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2

Secret sharing captures a really wide set of techniques, and "not using secret sharing" is a bit ill-defined. Let me take an example: the seminal solution for two-party computation uses Yao's garbled circuits. It works as follows (very roughly): The sender garbles the circuit of the target function, which gives the following guarantees: given an appropriate ...


1

No. If you split the data between the parties, say using additive secret sharing, anyone controlling all parties can recover the full data. That is part of the very definition of secret sharing. If you want to ensure that the data will remain hidden even when the adversary controls all parties, then you cannot simply run a secure MPC protocol on shares of ...


3

This problem was studied under the name of private set-intersection cardinality (PSI-CA) by De Cristofaro et al. They give protocols for the two-party case both in the honest-but-curious and malicious setting, and the complexity grows only linearly in the size of the sets. A result for the multi-party case was given by Egert et al. using Bloom Filters. In ...


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There is no way to avoid that a party infers knowledge about another party input by looking at the result and his or her input. This is not considered a security issue of the protocol.


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