Secure multi-party computation is one of the hot issues in international cryptographic community. The secure computation of intersection-sum is a new problem of secure multi-party computation. The problem has important theoretical significance and practical value in the fields of industry, commerce, and healthcare. The existing solutions are designed under the condition that the private sets are subsets of a universal set and the intersection cardinality will be leaked and there are some false probabilities. This study, based on the Paillier cryptosystem, designs three protocols for the intersection-sum problem. These protocols are secure in the semi-honest model. Protocol 1 privately computes the number of common identifiers (i.e., user identifier intersection cardinality) and the sum of the integer values associated with these users, Protocol 2 and Protocol 3 privately compute the sum of the associated integer values of intersection elements without leaking the intersection cardinality. The whole computation process does not reveal any more information about their private inputs except for the intersection-sum. The protocols do not restrict that the private sets are subsets of a universal set, and they can be applied in more scenarios. It is proved, by using the simulation paradigm, that these protocols are secure in the semi-honest model. The efficiency of the protocols is also tested by experiments.