A user registers a user public key PKU as a pseudonym at a trustee or issuer and obtains an signature for the pseudonym as a license. The sends the pseudonym, PKU identification information IdU and the amount of withdrawal x to the issuer institution. The issuer increments a balance counter of the pseudonym by x, then generates an issuer signature SKI(PKU, x) with a secret key SKI, and sends the issuer signature as an electronic cash to the user. The user verifies the validity of the issuer signature with a public key SKI, and if valid, increments an electronic cash balance counter Balance by x. At the time of payment, user sends the public key PKU and the license to a shop, and the shop verifies the validity of the license, and if valid, sends a challenge to the user. The user attaches a signature to the challenge with user secret key SKU, then sends it to the shop together with the amount due y, and decrements the electronic cash balance counter by y.