In this study, an improved, time sample cross correlation based power attack is applied on a Montgomery Ladder implementation of the RSA. In the attack, by using an implementation level property, power traces related to the all key bits are cross correlated with each other and resulting correlation values are summed and compared to a threshold to estimate the secret key of the target RSA implementation. The attack could retrieve all the key bits by using 75% lesser power traces when compared to the single fixed reference bit and 50% lesser power traces compared to the double fixed reference bits approaches which are applied on the same implementation earlier.