Optimal Asymmetric Encryption based on a paper by Mihir Bellare and Phillip Rogaway

1. Optimal Asymmetric Encryptionbased 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 : Me mod n Decryption : Md 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.