Mathematics for Cryptology

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: