Public Key Cryptography
This is much younger than other approaches and was first published in 1975. As we have discussed this has distinctive feature of only needing one key per individual/organization requiring encrypted authenticated messaging
It has nontrivial infrastructure to distribute the N public keys for N organizations but this is better than N2 keys for secret key cryptography
Roughly the public key is a very large number that is the product of two primes. The private key is (related to) one of these primes.
It is used differently in two cases which following foils do in detail
- Transmission over insecure network where one encodes with public key of receiver (and receiver decodes with his or her private key)
- Authentication where you encode your digital signature with your private key and receiver checks the signature with your public key -- only you can encode signature so it is correctly decoded with public key