Course topics

An introduction to applications of algebra and number theory in the field of cryptography. In particular, the use of elliptic curves in cryptography is studied in great detail.

  • Introduction to cryptography and in particular to public key systems, RSA, Diffie-Hellman, ElGamal.
  • Finite filelds, construction of all finite fields, efficient arithmetic in finite fields.
  • Elliptic curves, the group law of an elliptic curve, methods for counting the number of points of an elliptic curves over a finite field: Baby-step giant step, Schoof’s method.
  • Construction of elliptic curves based cryptographic systems.
  • Methods for prime decomposition, the elliptic curves method, the quadratic sieve method.
  • Safety of public key cryptographic methods.

Course Information

University course catalogue:
Advanced Undergraduate
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