Description:

Students will understand the mathematical foundations of cryptography and gain an overview of current cryptographic algorithms. They will be able to use cryptographic keys and certificates in systems based on them and learn the basics of safe use of symmetric and asymmetric cryptographic systems and hash functions in applications. Within labs, students will gain practical skills in using standard cryptographic methods with an emphasis on security and will also get acquainted with the basic procedures of cryptanalysis. Students are expected to be competent programmers in C/C++ (on a small scale). Basic Python knowledge is an advantage.

Contents:

1. Basic concepts in cryptology and computer security. Historical ciphers.
2. Exponential cipher, shared key establishment, and discrete logarithm problem.
3. Taxonomy of ciphers. Stream ciphers - RC4, A5/1, ChaCha20.
4. Block ciphers - 3DES, AES, Twofish. Operating modes of block ciphers.
5. Hash functions, SHA-x and HMAC.
6. Factorization problem, asymmetric cryptography, RSA, ElGamal.
7. Primality testing, Rabin-Miller test, key generation.
8. Security of cryptographic systems in terms of information theory and computational complexity.
9. Basics of elliptic curve cryptography.
10. Pseudorandom and true random number generators.
11. Quantum cryptography and post-quantum cryptography.
12. Public key infrastructure.
13. IT security.

Seminar contents:

1. Basics of modular arithmetic (repetition), historical ciphers.
2. Block ciphers (Hill, exponential cipher), Diffie-Hellman algorithm.
3. Stream ciphers. Hash functions.
4. Information theory (entropy, distance of uniqueness).
5. Block ciphers (AES), modes of operation.
6. Asymmetric cryptography (RSA, ElGamal).
7. Random number generators. Primality testing.
8. Use of cryptographic libraries.
9. Certificates. TLS encryption on the network.
10. Current trends in cryptography.

Recommended literature:

1. Padhye S., Sahu R. A., Saraswat V. : Introduction to Cryptography. CRC Press, 2018. ISBN 9781138071537.
2. Aumasson J.-P. : Serious Cryptography. A Practical Introduction to Modern Encryption. No Starch Press, 2017. ISBN 978-1593278267.
3. Rosen K. H. : Elementary Number Theory (5th Edition). Addison Wesley, 2004. ISBN 321237072.
4. Sadler T. L. : Cybersecurity for Everyone: Securing Your Home or Small Business Network. Signalman Publishing, 2014. ISBN 9781940145365.
5. Paar CH., Pelzl J. : Understanding Cryptography. Springer, 2009. ISBN 3642446498.

Keywords:

computer security, cryptography, cipher, hash, PKI, digital signature

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar