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Chair for Foundations of Software Reliability and Theoretical Computer Science
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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