In the password calculation method in an electronic component comprising the step of obtaining the point P on the elliptic curve that satisfies the following equation:
Wherein a _1, a _2, a _3, a ₄ and a ₆ ​​is deulyigo components of the set A, A is a modular integer ring (a ring of the modular integers) Z / qZ wherein q is obvious (strictly) greater than 3 finite field with q power of a different handful of (prime numbers) one can in the (number) of the amount of I integer times, I is an integer greater than or equal to 2, or a is a prime number (prime integer) ( _finite filed) F q, and; Wherein X and Y are coordinates of the point P, are the components of the A. The method includes the step 11 of determining the parameters, includes applying a function to the parameter 12, the X coordinate of the point P, step 13, for obtaining Y. Euler function (Euller function) of A The equation It corresponds to.
The function is _{a 1, a 2, a 3} , a 4 and a ₆ And a reversible function that is represented by a glass fraction (a rational fraction) from the parameters in the A (invertible function) and the definite function (deterministic function) acquire and, at least one value of the point P q / 4 ^I is, I is Co. I have the same value and 1 for the field Fq.
The method encryption (cryptographic encryption) or hash (hash) authentication (authentication), or recognition applications (application identification) further includes using the points in P.