METHOD FOR GENERATING FIRST PROVEN NUMBERS ADAPTED TO CHIP CARDS

摘要

The invention relates to a method for generating a prime number, implemented in an electronic device (DV), the method comprising steps of calculating a prime candidate number (Pr) having a number of bits (L), by the formula: Pr = 2P? R + 1, where P is a prime number and R is an integer, applying the Pocklington primality test to the first candidate number, rejecting the first candidate number if it fails the Pocklington test, generating the integer (R) from an invertible number (X) belonging to a set of invertible elements modulo the product (piv) of numbers (Qj) belonging to a group of small prime numbers greater than 2, so that the prime candidate number (Pr) is not divisible by any of the numbers in the group, the prime number P having a bit number equal to one bit to one-half to one-third of the number of bits of the first candidate number.