## IA174 Fundaments of Cryptography

Faculty of Informatics
Autumn 2024
Extent and Intensity
2/0/1. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. RNDr. Petr Novotný, Ph.D. (lecturer)
RNDr. Antonín Dufka (assistant)
RNDr. Ján Jančár (assistant)
Mgr. Jan Kvapil (assistant)
RNDr. Vojtěch Suchánek (assistant)
Mgr. Marek Sýs, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Petr Novotný, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Tue 17. 9. to Tue 10. 12. Tue 16:00–17:50 A217
Prerequisites
Grasp of basic concepts from discrete mathematics (e.g. groups, see the MB154 and MV008 courses). Awareness of basic aims and building blocks of cryptography, corresponding to the respective parts of the PV080 course.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 31 fields of study the course is directly associated with, display
Course objectives
The course covers theoretical foundations of cryptography. We will learn why are the state-of-the-art cryptographic algorithms constructed in the way they are, and how to reason about their mechanics and security guarantees via the language of mathematics.
Learning outcomes
Upon a successful completion of the course, the student will be able to:
*Explain and understand the mechanics of basic primitives of both symmetric and asymmetric cryptography, including the underlying mathematics.
*Explain and understand the function, construction, and the use of cryptographic hash functions.
*Explain and understand cryptographic techniques for ensuring data authenticity and integrity, including digital signature schemes.
*Understand possible weaknesses of cryptosystems and various trade-offs in their design.
*Analyse weaknesses of simple cryptosystems.
Syllabus
• Symmetric cryptography:
• *Symmetric block ciphers: design principles and basic notions (boolean functions, random permutations, confusion, diffusion, non-linearity); design of iterated block ciphers, rounds, key schedules; AES; modes of operations of block ciphers.
• *Symmetric stream ciphers: General principles, ChaCha cipher, relation to pseudorandom number generators.
• Asymmetric cryptography:
• *General principles and design elements, "reductions" to hard problems.
• *RSA algorithm: math foundations (modular arithmetic, multiplicative Z_n^x groups, Euler's theorem, Chinese remainder theorem, extended Euclidean algorithm); RSA encryption, possible attacks, relationship to integer factorization.
• *Cryptography based on discrete logarithm (DL): refresher of basic group theory; DL in (Z_n )^x groups, Diffie-Hellman key exchange, DSA; discrete logarithm on elliptic curve groups, elliptic curve cryptography, ECDSA.
• Cryptographic hash functions: Design principles, Merkle–Damgård construction, sponge construction, collision-resistant CHFs, Keccak CHF, attacks against CHFs.
• Authentication, signatures:
• *Message authentication codes (MACs): integrity, authenticity, construction from block ciphers, construction from hash functions; authenticated encryption, AEAD.
• *Digital signatures: non-repudiation, signature schemes (RSA, DSA, Schnorr), attacks against dig. signature schemes, blind signatures.
• *Integrity of data structures: hash trees, their use in Bitcoin.
• *Basics of post-quantum cryptography.
• *Zero-knowledge proofs.
Literature
• MENEZES, A. J., Paul van OORSCHOT and Scott A. VANSTONE. Handbook of applied cryptography. Boca Raton: CRC Press, 1997, xiii, 780. ISBN 0-8493-8523-7. info
Teaching methods
lecture, homework assignments
Assessment methods
homework assignments, final written exam
Language of instruction
English