A smart card is adapted to partially include and employ a triply-secure
algorithm for data exchange. The algorithm verifies a user's identity and
his simultaneous membership in any groups that he has joined. For this
purpose, the algorithm requires only a single insertion of the smart card
and only a single input of the user's personal identification number. The
algorithm can be used in smart cards or in computer networks for identity
verification and membership proof. A combination of three different hard
problems is used. The first one is based on integer factorization, such as
the RSA authenticating technique, and the second one is based on a
discrete logarithm, and the third one is based on the coefficients of a
polynomial function. In a typical application using smart cards, a
certification authority (CA) establishes requirements for preparation and
issuance of a multi-purpose card.
