The paper presents counter-measures based on dynamic randomization against side channel analysis like differential and correlation power analysis. The building block of the proposed counter-measure is a randomization of the modular multiplication in AMNS for a prime $p$. We use this randomized modular multiplication to inject randomization during the whole computation in DSA exponentiation and Co-Z elliptic curve scalar multiplication. We analyze the level of randomization injected and, through implementations results, we evaluate the penalty in terms of performance of the proposed counter-measures.