Power analysis attacks uses the intermediate power consumption details of a cryptosystem to retrieve the secret key used. In order to resist such attack there can be mainly two possibilities, first is to make the system so secure that its power consumption details do not leave any trace for the attacker. The second is to make the system work in such a way that power consumption detail will be independent of the intermediate values. The first approach is quite difficult to achieve, however the second approach has proved to be effective in many consequences. Randomizing the operations of a cryptosystem has been quite widely used from some years back as it prevents power consumption details from revealing the exact intermediate values. In this paper we try to investigate the various ways in which randomization has been applied in exponentiation based cryptosystems to resist power analysis attacks.