NDLI: Public-key cryptography from different assumptions

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Public-key cryptography from different assumptions

Content Provider	ACM Digital Library
Author	Barak, Boaz Applebaum, Benny Wigderson, Avi
Abstract	This paper attempts to broaden the foundations of public-key cryptography. We construct new public-key encryption schemes based on new hardness-on-average assumptions for natural combinatorial NP-hard optimization problems. We consider the following assumptions: It is infeasible to solve a random set of sparse linear equations mod 2, of which a small fraction is noisy. 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. There is a pseudorandom generator in NCz where every output depends on a random constant-size subset of the inputs. We obtain semantically secure public key encryption schemes based on several combinations of these assumptions with different parameters. In particular we obtain public key encryption from Assumption~1 on its own, yielding the first noisy-equations type public key scheme in which the noise rate is higher than one over the square root of the number of equations. We also obtain public-key encryption based on a combination of Assumptions~2 and~3. These are arguably of more "combinatorial"/"private-key" nature than any assumptions used before for public-key cryptography. Our proof involves novel "search to decision" and "search to prediction" reductions for sparse noisy linear equations. The strength of our assumptions raise new algorithmic and pseudorandomness questions (and new parameters for old ones). We give some evidence for these assumptions by studying their resistance to certain classes of natural algorithms, including semi-definite programs, ACO circuits, low-degree polynomials, and cycle counting. We also relate our assumptions to other problems such as planted clique and learning juntas.
Starting Page	171
Ending Page	180
Page Count	10
File Format	PDF
ISBN	9781450300506
DOI	10.1145/1806689.1806715
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-06-05
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Learning juntas 3lin Expander graphs Learning parity with noise Public key cryptography Nc0 Densest subgraph problem
Content Type	Text
Resource Type	Article

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