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CRYPTOGRAPHIC METHOD USING A NON-SUPERSINGULAR ELLIPTIC CURVE E IN CHARACTERISTIC 3
CRYPTOGRAPHIC METHOD USING A NON-SUPERSINGULAR ELLIPTIC CURVE E IN CHARACTERISTIC 3
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机译:特征3中使用非奇异椭圆曲线的密码学方法
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摘要
A cryptographic method is provided of a type with public key over a non-supersingular elliptic curve E, determined by the simplified Weirstrass equation y2=x3+a.x2+b over a finite field GF(3n), with n being an integer greater than or equal to 1. The method includes associating an element t of said finite field with a point P′ of the elliptic field. The step of associating includes: obtaining a pre-determined quadratic non-residue η on GF(3n); obtaining a pre-determined point P=(zP, yP) belonging to a conic C defined by the following equation: a.η.z2−y2+b=0; obtaining a point Q=(zQ, yQ), distinct from the point P belonging to the conic C and a straight line D defined by the following equation: y=t.z+yP−t.zP; obtaining the element ξ of GF(3n) verifying the following linear equation over GF(3): ξ3−η.ξ=(η2.zQ)/a; and associating, with the element t of the finite field, the point P′ of the elliptic curve, for which the coordinates are defined by the pair (η.zQ/ξ, yQ).
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机译:提供一种在非超奇异椭圆曲线E上具有公钥的加密方法,该方法由简化的Weirstrass方程y 2 Sup> = x 3 Sup> + ax 确定在有限域GF(3 n Sup>)上为2 Sup> + b,其中n为大于或等于1的整数。该方法包括将所述有限域的元素t与一个点相关联椭圆场的P'。关联的步骤包括:在GF(3 n Sup>)上获得预定的二次非残基η;获得属于由下式定义的圆锥C的预定点P =(z P Sub>,y P Sub>):a.η.z 2 < / Sup> -y 2 Sup> + b = 0;获得一个点Q =(z Q Sub>,y Q Sub>),该点不同于属于圆锥C的点P和由以下等式定义的直线D:y = t.z + y P Sub> -tz P Sub>;获得GF(3 n Sup>)的元素ξ,从而验证GF(3)上的以下线性方程:ξ 3 Sup>-η.ξ=(η 2 Sup> .z Q Sub>)/ a;并将椭圆曲线的点P'与有限域的元素t关联,其坐标由对(η.z Q Sub> /ξ,y Q Sub>)。
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