In [1] the authors introduced the leak resistant arithmetic in RNS to randomize RSA modular exponentiation. This randomization is meant to protect implementations on embedded device from side channel analysis. We propose in this paper a lazy version of the approach of [1] in the case of right-to-left square-and-multiply exponentiation. We show that this saves roughly 30% of the computation when the randomization is done at each loop iteration. We also show that the level of randomization of the proposed approach is better than the one of [1] after a few number of loop iterations.