Generating Primes Using Partitions

This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested using either Miller Rabin or AKS primality tests. Introduction Generation of large prime numbers is fundamental to modern cryptography protocols [1],[2], generation of pseudorandom sequences [3]-[5], and in new application of these protocols to multi-party computing and cryptocurrencies [6]-[8]. Public-key cryptography requires random generation of prime numbers to derive public key. This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions [10]. The algorithm is described and experiments are presented showing how this method gives large primes in an effective manner. A candidate prime will be tested using either Miller-Rabin (MR) or AKS primality tests [11],[12]. Generation of random primes Large prime numbers are generated randomly by considering a random number and testing it with MR or AKS primality test or one might use different sieves [13]-[18], with applications to a variety of cryptography areas (e.g. [19],[20]). The table below presents the average of 10 executions for random generation of prime numbers in a typical experiment. Table 1. Average attempts to generate a random prime Length of the Random Prime number Average attempts to generate a prime number 45 98 50 159 55 172 60 211 70 224