Proving prime integers for encryption

A device, comprising:

• one or more memories;
• and
• one or more processors to:
• 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;
• 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;
• 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 and based on determining a status of a proving process associated with the integer;
• and
• authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

A non-transitory computer-readable medium storing instructions, the instructions comprising:

• one or more instructions that, when executed by one or more processors, cause the one or more processors to:
• receive a set of cryptographic parameters associated with an integer,
• wherein the set of cryptographic parameters include a linked list of potential prime integers used to generate the integer in an order;
• 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;
• determine whether the integer is a proven prime integer based on determining that each potential prime integer included in the linked list of potential prime integers is a prime integer and based on determining a status of a proving process associated with the integer;
• and
• use, when the integer is a proven prime integer, the integer in a cryptographic protocol.