elliptic curve

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Today I finally submitted my diploma thesis. :) It is titled Mathematical Foundations of Elliptic Curve Cryptography and contains the following topics:

  • A short introduction to algebraic curves (including Riemann-Roch, but without proofs);
  • some parts of the general theory elliptic curves (including basics about the Tate module and the Weil and Tate pairings);
  • elliptic curves over the complex numbers;
  • elliptic curves over finite fields (Weil conjectured for elliptic curves);
  • elliptic curves over local fields (and the canonical lift);
  • division polynomials;
  • modular polynomials (also over finite fields);
  • an introduction to elliptic curve cryptography;
  • point counting (SEA and Satoh’s algorithm);
  • cryptoanalysis: MOV/Frey-Rück, anomalous curve and Weil descent attacks
  • and some connections to elliptic divisibility sequences.

Now all that is left to do is to prepare for the diploma examination…

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