| 摘要 |
A cryptographic calculation includes obtaining a point P(X,Y) from a parameter t on an elliptical curve Y2=f(X) and from polynomials satisfying: −f(X1(t)).f(X2(t))=U(t)2 in the finite body Fq, irrespective of the parameter t, q=3 mod 4. A value of the parameter t is obtained and the point P is determined by: (i) calculating X1=X1(t), X2=X2(t) and U=U(t); (ii) testing whether the term f(X−1) is a squared term in the finite body Fq and, if so, calculating the square root of the term f(X1), the point P having X1 as abscissa and Y1, the square root of the term f(X1), as ordinate; (iii) otherwise, calculating the square root of the term f(X2), the point P having X2, as abscissa and Y2, the square root of the term f(X2), as ordinate. The point P is useful in encryption, scrambling, signature, authentication or identification cryptographic applications. |
| 主权项 |
1. An electronic component configured to execute a cryptographic calculation and obtain a point P(X,Y) from at least one parameter t, on an elliptical curve that satisfies the equation: Y2=f(X) and from polynomials X1(t), X2(t), and U(t) satisfying the following equality: −f(X1(t)).f(X2(t))=U(t)2 in the finite field Fq, regardless of the parameter t, q satisfying the equation q=3 mod 4, said electronic component configured to:
obtain a value of the parameter t; determine the point P by:
(i) calculating X1=X1(t), X2=X2(t) and U=U(t)(ii) testing whether the term f(X1) is a squared term in the finite field Fq and in this case calculating the square root of the term f(X1), point P having X1 as abscissa and the square root of the term f(X1) as ordinate Y1;(iii) otherwise calculating the square root of the term f(X2), point P having X2 as abscissa and the square root of the term f(X2) as ordinate; and wherein said electronic component is further configured to use said point P in a cryptographic application selected from the group consisting of encryption or hashing or signature or authentication or identification. |
