Efficient Arithmetic in Optimal Extension Fields Using Simultaneous Multiplication

Mun-Kyu LEE  Kunsoo PARK  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.5   pp.1316-1321
Publication Date: 2003/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Security
cryptography,  elliptic curve,  optimal extension field,  finite field,  

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A new algorithm for efficient arithmetic in an optimal extension field is proposed. The new algorithm improves the speeds of multiplication, squaring, and inversion by performing two subfield multiplications simultaneously within a single integer multiplication instruction of a CPU. Our algorithm is used to improve throughputs of elliptic curve operations.