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Scalar multiplier and scalar multiplication program

*Abstract: Provided are a scalar multiplier which makes itpossible to execute scalar multiplication at high speed, and a scalar multiplication program. When calculating a scalar multiplication [s]Pof a rational point P of an additive group E
(F_p) comprising rational points on anelliptical curve wherein a characteristic p, an order r, and a trace t of a Frobenius endomorphism map atan embedded degree k=12 using an integer variable χ are provided as p(χ)=36χ⁴-36χ³+24χ²-6χ.+1, r(χ)=36X⁴-36χ³+18χ²-6χ+1=p(χ)+1-t(χ), t(χ)=6χ²+ 1，assuming that the twist degree d is 6 and a positive integer e is2 where k=dxe, [ s]P=([A]φ'₂+[B])Pis calculated using the Frobenius map φ'₂where[p²]p=φ'₂(P).

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