Introduction to cryptography

I teach Introduction to cryptography [NDMI100] in the summer semester of 2024/2025. The lecture will cover the basics of both theoretical and practical cryptography, focusing on protocols currently used on the Internet.

Lectures will be on Tuesdays from 14:00 in S5.

If you want to consult anything, please write an e-mail to mares+kry@kam.mff.cuni.cz and we will discuss possibilities.

date topics recording
18. 2. Cryptographic primitives: symmetric and asymmetric ciphers, hash functions, random generators. Protocols and roles. Kerckhoffs principle. Simple protocols: multi-party communication, signatures (symmetric and asymmetric) hybrid ciphers, challenge-response authentication. Designing an auction protocol: padding, nonces, sequence numbers, signatures, session IDs. Basic types of cryptographic attacks. Security level.
Exercise: How to toss a coin over a phone call? 		video
25. 2. Different kinds of "Birthday attacks". One-time pad and Vernam's cipher. Perfect security and its limits. Secret sharing and threshold schemes (Shamir's construction with polynomials). video
4. 3. Introduction to symmetric ciphers. Block ciphers: trivial examples, an attempt to define security. General constructions: iterated ciphers, substitution-permutation networks, Feistel networks. DES: history, structure, critique, work-arounds (3-DES). AES a.k.a. Rijndael: history, structure, critique.
Exercise: Why is the security level of 2-DES only 57 bits?
Further reading:: EFF DES cracker, details of AES, Serpent (another AES finalist), Twofish (another one). 		video (blurred)
11. 3. How to (mis)use a block cipher: padding, modes ECB, CBC, CTR, OFB. Padding oracle attacks on CTR and CBC. Information leaks in CBC and CTR modes. Ciphertext stealing in ECB mode (see here for CBC version). Stream cipher sketches: LFSR-based constructions, eSTREAM project, Trivium, ChaCha20.
Illustrations: Block cipher modes (plaintext, ECB, CBC), visual secret sharing (layer 1, layer 2, both layers put together), 		video
18. 3. Hash functions: requirements, Merkle-Damgård construction by iterating compression function, length extension attacks. Birthday attacks on hash functions: the tortoise, the hare, and the turtle. How to obtain a compression function: Davies-Meyer construction from a block cipher. Practical hash functions: MD5 (broken), SHA1 (broken), and the SHA2 family. video
25. 3. No lecture today, but please watch recordings from 2020: part 1 (from 1:20:00 to the end), part 2, part 3 (from start to 32:00). Sponge hashes: analysis for random permutations, Keccak, SHA3-n, SHAKE-n. Parallel hashing: Merkle trees and Sakura. Symmetric signatures (MACs): construction from hash functions (KMAC and HMAC), different ways of combining a MAC with a cipher. CBC-MAC. Information-theoretic MAC from 2-independent linear functions or from polynomials. Practical polynomial MACs: GCM mode, Poly1305 (sketch).
1. 4. Generating random bits: pseudo-random generators from symmetric ciphers, physical randomness (LavaRand, circular oscillators, …), combining both – Fortuna, RDRAND, /dev/random. Putting all symmetric cryptography together: a secure channel. Basics of algorithmic number theory: Complexity of arithmetics. Euclid's algorithm and Bézout's coefficients. Multiplicative group modulo N. Little Fermat's and Euler's theorem. Lagrange's theorem on subgroups (without proof). video
8. 4. More number theory: Chinese remainder theorem and its constructive version. Computing Euler's function. Factoring vs. primality testing. Fermat and Rabin-Miller tests (R-M without proof), Carmichael numbers, note on Agarwal's deterministic test. Generating large primes. Multiplicative group is cyclic, discrete logarithms, how to find a generator. Discrete square roots, Euler's criterion. video
15. 4. RSA cipher: Definition, correctness, acceleration tricks. Properties of RSA: swapping roles of keys, commutativity, homomorphism with respect to multiplication (application: blind signatures). Attacks: short messages, small secret exponent, meet in the middle, similar primes, similar messages, multiple keys with the same modulus, same message and multiple keys, effects of computation errors. RSA padding and a note on Bleichenbacher attack. Semantic security: RSA preserves Jacobi symbol, but determining the lowest-significant bit or the half of the interval is hard. video
22. 4. Diffie-Hellman key exchange, signing the result/transcript, quadratic residues, problems with subgroups, DH in general groups. ElGamal cryptosystem and its derivation from DH. Elliptic curves over reals and over finite fields (sketch only). Asymmetric signatures: attack types, signatures using RSA, hashing is essential.
Further reading on elliptic curves: blog post series by Andrea Corbellini, the SafeCurves project. 		video
29. 4. Plan: Putting bits together: secure channel protocol, forward security. Implementation issues: how to not develop software, real-world attacks, various kinds of side channels, storing and destroying secrets. Lessons from physical security.

Sources

This page is maintained by Martin Mareš