1 / 7

ElGamal

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.

curtishoward
Download Presentation

ElGamal

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. 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 (, ).

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

  4. 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!

  5. 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.

  6. 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.

  7. 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.).

More Related