SECRET SHARING SYSTEM, SHARING APPARATUS, SHARE MANAGEMENT APPARATUS, ACQUISITION APPARATUS, PROCESSING METHODS THEREOF, SECRET SHARING METHOD, PROGRAM, AND RECORDING MEDIUM

摘要

A secure secret sharing system is implemented. Shares SH(α, h(α)) are generated by secret sharing of secret information separately for each subset SUB(α); each of share management apparatuses PA(α, h(α)) generates a shared secret value DSH(α, h(α)) by performing a common operation to a corresponding share SH(α, h(α)) and common information containing a common valueσ(α) shared in each subset SUB(α); and an acquisition apparatus generates a reconstructed secret value SUBSK(α) by reconstruction processing for each subset SUB(α), using a plurality of shared secret values DSH(α, h(α)) corresponding to the same subset SUB(α), and generates generation information SK by using the reconstructed secret values SUBSK(α).