TY - GEN
T1 - Perfect constant-round secure computation via perfect randomizing polynomials
AU - Ishai, Yuval
AU - Kushilevitz, Eyal
PY - 2002
Y1 - 2002
N2 - Various information-theoretic constant-round secure multiparty protocols are known for classes such as NC1 and polynomial-size branching programs [1,13,18,3,19,10]. All these protocols have a small probability of failure, or alternatively use an expected constant number of rounds, suggesting that this might be an inherent phenomenon. In this paper we prove that this is not the case by presenting several constructions of perfect constant-round protocols. Our protocols are obtained using randomizing polynomials - a recently introduced representation [19], which naturally relaxes the standard polynomial representation of boolean functions. Randomizing polynomials represent a function f by a low-degree mapping from its inputs and independent random inputs to a vector of outputs, whose distribution depends only on the value of f.We obtain several constructions of degree-optimal perfect randomizing polynomials, whose distinct output distributions are perfectly separated. These results on randomizing polynomials are of independent complexity-theoretic interest.
AB - Various information-theoretic constant-round secure multiparty protocols are known for classes such as NC1 and polynomial-size branching programs [1,13,18,3,19,10]. All these protocols have a small probability of failure, or alternatively use an expected constant number of rounds, suggesting that this might be an inherent phenomenon. In this paper we prove that this is not the case by presenting several constructions of perfect constant-round protocols. Our protocols are obtained using randomizing polynomials - a recently introduced representation [19], which naturally relaxes the standard polynomial representation of boolean functions. Randomizing polynomials represent a function f by a low-degree mapping from its inputs and independent random inputs to a vector of outputs, whose distribution depends only on the value of f.We obtain several constructions of degree-optimal perfect randomizing polynomials, whose distinct output distributions are perfectly separated. These results on randomizing polynomials are of independent complexity-theoretic interest.
UR - http://www.scopus.com/inward/record.url?scp=84869164571&partnerID=8YFLogxK
U2 - 10.1007/3-540-45465-9_22
DO - 10.1007/3-540-45465-9_22
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AN - SCOPUS:84869164571
SN - 3540438645
SN - 9783540438649
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 244
EP - 256
BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
A2 - Widmayer, Peter
A2 - Eidenbenz, Stephan
A2 - Triguero, Francisco
A2 - Morales, Rafael
A2 - Conejo, Ricardo
A2 - Hennessy, Matthew
T2 - 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002
Y2 - 8 July 2002 through 13 July 2002
ER -