A Whirlwind Tour of Cryptology

Kevin McCurley
IBM Almaden Research Center

Goals:

• some history
• description of the field
• identify mathematical activities
• identify some open problems

• Terminology
• What is information protection?
• Some Applications
• The role of mathematics
• Mathematical activities
• Mathematical activities (continued)
• Define security by characterizing adversary
• What does ``breaking'' mean?
• Cryptographic Milestones
• The birth of mathematical rigor
• Basics of encryption
• Shannon's approach to secrecy
• Emergence of public key cryptography
• Diffie-Hellman key exchange
• One way and collision-free functions
• Digital signatures Merkle, Diffie, Hellman
• Footnote from the parallel universe
• More cryptographic milestones
• Secret sharing
• Pseudorandom number generators
• Pseudo-random functions
• More cryptographic milestones
• Zero-knowledge proofs
• Zero knowledge example: Fiat-Shamir proof of identity
• Some open problems
• About this document ...