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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.
Last update: T_KA (04.05.2012)
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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 Last update: T_KA (04.05.2012)
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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.
Last update: T_KA (04.05.2012)
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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. Last update: Příhoda Pavel, doc. Mgr., Ph.D. (09.10.2012)
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