Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: Two keys which are updated in the same updating cycle at different times are prepared as signature keys (main key and auxiliary key) for electronic signature, and the updating cycle of each key is divided into, for example, three periods. The first and last periods after the updating are used for the auxiliary key while the intermediate period is used for the main key, and an electronic signature is carried out with the main key. The electronic signature is confirmed with either of two confirmation keys which are updated synchronously with updating the two keys used as the signature keys. This eliminates the need of stopping issuance of the electronic signature or limiting a service offer upon updating the signature keys.

Abstract: A user 300 generates a cipher key EK and pieces of information IA and IB, and sends information EK(IB), obtained by enciphering the information IB with the cipher key EK, and the information IA to an institution 100. The institution 100 registers the information IA as information of the user 300, and sends the information EK(IB) to an institution 200. The institution 200 enciphers its received information EK(IB) with the cipher key EK to obtain the information IB and registers the deciphered information IB.

Abstract: 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.

Abstract: A collecting agency supplies a collecting agency name and a money bag number to a service providing terminal. In response to dealing requests from user terminals, the service providing terminal sends, to the user terminals, information which contains the collecting agency name (Id) and the money bag number (Gb) supplied from the collecting agency. The user terminals generate digital signatures containing the received request information, affix the generated signatures to electronic tickets to be used, and send the electronic tickets with the signatures to the service providing terminal. The service providing terminal, which has received the used electronic tickets, collects those electronic tickets which include the same money bag number supplied from the collecting agency into a group (a money bag), and sends the group of electronic tickets to the collecting agency.