PURPOSE: To shorten and accelerate time required for a calculation processing and to improve safety by placing a cryptological assumption on a discrete logarithm problem on a link and reducing the frequency of power raising calculation required for a signing or authenticating processing.

CONSTITUTION: In the signing processing, a signature (x) for a document (m) is prepared from one's own secret information by using a signing person side device 200 and information (m, x) is sent through a communication channel 400 to a confirming person side device 300. A confirming person checks the propriety of the received signature and confirms the propriety of the received document (m) at the confirming person side device 300 by using the open information of a certifying person. In this case, the signing person prepares the signature (x) for satisfying the function of x4-4f(m)x2+4ν=0 (mod N) obtained by using one-directional hash function (f) or x4-4mx2+4ν=0(mod N) for positive constants ν and N which are the open information of the signing person. Thus, since the frequency of the power raising calculation is less, signing and authenticating can be efficiently performed.