Efficient software-implementation of finite fields with applications to cryptography

DOI10.1007/S10440-006-9046-1zbMath1105.12004OpenAlexW2157986576MaRDI QIDQ850780

Sandeep S. Kumar, Christof Paar, Jan Pelzl, Jorge Guajardo

Publication date: 6 November 2006

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-006-9046-1

zbMATH Keywords

cryptographyfield arithmeticefficient implementationoptimal extension fieldbinary field arithmeticextension field arithmeticprime field arithmetic

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Special polynomials in general fields (12E10) Field arithmetic (12E30) Research exposition (monographs, survey articles) pertaining to field theory (12-02)

Uses Software

• DSP56000

Cites Work

• A fast algorithm for computing multiplicative inverses in \(\text{GF}(2^ m)\) using normal bases
• Constructive and destructive facets of Weil descent on elliptic curves
• Itoh-Tsujii inversion in standard basis and its application in cryptography and codes
• Modular Multiplication Without Trial Division
• A Computer Algorithm for Calculating the Product AB Modulo M
• New directions in cryptography
• Efficient arithmetic in finite field extensions with application in elliptic curve cryptography.
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