Abstract: An identification scheme, a digital signature scheme giving message recovery, and a digital signature scheme with appendix are disclosed. In processing and transmitting information, a transmitting counterpart of a transmission message is confirmed. The unauthorized modification of the message is confirmed and transmitting behavior is detected, thereby providing the reliable information service.

Abstract: An identification scheme which allows a prover to identify his own identity to a verifier more certainly and prevents already used authentication information from being re-used, a key exchange which uses a common secret key between two users in order not to allow an unauthorized to find it out, a digital signature scheme giving message recovery and digital signature scheme with appendix for producing a digital signature of a message recovery type or appendix type according to the size of a message to be signed, a multi-digital signature scheme for allowing multiple signers to generate digital signatures with respect to the same message and producing them in a message recovery type or appendix type according to the length of the message to be signed, and a blind digital signature scheme for producing a digital signature when a message to be signed should not be opened to the public as well as the signer and therefore a signer does not know the contents thereof.

Abstract: A method for exchanging an authentication and signing an electronic signature, capable of providing a high security and achieving a high efficiency. The method includes the steps of setting p, q and g as system parameters, where p and q are prime numbers while g is an integer, between 1 and p, having the value of 1 when multiplied by the q-th power and then divided by p, and using n secret keys and n public keys for each user, where n is a number not less than 2, the public keys v.sub.n respectively corresponding to the secret keys S.sub.n, integers between 1 and q, and being produced based on an equation of v.sub.n =g.sup.-sn mod p.