On Constructing Parallel Pseudorandom Generators from One-Way Functions

Pseudorandom generators with long stretch and low locality from random local one-way functions

Proceedings of the 44th symposium on Theory of Computing - STOC '12 ◽

10.1145/2213977.2214050 ◽

2012 ◽

Cited By ~ 12

Author(s):

Benny Applebaum

Keyword(s):

Pseudorandom Generators

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On linear-size pseudorandom generators and hardcore functions

Theoretical Computer Science ◽

10.1016/j.tcs.2014.06.013 ◽

2014 ◽

Vol 554 ◽

pp. 50-63 ◽

Cited By ~ 1

Author(s):

Joshua Baron ◽

Yuval Ishai ◽

Rafail Ostrovsky

Keyword(s):

Linear Size ◽

Pseudorandom Generators ◽

Hardcore Functions

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Pseudorandom Generators for Combinatorial Shapes

SIAM Journal on Computing ◽

10.1137/110854990 ◽

2013 ◽

Vol 42 (3) ◽

pp. 1051-1076 ◽

Cited By ~ 9

Author(s):

Parikshit Gopalan ◽

Raghu Meka ◽

Omer Reingold ◽

David Zuckerman

Keyword(s):

Pseudorandom Generators

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A Mathematical Problem for Security Analysis of Hash Functions and Pseudorandom Generators

International Journal of Foundations of Computer Science ◽

10.1142/s0129054115500100 ◽

2015 ◽

Vol 26 (02) ◽

pp. 169-194 ◽

Cited By ~ 1

Author(s):

Koji Nuida ◽

Takuro Abe ◽

Shizuo Kaji ◽

Toshiaki Maeno ◽

Yasuhide Numata

Keyword(s):

Mathematical Problem ◽

Security Analysis ◽

Hash Functions ◽

Future Research ◽

Theoretical Frameworks ◽

Pseudorandom Generators ◽

Mathematical Problems ◽

Security Evaluations ◽

Security Property ◽

Provably Secure

In this paper, we specify a class of mathematical problems, which we refer to as “Function Density Problems” (FDPs, in short), and point out novel connections of FDPs to the following two cryptographic topics; theoretical security evaluations of keyless hash functions (such as SHA-1), and constructions of provably secure pseudorandom generators (PRGs) with some enhanced security property introduced by Dubrov and Ishai (STOC 2006). Our argument aims at proposing new theoretical frameworks for these topics (especially for the former) based on FDPs, rather than providing some concrete and practical results on the topics. We also give some examples of mathematical discussions on FDPs, which would be of independent interest from mathematical viewpoints. Finally, we discuss possible directions of future research on other crypto-graphic applications of FDPs and on mathematical studies on FDPs themselves.

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