## IA174 Fundaments of Cryptography

Fakulta informatiky
podzim 2024
Rozsah
2/0/1. 3 kr. (plus ukončení). Ukončení: zk.
Vyučováno kontaktně
Vyučující
doc. RNDr. Petr Novotný, Ph.D. (přednášející)
RNDr. Antonín Dufka (pomocník)
RNDr. Ján Jančár (pomocník)
Mgr. Jan Kvapil (pomocník)
RNDr. Vojtěch Suchánek (pomocník)
Mgr. Marek Sýs, Ph.D. (pomocník)
Garance
doc. RNDr. Petr Novotný, Ph.D.
Katedra teorie programování – Fakulta informatiky
Dodavatelské pracoviště: Katedra teorie programování – Fakulta informatiky
Rozvrh
Út 17. 9. až Út 10. 12. Út 16:00–17:50 A217
Grasp of basic concepts from discrete mathematics (e.g. groups, see the MB154 and MV008 courses) is required. Awareness of basic aims and building blocks of cryptography, corresponding to the respective parts of the PV080 course.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 31 mateřských oborů, zobrazit
Cíle předmětu
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.
Výstupy z učení
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.
Osnova
• 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.
Literatura
• MENEZES, A. J., Paul van OORSCHOT a Scott A. VANSTONE. Handbook of applied cryptography. Boca Raton: CRC Press, 1997, xiii, 780. ISBN 0-8493-8523-7. info
Výukové metody
lecture, homework assignments
Metody hodnocení
homework assignments, final written exam
Vyučovací jazyk
Angličtina
Informace učitele
https://www.fi.muni.cz/~xnovot18/IA174_student_info.html
Další komentáře
Předmět je vyučován každoročně.
Nachází se v prerekvizitách jiných předmětů
Předmět je zařazen také v obdobích podzim 2021, podzim 2022, podzim 2023.
• Statistika zápisu (nejnovější)