Mathematics for Cryptology
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
MI-MKY | Z,ZK | 4 | 3P+1C | Czech |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Information Security
- Synopsis:
-
Students will become acquainted with mathematics necessary to understand the methods of asymmetric cryptography, quantum cryptography and quantum computing.
- Requirements:
-
Good knowledge of algebra, linear algebra and basics of number theory (BI-LIN, BI-ZDM, MI-MPI).
- Syllabus of lectures:
-
1. Algebra - Group, ring, field, vector space, extended finite fields and their bases
2. Discrete logarithm - Diffie-Hellman key exchange, ElGamal, Babystep-giantstep algorithm, Pollard rho-method, Pohling-Hellman algorithm, Index calculus
3. Elliptic curves - elliptic curves over reals and over Galois fields, factorization with elliptic curves, MOV algorithm
4. Quantum computing - Quantum mechanics basics, operations with qubits, Deutsch and Deutsch-Jozsa algorithm, quantum Fourier transform, Shor's algorithm - factorization and solution to DLP on a quantum computer
- Syllabus of tutorials:
-
Examples of various mathematical structures will be discussed.
- Study Objective:
- Study materials:
-
1. Hoffstein, Pipher, Silverman - An Introduction to Mathematical Cryptography
2. Lidl, Nierreiter - Finite Fields, Encyclopedia of Mathematics and its
applications
3. Nielsen, Chuang - Quantum Computation and Quantum Information
- Note:
- Further information:
- https://courses.fit.cvut.cz/MI-MKY/
- No time-table has been prepared for this course
- The course is a part of the following study plans: