Summary: Public­Key Cryptography from Di#erent Assumptions
Benny Applebaum # Boaz Barak + Avi Wigderson #
November 7, 2009
Abstract
This paper attempts to broaden the foundations of public­key cryptography. We construct
new public key encryption schemes based on new hardness­on­average assumptions for natural
combinatorial NP­hard optimization problems. We consider the following assumptions:
1. It is infeasible to solve a random set of sparse linear equations mod 2, of which a small
fraction is noisy.
2. It is infeasible to distinguish between a random unbalanced bipartite graph, and such a
graph in which we ``plant'' at random in the large side a set S with only |S|/3 neighbors.
3. There is a pseudorandom generator in NC 0 where every output depends on a random
constant­size subset of the inputs.
We obtain semantically secure public key encryption schemes based on several combinations
of these assumptions with di#erent parameters. In particular we obtain public key encryption
from Assumption 1 on its own, yielding the first noisy­equations type public key scheme in
which the noise rate is higher than one over the square root of equations. We also obtain
public key encryption based on a combination of Assumptions 2 and 3. These are arguably
of more ``combinatorial''/``private­key'' nature than any assumptions used before for public
key cryptography. Our proof involves novel ``search to decision'' and ``search to prediction''

Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science

Collections: Computer Technologies and Information Sciences