1. Lecture 14 Public Key Cryptography and RSA

2. Summary principles of public-key cryptography principles of public-key cryptography RSA algorithm, implementation, security RSA algorithm, implementation, security distribution of public keys distribution of public keys public-key distribution of secret keys public-key distribution of secret keys Diffie-Hellman key exchange Diffie-Hellman key exchange Elliptic Curve cryptography Elliptic Curve cryptography

3. Public-Key Cryptography

4. Public-Key Cryptosystems Secrecy and Authentication Public-key schemes can be used for either secrecy or authentication, or both (as shown here). In this case, separate key pairs are used for each of these purposes. The receiver owns and creates secrecy keys, sender owns and creates authentication keys. This approach is unfeasible because of the computational cost of public-key schemes.

5. RSA Use  to encrypt a message M the sender: obtains public key of recipient PU={e,n} obtains public key of recipient PU={e,n} computes: C = M e mod n, where 0≤M<n computes: C = M e mod n, where 0≤M<n  to decrypt the ciphertext C the owner: uses their private key PR={d,n} uses their private key PR={d,n} computes: M = C d mod n computes: M = C d mod n  note that the message M must be smaller than the modulus n (block if needed)

6. Publicly Available Directory  can obtain greater security by registering keys with a public directory  directory must be trusted with properties: contains {name,public-key} entries contains {name,public-key} entries participants register securely with directory participants register securely with directory participants can replace key at any time participants can replace key at any time directory is periodically published directory is periodically published directory can be accessed electronically directory can be accessed electronically  still vulnerable to tampering or forgery

7. Public-Key Authority

8. Public-Key Certificates

9. Public-Key Distribution of Secret Keys  if have securely exchanged public-keys:

10. Hybrid Key Distribution  Yet another way to use public-key encryption to distribute secret keys is a hybrid approach in use on IBM mainframes  retain use of private-key KDC that shares secret master key with each user and  distributes session key using master key  A public-key scheme is used to distribute master keys especially useful with widely distributed users especially useful with widely distributed users  The addition of a public-key layer provides performance performance backward compatibility backward compatibility

11. Real Elliptic Curve Example Example of Elliptic Curves

12. Comparable Key Sizes for Equivalent Security Symmetric scheme (key size in bits) ECC-based scheme (size of n in bits)RSA/DSA (modulus size in bits) 56112512 801601024 1122242048 1282563072 1923847680 25651215360

13. References  William Stallings“Cryptography and Network Security”, 4/e,

14. See you at the Exams! jh