Protocols for evaluating conditional sum on encrypted data

In this paper, we propose a protocol to evaluate conditional sum on encrypted data. Here, conditional sum is a sort of computation which takes pair of data (a_i, d_i) ∈ A × D (i = 1, 2, ...) and a condition à ⊆ A as input and output summation of d_is such that corresponding a_i satisfies a_i ∈ à (i.e., Σ_ai∈à d_i.) Such a computation is used in statistical analysis of large scale data. For example, it is used to analyze a total medical cost of employee on their 50s, 40s and 30s. We construct protocols based on additive homomorphic encryption and 2-DNF cryptosystems, respectively, where 2-DNF cryptosystem is a homomorphic cryptosystem which allows arbitrary number of addition and single multiplication on encrypted data. The size of ciphertext for (a_i, d_i) of the proposed schemes protocols on additive homomorphic encryption and 2-DNF encryption are O(n) and O(√n), respectively, where n denotes the cardinality of the set A.