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Implementation of extension field arithmetic with applications to torus-based cryptography. (English) Zbl 1101.11051

Dorfer, G. (ed.) et al., Proceedings of the 70th workshop on general algebra “70. Arbeitstagung Allgemeine Algebra”, Vienna, Austria, May 26–29, 2005. Klagenfurt: Verlag Johannes Heyn (ISBN 3-7084-0194-8/pbk). Contributions to General Algebra 17, 201-216 (2006).
The authors consider the use of Karatsuba multiplication and squaring algorithms over finite extension fields with respect to different bases. There are some comparisons between complexities of multiplication and squaring tables and their algorithms. Applications of extension field arithmetic to torus-based cryptography is described. The authors extend the analysis of the cryptosystems by using different bases to perform arithmetic on extension field elements, focusing on multiplication and squaring techniques.
For the entire collection see [Zbl 1089.08001].

MSC:

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
68P25 Data encryption (aspects in computer science)
94A60 Cryptography
68Q25 Analysis of algorithms and problem complexity
11Y16 Number-theoretic algorithms; complexity
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