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    • 10. 发明申请
    • CRYPTOGRAPHY ON A ELLIPTICAL CURVE
    • 椭圆曲线的曲线图
    • US20120082307A1
    • 2012-04-05
    • US13377404
    • 2010-06-15
    • Thomas IcartJean-Sebastien Coron
    • Thomas IcartJean-Sebastien Coron
    • H04L9/28
    • G06F7/725G06F2207/7261H04L9/3066
    • A cryptographic calculation includes obtaining a point P(X,Y) from a parameter t on an elliptical curve Y2=f(X); and from polynomials X1(t), X2(t), X3(t) and U(t) satisfying: f(X1(t)).f(X2(t)).f(X3(t))=U(t)2 in Fq, with q=3 mod 4. Firstly a value of the parameter t is obtained. Next, the point P is determined by: (i) calculating X1=X1(t), X2=X2(t), X3=X3(t) and U=U(t); (ii) if the term f(X1)·f(X2) is a square, then testing whether the term f(X3) is a square in Fq and if so calculating the square root of f(X3) in order to obtain the point P(X3); (iii) otherwise, testing whether the term f(X1) is a square and, if so, calculating the square root of f(X1) in order to obtain the point P(X1); (iv) otherwise, calculating the square root of f(X2) in order to obtain the point P(X2). This point P is useful in a cryptographic application.
    • 密码计算包括从椭圆曲线Y2 = f(X)上的参数t获得点P(X,Y); 和(x(t))f(X3(t))= U(t(x) t)2,其中q = 3 mod 4.首先获得参数t的值。 接下来,通过以下方式确定点P:(i)计算X1 = X1(t),X2 = X2(t),X3 = X3(t)和U = U(t); (ii)如果术语f(X1)·f(X2)是一个平方,则测试f(X3)是否是Fq中的平方,如果是,则计算f(X3)的平方根,以获得 点P(X3); (iii)否则,测试术语f(X1)是否为平方,如果是,则计算f(X1)的平方根以获得点P(X1); (iv)否则,计算f(X2)的平方根,以获得点P(X2)。 这一点P在加密应用程序中很有用。