An Efficient and Secure Frequent Multiparty Summation protocol

In secure multiparty computation (SMC), a group of users jointly and securely computes a mathematical function on their private inputs, such that the privacy of their private inputs will be preserved. One of the widely used applications of SMC is the secure multiparty summation which securely computes the summation value of the users’ private inputs. In this paper, we consider a secure multiparty summation problem where each group member has m private inputs and wants to efficiently and securely computes the summation values of their corresponding inputs; in other words, users compute m summation values where the first value is the summation of users’ first private inputs, the second one is the summation of users’ second private inputs and so on. We propose an efficient and secure protocol in the semi honest model, called frequent-sum, which computes the desired values while preserving the privacy of users’ private inputs as well as the privacy of the summation results.
Let  be a set of n users and the private inputs of user  is denoted as . The proposed frequent-sum protocol includes three phases:

In the first phase, each user  selects a random number , computes and publishes the vectors  of  components where each component  of  is of  form . After it,  computes the vector , such that each component  is of form.
In the second phase, users jointly and securely compute their AV-net (Anonymous Veto network) masks and the Burmester-Desmedt (BD) conference key. To do so, each user  selects two random numbers  and  and publishes  to the group. Then,  computes and sends  to the group. Then, each user is able to compute  and ;  is the AV-net mask of  and  is the conference key.
In the third phase, using the AV-net mask and the conference key, group members securely and collaboratively compute the summation of their random numbers , . To achieve this, each user broadcasts  to the group, where  is the AV-net mask of  and  is the ’s portion of the conference key. Multiplying all s results in canceling the AV-net mask and getting the value of . Then each member is able to compute  by the following Eq.:

Now each user is able to compute  by subtracting  from each component of :
It is shown that the proposed protocol is secure against collusion attack of at most  users. In other words, the frequent-sum protocol is secure against partial collusion attack; only a full collusion (collusion of  users) would break the privacy of the victim user, in this situation there is no reason for the victim user to join to such a group. The performance analysis shows that the proposed protocol is efficient in terms of the computation and communication costs, comparing with previous works. Also, the computation cost of the frequent-sum protocol is in-dependent of the number of inputs of each user  which makes the protocol more efficient than the previous works. Table 1 compares the proposed protocol with previous works.