On the Randomness Cost of Linear Secure Computation

We consider the problem of secure computation, where K users, each holding an independent message, wish to compute a function on the messages without revealing any additional information. We show that to compute M generic linear independent combinations of the messages securely (i.e., for the linear secure computation problem), it suffices to use min(inverted right perpendicularK - M - 1/2inverted left perpendicular, M) randomness symbols per message symbol (i.e., the randomness cost is no larger than min(inverted right perpendicularK - M - 1/2inverted left perpendicular, M)). The optimality of the achieved randomness cost remains open.