102015-03-24 , 法政大学大学院情報科学研究科
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 (ai; di) 2 A_D (i = 1; 2; :::) and a condition A~ _ A as input and output summation of dis such that corresponding ai satisfies ai 2 A~ (i.e.,Σai 2A~ di.) 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 with 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 (ai; di) of the proposed schemes protocols on additive homomorphic encryption and 2-DNF encryption are O(n) and O( p n), respectively, where n denotes the cardinality of the set A. We also proposed protocols for more complex conditions based on 2-DNF cryptsystems and Somewhat Homomorphic Encryption. These protocols are able to calculate conditional sum which takes the data (ai; bi; di) and conditon ~ A; ~B Σ as input, and output ai 2A~^bi 2 ~B di or Σ ai 2A~_bi 2 ~B di.