Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.

Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.

Abstract: A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

Abstract: A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.