Mathematics for Cryptology
Code  Completion  Credits  Range  Language 

MIMKY  Z,ZK  4  3+1  Czech 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Applied Mathematics
 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 (BILIN, BIZDM, MIMPI).
 Syllabus of lectures:

1. Algebra  Group, ring, field, vector space, extended finite fields and their bases
2. Discrete logarithm  DiffieHellman key exchange, ElGamal, Babystepgiantstep algorithm, Pollard rhomethod, PohlingHellman 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 DeutschJozsa 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:
 No timetable 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)