This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose two dual protocols with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using cryptographic protocol verification tools, we are able to check the security of both protocols and provide a countermeasure for each attack found by the tools. We also give a generic randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.