Patent ID: 8666066

Claim:
A method of executing a cryptographic computation in an electronic component comprising: obtaining points P on an elliptic curve satisfying the following equation: Y 2 +a 1 XY+a 3 Y=X 3 +a 2 X 2 +a 4 +X+a 6 (1) where a 1 a 2 , a 3 , a 4 and a 6 are elements of a set A of elements, where A is a ring of the modular integers Z/qZ where q is a positive integer product of a number I of different prime numbers that are strictly greater than 3, I being an integer greater than or equal to 2, or A is a finite field F q with q a power of a prime integer; where X and Y are the coordinates of the points P and are elements of A, said method further comprising: /a/ determining a parameter; /b/ obtaining coordinates X and Y of a point P by applying a function to said parameter; the Euler function φ of A satisfying the equation: φ(A) mod 3=1, the function being an invertible and deterministic function expressed by a rational fraction in a 1 , a 2 , a 3 , a 4 and a 6 and in said parameter within A, and attaining at least a number q/4 I of points P, with I equal to 1 for a finite field F q ; /c/ using said point P in a cryptographic encryption or hash or signature or authentication or identification application.