| 摘要 |
Provided are a scalar multiplier and a scalar multiplication program for performing a scalar multiplication at a high speed. In computing a scalar multiplication [s]P of a rational point P of an additive group E(F p ) including rational points on an elliptic curve where a characteristic p, an order r, and a trace t of a Frobenius endomorphism at an embedding degree k=12 using an integer variable Ç are given by: p(Ç)=36Ç 4 -36Ç 3 +24Ç 2 -6Ç+1, r(Ç) =36Ç 4 -36Ç 3 +18Ç 2 -6Ç+1=p (Ç)+1-t (Ç) , t (Ç) =6Ç 2 +1, the scalar multiplication [s]P is computed as: [s]P=([A] Õ' 2 +[B])P, using a Frobenius map Õ' 2 given by: [p 2 ]P=Õ' 2 (P) assuming that a twist degree d is 6 and a positive integer e is 2 where k=dxe. |
