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diffie hellman and elgamal (diffie hellman goal (security (perfect forward…
diffie hellman and elgamal
problem
two parties must agree on the secret before hand
diffie hellman goal
objective
agree a secret in the face of an adversary but cannot modify
1) alice and bob choose secret numbers
2) alice computes public key A = g^a mod p
3) bob computes his public key B = g^b mod p
4) both parties exchange public keys and generate shared
secret S = g^ab = B^a = A^b mod p
security
no authentication of the remote party
attacker can substitute public keys for his own and decrypt and re-encrypt
perfect forward secrecy
diffie hellman keys discarded after sharing secret key
ElGamal
1) alice wants to send message m to bob
2) message is then mapped to number in the range
{1,...,p-1}
3) alice computes the share secret s=B^a
4) She then calculates: C = s . M and sends it along with her public key A to Bob.
5) Bob derives the shared secret (s = Ab) and then calculates the message with M = s^-1 . C