06: Public-key cryptography

Public-key cryptography. Key agreement. The Diffie-Hellman key agreement protocol. Elliptic curve cryptography. Ephemeral keys. ECDHE key agreement.

Symmetric Key Cryptography (secret key)

• do key = undo key

• eve shouldn't be able to guess k at all

How does Alice communicate k to Bob while keeping it secret from Eve?

Ralph Merkle Puzzle:

• alice makes moderately difficult puzzle, solved reveals independent random secret key k and ID
• Alice repeats step1 to generate a set of n puzzles p1... pn, which will wolve to keys k1... kn and IDs d1...dn
• Puzzle set it sent to Bob, he randomly picks puzzle pi and solves it --> ki and di
• Bob sends ID di to Alice
• Alice and Bob communicate securly with ki
• but how's this practical and prevent eve from guessing ki?

Asymmetric(Public) Key Cryptography (private Key)

• Key Pair:

  • do = PU
  • undo = PR (can't guess, and can't recover w\/ PU)

• alice, eve, bob = PU; bob = PR

• applications:

  • Encryption\/decryption(e.g.,R.SA)

  • Keyagreement\/exchange (e.g., Diffie-Hellman: DHE, ECDHE, etc)

  • Digital signatures(e.g., RSA, Elgamal, DSA, ECDSA, etc)

  • Advanced: secure\/homomorphic computation, zero-knowledge proofs, etc