  We propose a protocol able to show publicly addition and multiplication on
secretly shared values. To this aim we developed a protocol based on the use of
masks and on the FMPC (Fourier Multi-Party Computation). FMPC is a novel
multiparty computation protocol of arithmetic circuits based on secret-sharing,
capable to compute addition and multiplication of secrets with no
communication. We achieve this task by introducing the first generalisation of
Parseval's identity for Fourier series applicable to an arbitrary number of
inputs and a new algebra referred to as the "Theta-algebra". FMPC operates in a
setting where users wish to compute a function over some secret inputs by
submitting the computation to a set of nodes, without revealing them those
inputs. FMPC offloads most of the computational complexity to the end users,
and includes an online phase that mainly consists of each node locally
evaluating specific functions. FMPC paves the way for a new kind of multiparty
computation protocols; making it possible to compute addition and
multiplication of secrets stepping away from circuit garbling and the
traditional algebra introduced by Donald Beaver in 1991. Our protocol is
capable to compute addition and multiplication with no communication and its
simplicity provides efficiency and ease of implementation.
