Name
Abstract | ||
|---|---|---|
We present new algorithms computing 3P and $$2P+Q$$2P+Q by removing the same part of numerators and denominators of their formulas, given two points P and Q on elliptic curves defined over prime fields and binary fields in affine coordinates. Our algorithms save one or two field multiplications compared with ones presented by Ciet, Joye, Lauter, and Montgomery. Since $$2P+Q$$2P+Q takes $$\\frac{1}{3}$$13 proportion, 28.5﾿% proportion, and 25.8﾿% proportion of all point operations by non-adjacent form, binary/ternary approach and tree approach to compute scalar multiplications respectively, 3P occupies 42.9﾿% proportion and 33.4﾿% proportion of all point operations by binary/ternary approach and tree approach to compute scalar multiplications respectively, utilizing our new formulas of $$2P+Q$$2P+Q and 3P, scalar multiplications by using non-adjacent form, binary/ternary approach and tree approach are improved. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/978-3-319-22425-1_4 | International Workshop on Security |
Keywords | Field | DocType |
Elliptic curve,Double-base number system,Elliptic curve arithmetic,Scalar multiplication | Prime (order theory),Affine transformation,Scalar multiplication,Computer science,Scalar (physics),Algorithm,Elliptic curve point multiplication,Elliptic curve,Tripling-oriented Doche–Icart–Kohel curve,Binary number | Conference |
Volume | ISSN | Citations |
9241 | 0302-9743 | 1 |
PageRank | References | Authors |
0.35 | 13 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wei Yu | 1 | 1 | 0.35 |
| Kwang Ho Kim | 2 | 20 | 11.90 |
| Myong Song Jo | 3 | 1 | 0.35 |