Optimal Asymmetric Encryption
based on a paper by Mihir Bellare and Phillip Rogaway
Team Members
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


Chris Kellogg
Doug Wagers
Angela Johnston
Kris Anupindi
Overview
 Introduction
 Review RSA
 Optimal RSA Encryption Scheme
 Run Example Program
 Why Should We Use Optimal RSA?
 Conclusion
Introduction
What is Optimal RSA?
RSA Review
Public Key : pair (e, n)
Private Key : pair (d, n)
Message : M
Encryption : Me mod n
Decryption : Md mod n
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)
Optimal RSA Encryption Scheme
Encryption
1.
2.
3.
4.
5.
r : Pseudo-Random number of bit length 160
s : x  G(r)
(352 bits)
t : r  H(s)
(160 bits)
w : s concat t
(512 bits)
y : f(w)
Optimal RSA Decryption Scheme
Decryption
1.
2.
3.
4.
5.
w : f -1 (y)
(512 bits)
s : the first 352 bits of w
t : the last 160 bits of w
r : t  H(s)
(160 bits)
x : s  G(r)
(352 bits)
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
Semantic Security
• Must have all of w to recover the
message
• Must recover everything in a specific
order.
Project Demo
Conclusion
• Should have “ideal” G & H
functions.