Efficient multiplications in \(\mathbb F_5^{5n}\) and \(\mathbb F_7^{7n}\)

DOI10.1016/j.cam.2011.06.016zbMath1247.11150OpenAlexW2747621294WikidataQ114202152 ScholiaQ114202152MaRDI QIDQ645700

Murat Cenk, Ferruh Özbudak

Publication date: 10 November 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.06.016

zbMATH Keywords

algebraic function fieldspairing based cryptographyfinite field multiplication

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Number-theoretic algorithms; complexity (11Y16) Finite fields and commutative rings (number-theoretic aspects) (11T99) Finite fields (field-theoretic aspects) (12E20)

Uses Software

• Magma

Cites Work

• Unnamed Item
• Multiplication of polynomials modulo \(x^n\)
• Algebraic function fields and codes
• On the tensor rank of the multiplication in the finite fields
• Eta pairing computation on general divisors over hyperelliptic curves \(y^2=x^p - x+d\)
• On multiplication in finite fields
• The Magma algebra system. I: The user language
• Five, six, and seven-term Karatsuba-like formulae
• A generalized method for constructing subquadratic complexity GF(2/sup k/) multipliers
• Efficient Multiplication in $\mathbb{F}_{3^{\ell m}}$ , m ≥ 1 and 5 ≤ ℓ ≤ 18
• Comments on "Five, Six, and Seven-Term Karatsuba-Like Formulae
• Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem

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