Paper 2013/503
On secret sharing with nonlinear product reconstruction
Ignacio Cascudo, Ronald Cramer, Diego Mirandola, Carles Padro, and Chaoping Xing
Abstract
Multiplicative linear secret sharing is a fundamental notion in the area of secure multi-party computation (MPC) and,
since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that
``the product of two secrets is obtained as a linear function of the vector consisting of the
coordinate-wise product of two respective share-vectors''. This paper focuses on the following foundational question, which is novel to the best of our knowledge. Suppose we {\em abandon the latter linearity condition} and instead require that this product is obtained by {\em some},
not-necessarily-linear ``product reconstruction function''. {\em Is the resulting notion equivalent to
multiplicative linear secret sharing?} We show the (perhaps somewhat counter-intuitive) result that this relaxed notion is strictly {\em more general}.
Concretely, fix a finite field
Note: Updated publication info.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Published elsewhere. SIAM Journal on Discrete Mathematics 29 (2), 1114-1131
- DOI
- 10.1137/130931886
- Keywords
- (arithmetic) secret sharing
- Contact author(s)
- ignacio @ cs au dk
- History
- 2016-07-18: last of 5 revisions
- 2013-08-17: received
- See all versions
- Short URL
- https://ia.cr/2013/503
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/503, author = {Ignacio Cascudo and Ronald Cramer and Diego Mirandola and Carles Padro and Chaoping Xing}, title = {On secret sharing with nonlinear product reconstruction}, howpublished = {Cryptology {ePrint} Archive, Paper 2013/503}, year = {2013}, doi = {10.1137/130931886}, url = {https://eprint.iacr.org/2013/503} }