Public Key Cryptography

Goals

• Motivate the need for public key crypto
• Analyze relationships amongst public-key related assumptions
• Explain how Diffie-Hellman key exchange works and what properties it does/does not provide
• Explain how to safely use the RSA trapdoor one-way function for encryption
• Evaluate TLS key exchange options

Motivation

• What are some limitations of a purely symmetric-key-based world?

Public Key Exchange

• How does Diffie-Hellman (DH) work?
• What are the various DH-related assumptions?
  • Which ones imply others?
  • Which is the easiest/hardest to break?
• What property does DH give us?
• What property does it fail to provide?

Public Key Encryption

• What’s the basic definition of security public key encryption?
  • Is that definition sufficient for real-world usage?

RSA

• What is the RSA assumption?
  • How does it relate to factoring?
• Is the RSA permutation (aka textbook RSA) IND-CPA secure?
• How should RSA be used for encryption in practice?

TLS

• What properties should a secure key exchange provide?
• What are three different DH key exchange options?
  • Which of these properties does each provide?