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Topics in Algebra: Cryptography 2018

Professor Goulnara Arzhantseva and Dr Martin Finn-Sell

Where and When

Dienstag 09:45-12.15, Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock

Aims, contents and methods of the course

This introductory course is on selected chapters of modern cryptography. We discuss both classical and rather recent cryptographic topics. These include currently the most popular RSA (= Rivest-Shamir-Adleman) and ECC (= Elliptic Curve Cryptography) public-key cryptosystems as well as the use of cryptography in blockchain technology. Theoretical results are supported by exercises and concrete real life examples such as the discussion on security issues in WhatsApp and in the design of Bitcoin.

Assessment and permitted materials

Oral exam or written manuscript. The first oral exam will take place on January 31st 2019 in SR11 at 10.00am. Registration for the exam will take place between 1st January and 28th January 2019. The next exam will take place on October 9th 2019 at 13.15, in SR05.

Minimum requirements and assessment criteria

The course is open to students of all degrees (Bachelor, Master or PhD). The knowledge of the following fundamental concepts is required: groups, vector spaces, linear transformations, basics in number theory and probability.

Examination topics

Content of the lectures and exercises. You can find the exam questions below

Exam questions.

Topics to write a manuscript. It is also possible to write a manuscript on a topic of your own choosing, if you discuss this with Prof. Arzhantseva in advance. The deadline to choose a topic either through discussion or from the list is November 15th 2018.

Lecture materials

Chapter 1, Chapter 2, Annex to Chapter 2, Chapter 3, Annex to Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8.


Exercise Sheet 1, Exercise Sheet 2, Exercise Sheet 3, Exercise Sheet 4, Exercise Sheet 5, Exercise Sheet 6, Exercise Sheet 7, Exercise Sheet 8, Test Questions.

Please note, Exercise sheet 4 contains some remarks to clarify the discussions on Hasse's bound, and Exercise sheet 6 contains links to discussions on the notions of collision resistance for hash functions.