Outline for February 20/22, 2002

Reading: §9.3-9.4, §10.2, §10.4.2-10.4.3, §10.5.1-10.5.1.1, §10.5.2, §10.6 except §10.6.2.2

1. Greetings and Felicitations
2. Puzzle of the day
3. Public-Key Cryptography
1. Basic idea: 2 keys, one private, one public
2. Cryptosystem must satisfy:
4. given public key, CI to get private key;
5. cipher withstands chosen plaintext attack;
6. encryption, decryption computationally feasible [note: commutativity not required]
1. Benefits: can give confidentiality or authentication or both
7. RSA
1. Provides both authenticity and confidentiality
2. Go through algorithm:
   Idea: C = M ^e mod n , M = C ^d mod n , with ed mod PHI ( n ) = 1.
   Proof: M ^{PHI( n )} mod n = 1 [by Fermat's theorem as generalized by Euler]; follows immediately from ed mod φ ( n ) = 1.
   Public key is ( e , n ); private key is d . Choose n = pq ; then φ ( n ) = ( p -1)( q -1).
3. Example:
   p = 5, q = 7; n = 35, PHI ( n ) = (5-1)(7-1) = 24. Pick d = 11. Then de mod PHI ( n ) = 1, so choose e = 11. To encipher 2, C = M ^e mod n = 2¹¹ mod 35 = 2048 mod 35 = 18, and M = C ^d mod n = 18¹¹ mod 35 = 2.
4. Example: p = 53, q = 61, n = 3233, PHI ( n ) = (53-1)(61-1) = 3120. Take d = 791; then e = 71. Encipher M = RENAISSANCE: A = 00, B = 01, ..., Z = 25, blank = 26. Then:
   M = RE NA IS SA NC Eblank = 1704 1300 0818 1800 1302 0426
   C = (1704)⁷¹ mod 3233 = 3106; etc . = 3106 0100 0931 2691 1984 2927
8. Cryptographic Checksums
1. Function y = h ( x ): easy to compute y given x ; computationally infeasible to compute x given y
2. Variant: given x and y , computationally infeasible to find a second x' such that y = h ( x' ).
3. Keyed vs . keyless
4. MD5, HMAC
9. Key Exchange
1. Needham-Schroeder and Kerberos
2. Public key; man-in-the-middle attacks
10. Cryptographic Key Infrastructure
1. Certificates (X.509, PGP)
2. Certificate, key revocation
3. Key Escrow
11. Digital Signatures