The on-card implementation is actually a prime finding problem.So we should optimize the algorithms so that they become efficient, flexible and space saving. Along with these crypto coprocessors are also used to accelerate cryptography.Although smart cards are becoming used in an increasing number of applications, there is small literature of the implementation issues for smart cards. This paper describes the issues and considerations that need to be taken into account when implementing the key generation step of a cryptographic algorithm widely used nowadays, RSA.Smart cards are used in many applications that require a tamper resistant area. Therefore, smart cards that use cryptography have to provide encryption, decryption, as well as key generation inside its security perimeter. RSA key generation is a concern for on-card implementation of RSA cryptosystem, as it usually takes a long time. In this paper, two simple but efficient key generation algorithms are evaluated, in addition to a simple but not very efficient algorithm. The paper discusses in detail how to build fast implementations for the three algorithms presented, using smart cards with crypto-coprocessor.