RSA
by chosing large primes, it becomes very hard to factor the result
construct public and private keys, discard original primes
example for enc and dec
n = pq where p and q are primes
77 = 7*11
pub key (e,n)
priv key (d,n)
eg, e=7,d=43
c = m^(e)%n
m = c^(d)%n

m = 9 -> c = 9^(7)%77 = 37
c = 37 -> 37^(43)%77 = 9

hash function
transformation that takes a variable size input m an dreturns a fixed size string, called the hash value h = H(m), main role is in provision of digital sigs, for dig sig apps where a large message has to be "compressed" in a secure manner before being signed with the private key

how cryptographic hashes work
m -MD-> H(m) -RSA-> E[H(m)] -(concat crypto hash with original message)-> insecure network -> split to perceived message and crypto hash,E[H(m)], E -unRSA-> H(m), m' -(hash perceived message)-> H(m'), h - h' = m

to verify identity, enc token with B's public key, send to B, wait for response from B with correct token

3 way handshake
send id, encrypted token, secret key to server, responds with inc'd encrypted token and a new encrypted token along with handshake key, client responds with new token inc'd and secret key, server responds with encrypted handshake and shared key