Pseudorandomness & Proof by Reduction

Goals

• Learn how to capture security notions via “games”
• Master the definition of PRF security
• Begin to master proofs of security by reduction

Secrecy and Definitions

• Can we use pseudorandom functions/permutations to bypass the “bad news” theorem?

• How do we bypass the “bad news” theorem in practice?

• What is an indistinguishability game?
• How is PRF security defined?
  • How can we sanity check the definition?
• How does the PRP security definition differ from that of PRF security?

Proofs

• What constitutes a valid proof?
• What is the structure of a typical proof by contradiction?

Security Proofs

• How do we prove that a crypto construction is secure?
  • How does reduction play a role?