Cryptography I

elective monographs

Algorithms and data structures 1000-213bASD
Discrete mathematics 1000-212bMD
Foundations of mathematics 1000-211bPM
Geometry with linear algebra 1000-211bGAL
Languages, automata and computations 1000-214bJAO
Mathematical analysis for computer science I 1000-211bAM1
Mathematical analysis for computer science II 1000-212bAM2
Probability theory and statistics 1000-213bRPS

Computability Theory 3800-KOG-MS1-TO
Information theory 1000-2N03TI
Security of computer systems 1000-215bBSK

Basic knowlege of the discreete mathematics and probability theory.

The course provides an introduction to modern cryptography, focusing on the CS foundations of the field. We present the most essential cryptographic techniques used today to secure digital communications. Particular emphasis is placed on formal security analysis and understanding its assumptions. The last few lectures are devoted to an introduction to more advanced aspects of cryptography. These topics will be deepened in the subject "Cryptography 2", to which the subject "Cryptography 1" is an introduction.

1. Introduction to cryptography

2. Symmetric encryption

3. Hash functions and message authentication

4. Introduction to public key cryptography

5. Introduction to number theory and algebra

6. Public key encryption

7. Signature schemes

8. Informal introduction to advanced cryptographic protocols (commitment schemes, interactive and zero-knowledge proofs, secure multiparty computations)

• Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography

• Dan Boneh and Victor Shoup A Graduate Course in Applied Cryptography

• Doug Stinson Cryptography Theory and Practice, Third Edition

• Stefan Dziembowski, slides from the web-page http://www.crypto.edu.pl/teaching/

Knowledge

1. Has knowledge about basics and main problems of modern cryptography.

2. Knows graph of implications between main cryptographical hipotesis.

3. Knows basis of the history of cryptography.

Skills

1. Can analyze security of cryptophical protocols.

2. Can propose safe and secure protocol to actual problem.

Competence

1. Understands the need for proving facts in cryptography.

2. Knows the limits: what is and what is not possible.

3. Can assess the suitability of various cryptographical protocols.

2024: To pass the course, you must pass the exercises and the exam.

To pass the exercises, you must :

• deliver homework and

• pass the mid-term exam

The passing of the exercises is decided by the instructor.

The exam is conducted in written form.

Both the mid-term exam and the exam will consist of two parts:

1. testing knowledge (no materials such as notes and books will be allowed on it)

2. testing skills (without the above restriction)

The final grade for the course will be determined (on the first date) based on the weighted average of the mid-term exam (50%) and the exam results (50%).

Lecture and exercise instructors may decide to increase the grade for particularly active students.