Lecture 9 - Key Agreement

Question 1

What is the purpose of Key Agreement protocols and what is a protocol?

Answer 1

To distribute the secret key securely over insecure communication channel (e.g. Internet).

A protocol specifies a sequence of communications to achieve a particular purpose (secret key exchange, authentication, etc.)

Question 2

What is the The Diffie-Hellman Protocol?

Answer 2

• A protocol for key agreement: Diffie-Hellman
• Some central authority chooses a function e() which has “good” mathematical properties
  
  • e(x)y = e(y)x for any x, y
  • Difficult to compute x from e(x)

1. Alice chooses a random value a, computes e(a)
2. Bob chooses a random value b, computes e(b)
3. Alice sends e(a) to Bob, Bob sends e(b) to Alice
4. Alice computes e(b)a , Bob computes e(a)b
5. The secret value is e(a)b = e(b)a

Question 3

What is the Security of Diffie-Hellman Protocol?

Answer 3

• By the property of e(.), e(a)b = e(b)a and Alice and Bob has agreed a common secret value, e(a)b
• What if someone eavesdrops the transmission?
  
  • Note that e() is public
  • Gets e(a), e(b), but nothing more
• One such function: e(x) = gx mod p for some “good” g and p
  
  • Difficult to obtain x given e(x)
  • Discrete logarithm problem

Question 4

Give some more about the Diffie-Hellman Protocol?

Answer 4

• No single party can specify the secret value
• The protocol can be expanded to three or more parties
• A public-key view of the protocol
  
  • a and b can be regarded as the private keys of Alice and Bob, respectively
  • e(a) and e(b) are the corresponding public keys
  • Only need to exchange the public key
  • Properties of e(): difficult to obtain private key from public key

Question 5

What is SKIP?

Answer 5

• Simple Key Management for Internet Protocols
• A standard for using Diffie-Hellman for key agreement

Question 6

What attack can occur on the Diffie-Hellman Protocol?

Answer 6

• There is no authentication: man-in-the-middle attack possible
• Alice and Bob think they share a secret key; in fact they share (separately) a key with Trudy
• Subsequent communication between Alice and Bob encrypted using the “agreed key” are intercepted, decrypted and re-encrypted by Trudy
• Solution: use signatures or other means to authenticate first