Constructive Methods for the Generation of Prime Numbers

Public-key cryptography is rapidly becoming ubiquitous in many aspects of “electronic” life. It is used to provide various security services such as data integrity, confidentiality, authentication and nonrepudiation. Most public-key cryptographic methods require the generation of random prime numbers. A naive solution to obtain a prime number consists in randomly choosing a number and testing it for primality. Such a solution is however not satisfactory in all respects as it is not efficient. This note is aimed at making strides towards the provision of practical (i.e., efficient) solutions for generating prime numbers.