Cryptography 2010/2011

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Expected previous knowledge

You should have a rough idea of the definition of the following terms:

• group, field, ℤ/3ℤ
• 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, chosen-cipher-text
  • Cryptographic primitives:
    • Pseudorandom generators/functions/permutations
    • One-way functions and permutations (with trapdoor information)
    • Equivalence of cryptographic primitives
    • Relation to complexity theory (P vs NP, P vs UP)
    • Collision-resistant hash functions
      • Birthday paradox
  • ...
• Private-key encryption and message authentication codes (MACs)
  • Theoretical constructions using cryptographic primitives
    • stream cipher, block cipher
  • Practical constructions of block ciphers
    • Substitution-permutation Networks (AES)
    • Feistel networks (DES)
    • Tweakable block ciphers (XEX-mode)
  • Construction of MACs:
    • from pseudorandom functions
    • from collision-resistant hash functions using the Merkle-Damgard construction:
      • NMAC, HMAC
  • ...
• Public-key encryption and signatures
  • Diffie-Hellman key exchange
  • Algebraic and number theoretical foundations
    • Factoring, RSA-assumption, discrete logarithm, (elliptic curves)
    • Relation to cryptrographic primitives
  • Public-key encryption schemes:
    • RSA, El Gamal, Rabin
  • Signatures
  • ...