A multi-application smart card system consists of an issuer, service vendors and cardholders, where cardholders are recipients of smart cards (from the issuer) to be used in connection with applications offered by service vendors. Authentic post-issuance program modification is necessary for a multi-application smart card system because applications in the system are realized after the issuance of a smart card. In this paper, we propose a system where only authentic modification is possible. In the proposed system, the smart card issuer stores a unique long bitstring called PID in a smart card. The smart card is then given to the cardholder. A unique substring of the PID (subPID) is shared between the cardholder and a corresponding service vendor. Another subPID is shared between the issuer and the cardholder. During program modification, a protocol using the subPIDs, a one-way hash function and a pseudorandom number generator function verifies the identity of the parties and the authenticity of the program.