TY - JOUR
T1 - On pseudorandom generators with linear stretch in NC0
AU - Applebaum, Benny
AU - Ishai, Yuval
AU - Kushilevitz, Eyal
N1 - Funding Information:
We thank Eli Ben-Sasson, Amir Shpilka and Amnon Ta-Shma for helpful discussions. WealsothankOdedGoldreichformanyusefulsuggestionswhichim-proved the presentation of this paper. Research supported by grants 1310/06 and 36/03 from the Israel Science Foundation.
PY - 2008/4
Y1 - 2008/4
N2 - We consider the question of constructing cryptographic pseudorandom generators (PRGs) in NC0, namely ones in which each bit of the output depends on just a constant number of input bits. Previous constructions of such PRGs were limited to stretching a seed of n bits to n + o(n) bits. This leaves open the existence of a PRG with a linear (let alone superlinear) stretch in NC0. In this work we study this question and obtain the following main results: 1. We show that the existence of a linear-stretch PRG in NC 0 implies non-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. 2. We construct a linear-stretch PRG in NC0 under a specific intractability assumption related to the hardness of decoding "sparsely generated" linear codes. Such an assumption was previously conjectured by Alekhnovich (FOCS 2003).
AB - We consider the question of constructing cryptographic pseudorandom generators (PRGs) in NC0, namely ones in which each bit of the output depends on just a constant number of input bits. Previous constructions of such PRGs were limited to stretching a seed of n bits to n + o(n) bits. This leaves open the existence of a PRG with a linear (let alone superlinear) stretch in NC0. In this work we study this question and obtain the following main results: 1. We show that the existence of a linear-stretch PRG in NC 0 implies non-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. 2. We construct a linear-stretch PRG in NC0 under a specific intractability assumption related to the hardness of decoding "sparsely generated" linear codes. Such an assumption was previously conjectured by Alekhnovich (FOCS 2003).
KW - Constant depth circuits
KW - Cryptography
KW - Pseudorandom generators
KW - nc0
UR - http://www.scopus.com/inward/record.url?scp=45049086177&partnerID=8YFLogxK
U2 - 10.1007/s00037-007-0237-6
DO - 10.1007/s00037-007-0237-6
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AN - SCOPUS:45049086177
SN - 1016-3328
VL - 17
SP - 38
EP - 69
JO - Computational Complexity
JF - Computational Complexity
IS - 1
ER -