This master's thesis concerns secure multi-party computations (MPC) using secret sharing schemes (SSS) based on linear codes.

We introduce actively and passively secure protocols for MPC throughout the project, and give several examples using linear SSSs based on linear codes, particularly a ramp version of Massey's SSS.

First we consider an actively secure protocol for MPC using linear SSS, however, this only allows for addition and scalar multiplication. Therefore, we introduce multiplicative and strongly multiplicative SSSs, which allows us to construct passively and actively secure protocols for any function. Since multiplicative SSSs, and their associated matrices, are difficult to find we give several examples of multiplicative SSSs in the project.

Lastly, we introduce a passively secure protocol for MPC, which reduces the communication between participants by grouping multiplications.