    Abstract : The subject for this thesis is to find a basis which minimizes the number of bit operations involved in a finite field multiplication. The number of bases of a finite field increases quickly with the extension degree, and it is therefore important to find efficient search algorithms. Only fields of characteristic two are considered. READ MORE