Abstract: The essence of the invention is in that when making a digital blind RSA-signature a new technique for blinding an initial data by a RSA-encryption and corresponding technique for unblinding the signed blinded data are employed, which gives the possibility to use an unlimited number of kinds of the signature in electronic systems of the mass scale service. The untraceability is ensured by a corresponding choice of the randomized exponent R, RSA-key used in RSA-encryption the initial data, and by the public module N properties verified in an arbitrary time moment. In so doing, N=P·Q, where P and Q are secret prime factors, and R is multiple to N?1. In other variants of the invention the diversity of kinds of the signature is set by limitings on multiplicities of public exponents, said limitings being chosen prior to blinding the initial data.

Abstract: A method for a cardholder to request fulfillment of an obligation associated with the card and for the issuer to acknowledge this obligation, which method allows a remote interaction of the parties and ensures their security. The issuer issues cards each of which has an identifier and the corresponding verifier, the latter being concealed by a masking device. A cardholder sends the identifier of the card and directions specifying fulfillment of the obligation to the issuer. The issuer checks that he has never issued to anybody a signed reply binding the presented identifier and directions different from the presented directions, signs the reply binding the identifier and the directions, and sends the signed reply to the cardholder. The cardholder verifies the issuer's signature on the reply and checks that the reply binds the identifier and directions he has sent to the issuer, after which he sends the verifier of the card to the issuer.