SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Number field sieve - NMIB030
Title in English: Číselné síto
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: doc. Mgr. Pavel Příhoda, Ph.D.
Classification: Mathematics > Algebra
Interchangeability : NMMB531
Is incompatible with: NMMB531
Is interchangeable with: NMMB531
Annotation -
Last update: T_KA (04.05.2012)
The aim of the lecture is to expose the mathematical principles of the quadratic sieve and of the number field sieve which are used when factorizing large integers and when solving the discrete logarithm problem. To this purpose the relevant parts of algebraic number theory will be presented. An attention, while in a limited scale, will be paid to implementation aspects as well.
Literature -
Last update: T_KA (04.05.2012)

H. Cohen: A Course in Computational Algebraic Number Theory, Springer, 2000

The Development of the Number Field Sieve, (eds. A. K. Lenstra and H. W. Lenstra, Jr.) Lecture Notes in Mathematics 1554, Springer, 1993

M. Pohst, H. Zassenhaus: Algorithmic Algebraic Number Theory, Cambridge University Press, 1989

Syllabus -
Last update: T_KA (04.05.2012)

The aim of the lecture is to expose the mathematical principles of the quadratic sieve and of the number field sieve which are used when factorizing large integers and when solving the discrete logarithm problem. To this purpose the relevant parts of algebraic number theory will be presented. An attention, while in a limited scale, will be paid to implementation aspects as well.

Entry requirements - Czech
Last update: doc. Mgr. Pavel Příhoda, Ph.D. (09.10.2012)

Předpokládá se znalost základů komutativní algebry v rozsahu předmětu Komutativní okruhy a jednoduchých metod založených na Fermatově faktorizaci. Vše podstatné bude stručně zopakováno v průběhu přednášky.

 
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