Abstract: This disclosure relates to methods for generating a prime number, which can be implemented in an electronic device. An example method can include calculating a candidate prime number using a formula Pr=2P·R+1, where P is a prime number and R is an integer. The method can also include applying the Pocklington primality test to the candidate prime number and rejecting the candidate prime number if it fails the Pocklington test. The integer can be generated from an invertible number belonging to a set of invertible elements modulo the product of numbers belonging to a group of small prime numbers greater than 2, where the candidate prime number is not divisible by any number of the group. The prime number P having a number of bits equal to within one bit, to half or a third of the number of bits of the candidate prime number.

Abstract: The invention relates to a method for generating a prime number, implemented in an electronic device, the method including steps of generating a prime number from another prime number using the formula Pr=2P·R+1, where P is a prime number having a number of bits lower than that of the candidate prime number, and R is an integer, and applying the Pocklington primality test to the candidate prime number, the candidate prime number being proven if it passes the Pocklington test. According to the invention, the size in number of bits of the candidate prime number is equal to three times the size of the prime number, to within one unit, the generated candidate prime number being retained as candidate prime number only if the quotient of the integer division of the integer by the prime number is odd.

Abstract: The invention relates to a method for generating a prime number, implemented in an electronic device, the method including steps of generating a prime number from another prime number using the formula Pr=2P·R+1, where P is a prime number having a number of bits lower than that of the candidate prime number, and R is an integer, and applying the Pocklington primality test to the candidate prime number, the candidate prime number being proven if it passes the Pocklington test. According to the invention, the size in number of bits of the candidate prime number is equal to three times the size of the prime number, to within one unit, the generated candidate prime number being retained as candidate prime number only if the quotient of the integer division of the integer by the prime number is odd.

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