Elements of Cryptography and Coding Theory
General data
| Course ID: | 0600-MS1-2KTK | Erasmus code / ISCED: |
11.104
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(unknown)
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| Course title: | Elements of Cryptography and Coding Theory | Name in Polish: | Elementy kryptografii i teorii kodowania |
| Department: | (in Polish) Zakład Algebry | ||
| Course groups: |
(in Polish) 2 rok 1 stopnia sem. zimowy Matematyka spec. Teoretyczna (in Polish) 3L stac. I st. studia matematyki - przedmioty obowiązkowe |
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| ECTS credit allocation (and other scores): |
4.00  view allocation of credits |
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| Language: | Polish | ||
| Type of course: | obligatory courses |
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| Requirements: | Elementary Number Theory 0600-MS1-1ETL |
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| Mode: | (in Polish) w sali |
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| Short description: |
Course objectives: Introduction to classical and modern cryptography. |
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| Full description: |
Course profile: academic Form of study: stationary Course type: obligatory Academic discipline: Mathematics, field of study in the arts and science: mathematics Year: 2, semester: 3 Prerequisities: Algebra I, Elementary Number Theory, Linear Algebra II lecture 15 h. exercise class 30 h. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. ECTS credits: 4 Balance of student workload: attending lectures15x1h = 15h attending exercise classes 7x4h + 2h(preliminary teaching) = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x3h = 21h consultations 5x1h = 5h small projects: preparation and defense 40h = 40h final work: preparation and take 10h + 2h = 12h Quantitative description Direct interaction with the teacher: 53 h., 2 ECTS Practical exercises: 117 h., 4 ECTS |
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| Bibliography: |
Rosen, Kenneth H., Elementary number theory and its applications. Third edition. Addison-Wesley Publishing Company, Advanced Book Program, |
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| Learning outcomes: |
Learning outcomes: Knowledge of elements of finite field algebra, linear algebra and number theory, which are needed to describe error-correcting codes and cryptosystems, among other things, knowledge of base-b representation (especially binary and hexadecimal expansions), ability of conversion between two different base-b representations, ability of the use of the extended Euclidean algorithm, ability of the use of modular exponentiation, ability to find inverses of the ring Z/mZ, ability to solve systems of linear congruences.K_W04, K_W05, K_W06, K_U01, K_U02, K_U03 Knowledge of chosen cryptosystems (symmetric ones and asymmetric ones): ability to encript and decript messages.K_U29, K_U25, K_U17, K_U11 Knowledge of basic definitions and properties of block codes. K_U29, K_U25, K_U17, K_U06 Knowledge of notions: linear codes, encoding and decoding information..K_U29, K_U25, K_U17, K_U16 Uzyskuje metodologiczne podstawy do pogłębiania wiedzy o metodach kodowania informacji i problemów z tym związanychK_K01, K_K02, K_K06 |
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| Assessment methods and assessment criteria: |
The overall form of credit for the course: test |
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Classes in period "Academic year 2017/2018" (past)
| Time span: | 2017-10-01 - 2018-06-30 |
 
 see course schedule |
| Type of class: |
Class, 30 hours more information Lecture, 15 hours more information |
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| Coordinators: | Izabela Malinowska | |
| Group instructors: | Izabela Malinowska | |
| Students list: | (inaccessible to you) | |
| Examination: | Grading | |
| Type of course: | obligatory courses |
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| Requirements: | Elementary Number Theory 0600-MS1-1ETL |
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| Mode: | (in Polish) w sali |
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| Short description: |
(in Polish) Założenia i cele przedmiotu: Wprowadzenie do klasycznej i współczesnej kryptografii. | |
| Full description: |
(in Polish) Podzielność i reprezentacja liczb całkowitych, systemy liczbowe. Rozszerzony algorytm Euklidesa. Kongruencje i elementy odwrotne w pierscieniu Z/mZ, efektywny algorytm obliczania potęg w pierscieniu Z/mZ. Układy kongruencji liniowych: metody rozwiązywania. Systemy kryptograficzne symetryczne i asymetryczne. Ważne klasy szyfrów: szyfry podstawieniowe, przestawieniowe, afiniczne, Vigenera, Hilla i ich kryptoanaliza Szyfry blokowe Szyfr RSA. Szukanie błędów, poprawianie i dekodowanie | |
| Bibliography: |
(in Polish) Lindsey N. Childs, A concrete introduction to higher algebra, Springer-Verlag 2000 Johannes A. Buchmann, Wprowadzenie do kryptografii, Wydawnictwo Naukowe PWN, Warszawa 2006. William J. Gilbert, W. Keith Nicholson, Algebra współczesna z zastosowaniami, Wydawnictwa Naukowo-Techniczne Warszawa 2008. Koblitz Neal, Wykład z teorii liczb i kryptografii, Springer-Verlag, WNT Warszawa 2000. Rosen, Kenneth H., Elementary number theory and its applications. Third edition. Addison-Wesley Publishing Company, Advanced Book Program, Stinson Douglas R., Kryptografia w teorii i praktyce, WNT, Warszawa 2005 | |
| Notes: |
(in Polish) Obecność na zajęciach jest obowiązkowa. Nieobecność na 20% zajęć może być podstawą do niezaliczenia przedmiotu. Zaliczenie przedmiotu wymaga zaliczenia wszystkich sprawdzianów oraz aktywnego uczestnictwa w ćwiczeniach: dobrego rozwiązywania zadań w czasie ćwiczeń, pomysłowości w poszukiwaniu rozwiązań. Przewidziane są 2 kolokwia w semestrze. Listy zadań są wysyłane kilka dni przed ćwiczeniami. | |
Classes in period "Academic year 2018/2019" (future)
| Time span: | 2018-10-01 - 2019-06-30 |
see course schedule |
| Type of class: |
Class, 30 hours more information Lecture, 15 hours more information |
|
| Coordinators: | (unknown) | |
| Group instructors: | (unknown) | |
| Students list: | (inaccessible to you) | |
| Examination: | Grading |
Copyright by University of Bialystok.