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Conference Papers Year : 2012

Efficient Multiplication over Extension Fields

Abstract

The efficiency of cryptographic protocols rely on the speed of the underlying arithmetic and finite field computation. In the literature , several methods on how to improve the multiplication over extensions fields Fqm , for prime q were developped. These optimisations are often related to the Karatsuba and Toom Cook methods. However, the speeding-up is only interesting when m is a product of powers of 2 and 3. In general cases, a fast multiplication over Fqm is implemented through the use of the naive schoolbook method. In this paper, we propose a new efficient multiplication over Fqm for any power m. The multiplication relies on the notion of Adapted Modular Number System (AMNS), introduced in 2004 by [3]. We improve the construction of an AMNS basis and we provide a fast implementation of the multiplication over Fqm , which is faster than GMP and NTL.
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Dates and versions

hal-01197178 , version 1 (11-09-2015)

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Nadia El Mrabet, Nicolas Gama. Efficient Multiplication over Extension Fields. WAIFI 2012, Jul 2012, Ghent, Belgium. ⟨10.1007/978-3-642-31662-3_10⟩. ⟨hal-01197178⟩
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