1. Optimal Asymmetric Encryption based on a paper by Mihir Bellare and Phillip Rogaway Team Members  Chris Kellogg  Doug Wagers  Angela Johnston  Kris Anupindi

2. Overview  Introduction  Review RSA  Optimal RSA Encryption Scheme  Run Example Program  Why Should We Use Optimal RSA?  Conclusion

3. Introduction What is Optimal RSA?

4. RSA Review Public Key : pair (e, n) Private Key : pair (d, n) Message : M Encryption : M e mod n Decryption : M d mod n

5. Optimal RSA Encryption Scheme Terminology  f : RSA encryption function  x : binary message of bit length 352 (512-160)  G() : Generator function (160 bits -> 352 bits)  H() : Hash function (352 bits -> 160 bits)

6. Optimal RSA Encryption Scheme Encryption 1. r : Pseudo-Random number of bit length 160 2. s : x  G(r) (352 bits) 3. t : r  H(s) (160 bits) 4. w : s concat t (512 bits) 5. y : f(w)

7. Optimal RSA Decryption Scheme Decryption 1. w : f -1 (y) (512 bits) 2. s : the first 352 bits of w 3. t : the last 160 bits of w 4. r : t  H(s) (160 bits) 5. x : s  G(r) (352 bits)

8. Why should we use Optimal RSA? Efficiency  RSA Encryption is the largest factor in Optimal RSA’s running time.  The Hash Function, the Generator Function, and the Pseudo-Random Generator should have a much lower running time  Thus, Optimal RSA is basically as efficient as RSA Security  The Pseudo-Random generator increases security  Every part of w is required to recover the message

9. Semantic Security Must have all of w to recover the message Must recover everything in a specific order.

10. Project Demo

11. Conclusion Should have “ideal” G & H functions.