On Codes, Matroids, and Secure Multiparty Computation From Linear Secret-Sharing Schemes

Secure Multiparty Computation and Secret Sharing

In a data-driven society, individuals and companies encounter numerous situations where private information is an important resource. How can parties handle confidential data if they do not trust everyone involved? This text is the first to present a comprehensive treatment of unconditionally secure techniques for multiparty computation (MPC) and secret sharing. In a secure MPC, each party poss...

Unconditionally Secure Multiparty Computation and Secret Sharing

We suggest protocols for secure computation of the sum, product, and some other functions of three or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation, i.e., we do not let any party accumulate functions of other parties’ private numbe...

On Secret Sharing Schemes, Matroids and Polymatroids

The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. The optimization of this parameter for general access structures is an important and very difficult open problem in secret sharing. We explore in this paper the connections of this open problem with matroids and polymatroids. Matroid ports were introduced by L...

Secure Multiparty Computation and Secret Sharing - An Information Theoretic Appoach

Secure Multi-Party Computation from any Linear Secret Sharing Scheme

We present a general treatment of non-cryptographic (i.e. information-theoretically secure) multi-party computation, based on underlying linear secret sharing scheme. This general approach gives pure linear-algebra conditions on the linear mappings describing the scheme. The approach establishing the minimal conditions for security, can lead to design of more efficient Multi-Party Computation (...