This paper presents a side-channel attack on masked Galois-field (GF) multiplication used in authenticated encryptions including AES-GCM and a new countermeasure against the proposed attack. While the previous side-channel attack is likely to recover the full key of GHASH in AES-GCM, no countermeasure has been discussed and evaluated until now. In this paper, we first apply a straightforward masking countermeasure to GF multiplication for GHASH and show that the masked GF multiplication is resistant to the previous attack. We then show the straightforward masked GHASH can be defeated by a new attack utilizing the variance of power trace. The feasibility of the new attack is demonstrated by an experiment with power traces measured from a smart card operating the masked GHASH. Finally, we propose a new masking countermeasure against the proposed attack.