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Cryptography WS 2016/2017
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Expected previous knowledge
You should have a rough idea of the definition of the following terms:
- group, field, modular arithmetic
- discrete probability space, uniform distribution, random variable, stochastic independence, event, conditional probability,
- Turing machine, nondeterminism, polynomial time, P, NP
Preliminary outline
- Theoretical foundations of cryptography
- Perfect secrecy
- Computational security (w.r.t. probabilistic polynomial-time adversaries)
- Attacks: eavesdropping, chosen-plain-text (CPA), chosen-cipher-text (CCA1/2)
- Cryptographic primitives:
- Pseudorandomness: Generators (PRG), functions (PRF), (strong) permutations (PRP) as abstractions of secure blockciphers
- One-way functions (OWF) and permutations (OWP) (with trapdoor information (TDP))
- Cryptographic hash functions: collision resistance, Merkle-Damgård construction, Sponge construction (Keccak/SHA3), birthday paradox
- Relations between cryptographic primitives
- Relation to complexity theory (P vs NP)
- Private-key encryption and message-authentication codes (MACs)
- Blockciphers (''practical PRFs/PRPs'')
- DES, AES
- Construction principles underlying blockciphers: Feistel networks, substitution-permutation networks
- Construction of secure encryption schemes from PRFs/PRPs
- Modes of operation: randomized-counter (rCTR) mode, output-feed-back (OFB) mode, cipher-block-chaining (CBC) mode
- Tweakable blockciphers: XEX-mode
- Construction of secure MACs from PRFs
- Domain-extension of PRFs, NMAC, HMAC
- Public-key encryption and signatures
- Algebraic and number theoretical foundations
- Factoring and the RSA problem, trapdoor one-way permutations
- Discrete logarithm and the computational and decisional Diffie-Hellman (CDH/DDH) problems, elliptic curves
- Diffie-Hellman key exchange
- Public-key encryption schemes:
- Based on the RSA problem: RSA PKCS #1 v1.5, RSA-OAEP
- Based on the DDH problem: El Gamal, hashed Diffie-Hellman
- Hybrid encryption: Diffie-Hellman key exchange as key-encapsulating mechanism (KEM)
- (Lattice based)
- Digital signature schemes:
- Related to the RSA problem: RSA-FDH, RSA-PSS
- Related to the discrete logarithm: El Gamal's signature scheme, DSA
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Contact
Teaching
