Secure Computation by Secret Sharing Using Input Encrypted with Random Number (Full Paper)

Typically, unconditionally secure computation using a (k, n) threshold secret sharing scheme is considered impossible when n < 2k − 1. Therefore, in our previous work, we first took the approach of finding the conditions required for secure computation under the setting of n < 2k − 1 and showed that secure computation using a secret sharing scheme can be realized with a semi-honest adversary under the following three preconditions: (1) the result of secure computation does not include 0; (2) random numbers reconstructed by each server are fixed; and (3) each server holds random numbers unknown to the adversary and holds shares of random numbers that make up the random numbers unknown to the adversary. In this paper, we show that by leaving condition (3), secure computation with information-theoretic security against a semihonest adversary is possible with k ≤ n < 2k − 1. In addition, we clarify the advantage of using secret information that has been encrypted with a random number as input to secure computation. One of the advantages is the acceleration of the computation time. Namely, we divide the computation process into a preprocessing phase and an online phase and shift the cost of communication to the preprocessing phase. Thus, for computations such as inner product operations, we realize a faster online phase, compared with conventional methods.