Efficient Algorithms for Elliptic Curve Cryptosystems using Endomorphisms

Efficient Algorithms for Elliptic Curve Cryptosystems using Endomorphisms

Hakuta, Keisuke

Springer Verlag, Japan

04/2025

280

Dura

Inglês

9784431553472

Pré-lançamento - envio 15 a 20 dias após a sua edição

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Introduction.- Mathematical Background.- Groups, Rings, Fields.- Elliptic Curves.- Scalar Multiplication.- Fast Computation Methods of Scalar Multiplication.- Efficient Arithmetic on Subfield Elliptic Curves Over Small Finite Fields of Odd Characteristic.- Explicit Lower Bound for the Length of Minimal Weight Expansions on Koblitz Curves.- Lower Bound for the Length of Minimal Weight Expansions on Koblitz Curves.- Another Proof of the Minimality of the Hamming Weight.- Minimal Length Form on Koblitz Curves and its Cryptographic Application.
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Elliptic Curve;Endomorphism;Frobenius Expansion;Frobenius Map;Koblitz Curve;NAF;Scalar Multiplication