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CSE 331: Introduction to Networks and Security

CSE 331: Introduction to Networks and Security. Encrypted Knock Knock. Fall 2001 Instructor: Carl A. Gunter. ElGamal. Similar to Diffie-Hellman, but provides for encryption of a message M. Start as with Diffie-Hellman. Select and share the public information

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CSE 331: Introduction to Networks and Security

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  1. CSE 331: Introduction to Networks and Security Encrypted Knock Knock Fall 2001 Instructor: Carl A. Gunter

  2. ElGamal • Similar to Diffie-Hellman, but provides for encryption of a message M. • Start as with Diffie-Hellman. • Select and share the public information • Select a prime number q and a primitive root  of this prime. • Compute the private and public keys. • Alice chooses XA < q at random and takes YA to be **XA mod q. • Bob chooses XB < q at random and takes YB to be **XB mod q.

  3. ElGamal Encryption • Alice wishes to send the encryption of a message M to Bob. • Represent M as a number M < q. • Choose random r such that 1<=r<q. • Let R = YB**r mod q. • Let  = **r mod q. • Let  = R*M mod q. • The encrypted message is (, ).

  4. ElGamal Decryption • To decrypt: • **XB = (**r)**XB = (**XB)**r = (YB)**r  R (mod q) • *R-1 = (R*M)*R-1  M (mod q)

  5. EKK • Encrypted Knock! Knock! (EKK) uses ElGamal and DES. • It provides confidential channels without authentication. • Protocol notation: • Alice -> Bob: How are you? • Bob -> Alice: Ok, and you? • Alice -> Bob: Not bad, have a nice day! • Bob -> Alice: You too!

  6. EKK Set Up • Advanced setup: prime q and primitive root  where q is more than 64 bits. • Client C (you) and server S select key pairs (XC, YC) and (XS, YS) as in ElGamal/Diffie-Hellman.

  7. EKK Overview • Client initiates protocol with “Knock! Knock!” message and its public key YC. • Server responds with “Who’s there?”, its public key YS, and DES key K, encrypted using ElGamal. • Client responds with first part of joke encrypted using DES and key K. • Server plays along, using DES encryption with K.

  8. EKK Example • C->S: Knock! Knock! YC. • S->C: Who’s there? YS, (, ). • C->S: E(K, Boo!). • S->C: E(K, Boo! Who?). • C->S: E(K, Don’t cry, this will be easy!). • S->C: E(K, Don’t waste server time, connection closed.).

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