Investigation of the efficiency of the elliptic curve cryptosystem for multi-applications smart card

For the development of the multi-application smart card, the memory capacity of the chip is not big enough to store the larger and complex programs needed for the multi-applications operating system and the protocol codes of the cryptography algorithm of large integers. The elliptic curve cryptosystem (ECC) potentially provides equivalent security to existing public key schemes but with much shorter key lengths. This paper considers the efficiency of the ECC in the design of multi-application smart cards and describes the problems of the smaller memory met in public key cryptosystems for multi-application smart card. The ElGamal and ECC algorithms are compared, where the modeling of the cryptosystem clearly shows the source of the efficiency of the ECC algorithm as a basis for achieving the required processing efficiency for future applications