We analyze variations of multiplicative updates for learning linear functions online. These can be described as substituting exponentiation in the Exponentiated Gradient (EG) algorithm with quadratic and linear functions. Both kinds of updates substitute exponentiation with simpler operations and reduce dependence on the parameter that specifies the sum of the weights during learning. In partic...

In this thesis, we explain linear secret sharing schemes, in particular multiplicative threshold linear secret sharing schemes, over fields and rings in a compact and concise way. We explain two characterisations of linear secret sharing schemes, and in particular, we characterise threshold linear secret sharing schemes. We develop an algorithm to generate all multiplicative (t+ 1)-out-of-n thr...

We reformulate Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasi-linear algorithm. Linearity is obtained after observing that the disjoint-set unionfind at the core of the unification criterion is a special case of union-find with a real linear time solution.

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent calculus. In this paper we give an interpretation of proof nets in the syntax of string diagrams. Even though we lose standard proof equivalence,...

We consider both information-theoretic and cryptographic settings for Multi-Party Computation (MPC), based on the underlying linear secret sharing scheme. Our goal is to study the Monotone Span Program (MSP), that is the result of local multiplication of shares distributed by two given MSPs as well as the access structure that this resulting MSP computes. First, we expand the construction propo...