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Exponentiation in finite fields is an essential operation used in many applications ranging from error control coding to cryptographic computations, while representation in Gaussian normal basis (GNB) offers low complexity arithmetic, especially in hardware architectures. In this article, we propose several new hardware architectures for binary exponentiation in GNB. The proposed architectures make use of different levels of precomputation and the efficient digit-level parallel-in parallel-out, and hybrid-double multipliers. We support our new designs with novel countermeasures against side-channel analysis that require minimal implementation overhead. Moreover, we obtain implementation results for all architectures and provide realistic and fair comparisons with the previously known works available in the literature. It is shown that our newly proposed architectures outperform the existing hardware architectures in terms of area and time complexities and security. [ABSTRACT FROM AUTHOR]