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Topics in Algebra: Cryptography WS2019

Professor Goulnara Arzhantseva and Dr Martin Finn-Sell

Where and When

Dienstag 09:45-12.15, Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock.

Mittwoch 09.45-11.15, Seminarraum 09, 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.

Current Schedule

Our pre and post Christmas schedule is below:

Assessment and permitted materials

Oral exam or written manuscript. We will post exam times here. The first oral exams will take place on January 30th 2020, between 13.15 and 18.15 in SR5, and January 31st between 9.00 and 13.30 also in SR5. Registration for the exam will take place between 1st January and 28th January 2020, please go to the student services centre to register. The second exam will take place on March 11th 2020 between 9.00 and 13.30 in Seminarraum 3. You can also register for this exam now at the student services centre.

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.

Lecture materials

The lecture materials are below:

Chapter 1, Chapter 2, Updated Annex to Chapter 2, Chapter 3, Comments on Complexity, Chapter 4, Annex to Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Comments on the Cayley-Bacharach Theorem.

Update (29th January 2020): We have made minor corrections to Chapters 1,2 and 4 and the Annex to Chapter 2. You will also find a proof of the Cayley--Bacharach theorem above.


The exercises for this course will appear during the course as we need them.

Exercise Sheet 0, Exercise Sheet 1, Exercise Sheet 2, Exercise Sheet 3, Exercise Sheet 4, Exercise Sheet 5

,Exercise Sheet 6.


Below you'll find some encrypted messages. Try to decrypt them!

Message 1, Message 2.