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A New Elliptic Curve Based Analogue of RSA

refer:ANewEllipticCurveBasedAnalogueofRSA椭圆曲线令p和q是素数,都大于3。并且满足\(4a^3+27b^2\not\equiv0\pmod{p}\)。用\(E_p(a,b)\)表示模p参数为a,b的椭圆曲线。\(y^2\equivx^3+ax+b\pmod{p}\)。椭圆曲线的加法计算定义为\[P+Q=R\tag1\]设\(P=(x_1,y_1),Q=(x_2,y_2),R=(x_3,y_3)\)\[x3\equiv\lambda^2-x_1-x_2\mod{p}\tag2\]\[y_3\equiv\lambda(x_1-x_3)-y_1\pmod{p

A New Elliptic Curve Based Analogue of RSA

refer:ANewEllipticCurveBasedAnalogueofRSA椭圆曲线令p和q是素数,都大于3。并且满足\(4a^3+27b^2\not\equiv0\pmod{p}\)。用\(E_p(a,b)\)表示模p参数为a,b的椭圆曲线。\(y^2\equivx^3+ax+b\pmod{p}\)。椭圆曲线的加法计算定义为\[P+Q=R\tag1\]设\(P=(x_1,y_1),Q=(x_2,y_2),R=(x_3,y_3)\)\[x3\equiv\lambda^2-x_1-x_2\mod{p}\tag2\]\[y_3\equiv\lambda(x_1-x_3)-y_1\pmod{p