Secure Distributed Multiplication of Two Polynomially Shared Values: Enhancing the Efficiency of the Protocol

In view of practical applications, it is a high priority to optimize the efficiency of methods for secure multiparty computations. These techniques enable, for instance, truly practical double auctions and distributed signatures. The multiplication protocol for the secure multiparty multiplication of two polynomially shared values over Z_q with a public prime number q is an important module in these computations. The protocol of Gennaro, Rabin and Rabin (1998) is a well known and efficient protocol for this purpose. It requires one round of communication and O(n^2 k \log n + n k^2) bit-operations per player, where k is the bit size of the prime q and n is the number of players. In a previous paper (2007), the author has presented a modification of this protocol, that reduces its complexity to O(n^2k + nk^2). The present paper reduces this complexity further to O(n^2 k). This reduction is profitable in situations where n is smaller than k. The new protocol requires the same amount of communication as the original one and is unconditionally secure, as well.