1. A group signature process of a proving apparatus, comprising: reading, using a computing device, a data required for calculation; when N is set to one of security parameters and a knowledge of a discrete logarithm of (a, C) is proven, selecting at random N integers X — {[[1]]0j} and calculating X — {1j} for each j by using secret information x′ and X — {0j}; selecting r_{ij} for each j and calculating a hash value C_{ij} of a data including the X_{ij} and the r_{ij}; calculating, using the computing device, L_{j} for each j by raising the a to the power X — {0j}; selecting a challenge c_j for each j and setting ξ_{j} for each j to the X_{c_jj}; and outputting a data including the {C_{ij}} and the {ξ_{j}}, where i is 0 or 1.