TY - GEN

T1 - On basing one-way functions on NP-hardness

AU - Akavia, Adi

AU - Goldreich, Oded

AU - Goldwasser, Shafi

AU - Moshkovitz, Dana

PY - 2006

Y1 - 2006

N2 - We consider the possibility of basing one-way functions on NP-Hardness; that is, we study possible reductions from a worst-case decision problem to the task of average-case inverting a polynomial-time computable function J. Our main findings are the following two negative results: 1. If given y one can efficiently compute |f-1(y)| then the existence of a (randomized) reduction of NP to the task of inverting / implies that coN P ⊆ AM. Thus, it follows that such reductions cannot exist unless coNP ⊆ AM. 2. For any function f, the existence of a (randomized) non-adaptive reduction of NP to the task of average-case inverting f implies that coNP ⊆ AM. Our work builds upon and improves on the previous works of Feigenbaum and Fortnow (SIAM Journal on Computing, 1993) and Bogdanov and Trevisan (44th FOCS, 2003), while capitalizing on the additional "computational structure" of the search problem associated with the task of inverting polynomial-time computable functions. We believe that our results illustrate the gain of directly studying the context of one-way functions rather than inferring results for it from a the general study of worst-case to average-case reductions.

AB - We consider the possibility of basing one-way functions on NP-Hardness; that is, we study possible reductions from a worst-case decision problem to the task of average-case inverting a polynomial-time computable function J. Our main findings are the following two negative results: 1. If given y one can efficiently compute |f-1(y)| then the existence of a (randomized) reduction of NP to the task of inverting / implies that coN P ⊆ AM. Thus, it follows that such reductions cannot exist unless coNP ⊆ AM. 2. For any function f, the existence of a (randomized) non-adaptive reduction of NP to the task of average-case inverting f implies that coNP ⊆ AM. Our work builds upon and improves on the previous works of Feigenbaum and Fortnow (SIAM Journal on Computing, 1993) and Bogdanov and Trevisan (44th FOCS, 2003), while capitalizing on the additional "computational structure" of the search problem associated with the task of inverting polynomial-time computable functions. We believe that our results illustrate the gain of directly studying the context of one-way functions rather than inferring results for it from a the general study of worst-case to average-case reductions.

KW - Adaptive versus Non-adaptive machines

KW - Average-Case complexity

KW - Interactive Proof Systems

KW - One-Way Functions

KW - Reductions

UR - http://www.scopus.com/inward/record.url?scp=33748114891&partnerID=8YFLogxK

U2 - 10.1145/1132516.1132614

DO - 10.1145/1132516.1132614

M3 - Conference contribution

AN - SCOPUS:33748114891

SN - 1595931341

SN - 9781595931344

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 701

EP - 710

BT - STOC'06

PB - Association for Computing Machinery

T2 - 38th Annual ACM Symposium on Theory of Computing, STOC'06

Y2 - 21 May 2006 through 23 May 2006

ER -