SECRET SHARING SYSTEM, SHARING APPARATUS, SHARING MANAGEMENT APPARATUS, ACQUIRING APPARATUS, SECRET SHARING METHOD, PROGRAM AND RECORDING MEDIUM

摘要

A sharing apparatus independently shares a value corresponding to each element θ(ψ, i, β) · g2 of basis vectors bi*(θ) among each subset SUB(α) consisting of H(α) share management apparatuses PA(α, 1), ..., PA(α, H(α)) to generate share information SH(ψ, i, β, α, h(α)) corresponding to each element θ(ψ, i, β) · g2. The share management apparatus PA(α, h(α)) generates a share secret value DSH(ψ, α, h(α)) by performing a common calculation common in the subset SUB(α) on common information shared in the subset SUB(α) and the share information SH(ψ, i, β, α, h(α)). An acquisition apparatus generates reconstructed secret values SUBSK(ψ, α) for each subset SUB(α) by performing a reconstruction processing for the subset SUB(α) and generates generation information D*(ψ) from the reconstructed secret values SUBSK(ψ, α).