Computational Soundness of Uniformity Properties for Multi-party Computation based on LSSS

We provide a symbolic model for multi-party computation based on linear secret-sharing scheme, and prove that this model is com- putationally sound: if there is an attack in the computational world, then there is an attack in the symbolic (abstract) model. Our original contri- bution is that we deal with the uniformity properties, which cannot be described using a single execution trace, while considering an unbounded number of sessions of the protocols in the presence of active and adaptive adversaries