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

摘要

Gaussian normal bases (GNBs) are special set of normal bases (NBs) which yield low complexity arithmetic operations. In this paper, we present new architectures for the digit-level single, hybrid-double, and hybrid-triple multiplication of elements based on the GNB representation for odd values of . 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 limited. The proposed hybrid-double and hybrid-triple digit-level GNB multipliers perform, respectively, two and three field multiplications using the same latency required for a single digit-level 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.