Presentation 2007-07-20
Affine Precomputation with Sole Inversion in Elliptic Curve Cryptography
Erik DAHMEN, Katsuyuki OKEYA, Daniel SCHEPERS,
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Abstract(in English) This paper presents a new approach to precompute all odd points [3]P, [5]P,...,[2k-1]P, k≧2 on an elliptic curve over F_p. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
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Keyword(in English) affine coordinates / elliptic curve cryptosystem / precomputation / scalar multiplication
Paper # ISEC2007-57
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Committee ISEC
Conference Date 2007/7/13(1days)
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Language ENG
Title (in Japanese) (See Japanese page)
Sub Title (in Japanese) (See Japanese page)
Title (in English) Affine Precomputation with Sole Inversion in Elliptic Curve Cryptography
Sub Title (in English)
Keyword(1) affine coordinates
Keyword(2) elliptic curve cryptosystem
Keyword(3) precomputation
Keyword(4) scalar multiplication
1st Author's Name Erik DAHMEN
1st Author's Affiliation Technische Universitdt Darmstadt, Fachbereich Informatik()
2nd Author's Name Katsuyuki OKEYA
2nd Author's Affiliation Hitachi, Ltd., Systems Development Laboratory
3rd Author's Name Daniel SCHEPERS
3rd Author's Affiliation Technische Universitdt Darmstadt, Fachbereich Informatik
Date 2007-07-20
Paper # ISEC2007-57
Volume (vol) vol.107
Number (no) 141
Page pp.pp.-
#Pages 8
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