New Architectures for Digit-Level Single, Hybrid-Double, Hybrid-Triple Field Multiplications and Exponentiation Using Gaussian Normal Bases

Hayssam El-Razouk, Arash Reyhani-Masoleh
2016 IEEE transactions on computers  
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 is
more » ... ted. The proposed hybrid-double and hybrid-triple digitlevel GNB multipliers perform, respectively, two and three field multiplications using the same latency required for a single digitlevel multiplier, at the expense of increased area. In addition, we present a new eight-ary field exponentiation architecture which does not require precomputed or stored intermediate values.
doi:10.1109/tc.2015.2481408 fatcat:37s5j6rxezgwtggolstffkqk3q