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Gaussian normal bases (GNBs) are special set of normal bases (NBs) which yield low complexity GF (2 m ) arithmetic operations. In this paper, we present new architectures for the digit-level single, hybrid-double, and hybrid-triple multiplication of GF (2 m ) elements based on the GNB representation for odd values of m > 1. The proposed fully-serial-in single multipliers perform multiplication of two field elements and offer high throughput when the data-path capacity for entering inputs isdoi:10.1109/tc.2015.2481408 fatcat:37s5j6rxezgwtggolstffkqk3q