# TMA4160 Cryptography - Fall 2015

 Lecturer: Assistant: Schedule Kristian Gjøsteen Anna Vederhus Monday 15.15-17.00 EL4 R73 Wednesday 10.15-12.00 KJL4 R10 R73 Tuesday 10.15-11.00 KJL23 or Banachrommet (380B) Monday 13.15-14.00 848 in SBII December 5

## What you should know before taking the course

You should be familiar with basic abstract algebra such as groups, rings and fields.

It is helpful, but not required, to know something about computational complexity and the analysis of algorithms. Using a computer algebra system (or equivalent) is required for some of the exercises. Previous experience with computer algebra systems is helpful, but not required.

## Course material

Lecture notes:

• These notes follow the lectures fairly closely.

Main book:

Supplements:

## Messages

18/12: You can find the exam and proposed solution under Old exams. The grading is done, the grade distribution is A: 13, B: 6, C: 10, D: 4, E: 4, F:3.

There was no really difficult problem here, which is reflected in the grade distribution.

2c was the most difficult problem. Most of you did not realize that this is Pohlig-Hellman with most of the work already done. Some of you tried other approaches that worked. Many essentially used only one of the given equations (often dividing by 0 along the way), getting the wrong answer.

In 3a, it is not difficult to prove that an invertible matrix U exists, but some of you forgot to prove that it had integer entries.

3b was obviously somewhat challenging, but most of you realized that you needed to prove that decryption was correct, which is true if the input to the hash function during decryption is the same as during encryption.