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Point Multiplication using Integer Sub-Decomposition for Elliptic Curve Cryptography |
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PP: 517-525 |
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Author(s) |
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Ruma Kareem K. Ajeena,
Hailiza Kamarulhaili,
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Abstract |
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| In this work, we proposed a new approach called integer sub-decomposition (ISD) based on the GLV idea to compute any
multiple kP of a point P of order n lying on an elliptic curve E. This approach uses two fast endomorphisms y1 and y2 of E over prime
field Fp to calculate kP. The basic idea of ISD method is to sub-decompose the returned values k1 and k2 lying outside the range √n
from the GLV decomposition of a multiplier k into integers k11, k12, k21 and k22 with −√n < k11, k12, k21, k22 < √n. These integers
are computed by solving a closest vector problem in lattice. The new proposed algorithms and implementation results are shown and
discussed in this study. |
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