Title: New Architectures for Digit-Level Single, Hybrid-Double, Hybrid-Triple Field Multiplications and Exponentiation Using Gaussian Normal Bases
Abstract: Gaussian normal bases (GNBs) are special set of normal bases (NBs) which yield low complexity <inline-formula> <tex-math notation="LaTeX">$GF\left(2^{m}\right)$</tex-math></inline-formula> arithmetic operations. In this paper, we present new architectures for the digit-level single, hybrid-double, and hybrid-triple multiplication of <inline-formula><tex-math notation="LaTeX">$GF\left(2^{m}\right)$</tex-math></inline-formula> elements based on the GNB representation for odd values of <inline-formula><tex-math notation="LaTeX">$m > 1$</tex-math></inline-formula> . 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.
Publication Year: 2016
Publication Date: 2016-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 16
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