- Greetings and Felicitations!
- Projects sent back; do you want me to post a list of names and projects?
- Midterm is Friday; open book, open notes; review session dueing discussion section

- Puzzle of the Day
- All about "impossibilities" ...

- DES
- Go through the algorithm

- Public-Key Cryptography
- Basic idea: 2 keys, one private, one public
- Cryptosystem must satisfy:
- given public key, CI to get private key;
- cipher withstands chosen plaintext attack;
- encryption, decryption computationally feasible [note: commutativity NOT required]

- Benefits: can give confidentiality or authentication or both

- Use of PKC
- Normally used as key interchange system to exchange secret keys (cheap)
- Then use secret key system (too expensive to use PKC for this)

- RSA
- Provides both authenticity and confidentiality
- Go through algorithm:

Idea:*C*=*M*^{e}**mod***n*,*M*=*C*^{d}**mod***n*, with*ed***mod**PHI(*n*) = 1.

Proof:*M*=*M*^{PHI(n)}**mod***n*= 1 [by Fermat's theorem as generalized by Euler]; follows immediately from*ed***mod**PHI(*n*) = 1.

Public key is (*e*,*n*); private key is*d*. Choose*n*=*pq*; then PHI(*n*= (*p*-1)(*q*-1). - Example:

*p*= 5,*q*= 7;*n*= 35, PHI(*n*) = (5-1)(7-1) = 24. Pick*d*= 11. Then*ed***mod**PHI(*n*) = 1, so choose*e*= 11. To encipher 2,*C*=*M*^{e}**mod***n*=*2*^{11}**mod***35*= 2048**mod***35*= 18, and*M*=*C*^{d}**mod***n*=*18*^{11}**mod***35*= 2. - 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

- Authentication
- validating client (user) identity
- validating server (system) identity
- validating both (mutual authentication)

- Basis
- What you know
- What you have
- What you are

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Send email to cs153@csif.cs.ucdavis.edu.

Department of Computer Science

University of California at Davis

Davis, CA 95616-8562