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In order to secure the communication in Internet of Things era, a low overhead power analysis countermeasure called uniform distribution random power generator is proposed for stream ciphers. To alter the power signature of protected circuit, ring oscillators, which act as unit power generators, are grouped in a systematic approach to generate additional power with uniform probability distribution. Experiments from the proposed evaluation framework demonstrate that the secret key of unprotected device can be disclosed within 103 power traces with standard differential power analysis attack, whereas the same attack mounted on the proposed scheme cannot be disclosed even after 106 measurements. Moreover, the area and the power overhead are reduced by at least 29% and 22% compared with the state-of-the-art works, respectively. [ABSTRACT FROM PUBLISHER]