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On d-Multiplicative Secret Sharing

Content Provider	Springer Nature Link
Author	Barkol, Omer Ishai, Yuval Weinreb, Enav
Copyright Year	2010
Abstract	A multiplicative secret sharing scheme allows players to multiply two secret-shared field elements by locally converting their shares of the two secrets into an additive sharing of their product. Multiplicative secret sharing serves as a central building block in protocols for secure multiparty computation (MPC). Motivated by open problems in the area of MPC, we introduce the more general notion of d-multiplicative secret sharing, allowing to locally multiply d shared secrets, and study the type of access structures for which such secret sharing schemes exist.While it is easy to show that d-multiplicative schemes exist if no d unauthorized sets of players cover the whole set of players, the converse direction is less obvious for d≥3. Our main result is a proof of this converse direction, namely that d-multiplicative schemes do not exist if the set of players is covered by d unauthorized sets. In particular, t-private d-multiplicative secret sharing among k players is possible if and only if k>dt.Our negative result holds for arbitrary (possibly inefficient or even nonlinear) secret sharing schemes and implies a limitation on the usefulness of secret sharing in the context of MPC. Its proof relies on a quantitative argument inspired by communication complexity lower bounds.
Starting Page	580
Ending Page	593
Page Count	14
File Format	PDF
ISSN	09332790
Journal	Journal of Cryptology
Volume Number	23
Issue Number	4
e-ISSN	14321378
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-02-05
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Secret sharing Secure multiparty computation Secure multiplication Communications Engineering, Networks Probability Theory and Stochastic Processes Combinatorics Computational Mathematics and Numerical Analysis Coding and Information Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications Software

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