On an embedded device, an implementation of cryptographic operation, like an RSA modular exponentiation, can be attacked by side channel analysis. In particular, recent improvements on horizontal power analysis render ineffective the usual countermeasures which randomize the data at the very beginning of the computations. To counteract horizontal analysis it is necessary to randomize the computations all along the exponentiation. The leak resistant arithmetic (LRA) proposed in [1] implements modular arithmetic in residue number system (RNS) and randomizes the computations by randomly changing the RNS bases. We propose in this paper a variant of the LRA in RNS: we propose to change only one or a few moduli of the RNS basis. This reduces the cost of the randomization and makes it possible to be executed at each loop of a modular exponentiation.