CSE 599 b : Cryptography ( Winter 2006 ) Lecture 12 : Public Key ( Asymmetric ) Encryption

One way to use Diffie-Hellman’s 1976 secret key exchange protocol is to create a key to be used in later rounds for symmetric encryption. This requires multiple rounds of communication. Rivest, Shamir, and Adleman in 1978 developed the one round communication scheme discussed earlier. Namely, in order for Bob to receive messages Bob produces an integer N = pq where p and q are primes of equal length and Bob also produces e relatively prime to φ(N) = (p− 1)(q− 1) and computes d = e−1 mod (p− 1)(q − 1). Bob publishes the public key (N, e) and retains d as his private key. Given messageM , Alice can then compute C = RSA(N,e)(M) = M e mod N and send C to Bob. Bob decrypts by computing C mod N since