Public-Key Cryptography: a Mathematical Insight
summer semester

Language: English

Prerequisites (description): Basic knowlege of the probability theory, discrete mathematics and algebra. Basic knowledge of cryptographic protocols.

Brief description: The course focuses on the mathematics behind public-key cryptography. Several advanced cryptographic primitives will be analyzed and explained, including elliptic curves, lattices, and algebraic codes.

Full description
  1. Recap of Public-Key Cryptography (1-2 lectures)
    • Basic Protocols: Encryption, Signature etc.
    • Popular Schemes: RSA, El Gamal etc.
  2. Elliptic Curve Cryptography (3 lectures)
    • Introduction and Theory: Definition, Group Structure etc
    • Cryptographic Applications: El Gamal, ECDSA etc.
  3. Lattice-based Cryptography (4 lectures)
    • Introduction and Theory: Definition, Lattice Algorithms, LWE etc.
    • Cryptographic Applications: Regev's scheme, Signatures etc.
  4. Code-based Cryptography (4 lectures)
    • Introduction and Theory: Linear Codes, Algebraic Codes etc.
    • Cryptographic Applications: McEliece, Niederreiter, CFS etc.
  • Galbraith - "Mathematics of Public-Key Cryptography"
  • Stinson - "Cryptography Theory and Practice"
  • Washington - "Elliptic Curves, Number Theory and Cryptography"
  • Bernstein - "Post-Quantum Cryptography"
Learning outcomes:

The students will achieve an understanding of the main public-key cryptography protocols from a mathematical point of view. At the end of the course, they should know:
  • How these protocols work, and why they are secure.
  • How efficient these protocols are, and why.
  • What are the threats to currently used systems and possible solutions for the future.
The course will also serve as an excellent starting point for research, stimulating the students with questions and open problems.

Assessment criteria: written exam