The Mathematics of Public-Key Cryptography, Lecture 1

September 12, 2000

Reference

• read chapter 1 of the textbook for background

Summary of material covered in lecture 1

• goals of cryptography
  • confidentiality
  • data integrity
  • data origin authentication
  • entity authentication
  • non-repudiation
• cryptographic tools
  • encryption schemes
  • hash functions
  • signature schemes, MACs
  • identification schemes
  • key establishment schemes
• security of a cryptosystem
  • attack model (for encryption schemes)
    • ciphertext only
    • known plaintext
    • chosen plaintext
    • chosen ciphertext
  • security level
    • unconditional security
    • "provable" security
      • reduction to underlying mathematical problem
      • random oracle model
    • computational security against sepcified attacks
  • goal of adversary (for encryption schemes)
    • complete break (find secret key)
    • decrypt some ciphertexts
    • determine partial information about plaintext, given ciphertext
• public-key and symmetric-key cryptosystems
  • notation for encryption schemes (P,C,K,E,D)
  • protocol for encryption and decryption for symmetric key schemes
  • shift cipher
  • concept of public-key scheme
  • RSA