Mathematics for Cryptology
- Department of Applied Mathematics
Students will become acquainted with mathematics necessary to understand the methods of asymmetric cryptography, quantum cryptography and quantum computing.
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
3. Nielsen, Chuang - Quantum Computation and Quantum Information
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Specialization System Programming, Presented in Czech, Version 2014, 2015 (elective course)
- Specialization Web Engineering, Presented in Czech, for Students who Enrolled in 2014 and 2015 (elective course)
- Knowledge Engineering, in Czech, Presented in Czech, for Students who Enrolled in 2015 (elective course)
- Master Informatics, Presented in Czech, Version for Students who Enrolled in 2015 (elective course)