Fast prime number generation algorithms on smart mobile devices

As smart mobile devices are widely used, mobile threats are more serious, so security in mobile becomes more and more important. However, the performance of these devices are not powerful enough to use the same security algorithms as PCs. Public key cryptosystems such as RSA need big primes to enhance the security, however, generating a big prime takes substantial time even on a PC. In this paper, we study two prime generation algorithms for smart mobile devices. First, we analyze a previous prime generation algorithm using a GCD test, named PGCD-MR, and show it sometimes performs inferior to the traditional TD-MR test. Second, we propose a new GCD test, named m-bit GCD-MR, for fast prime generation in both PCs and smart mobile devices. We compare the running times of PGCD-MR, m-bit GCD-MR, and TD-MR combinations on PCs and Samsung Galaxy Tab 10.1. The experimental results show our running time analysis is accurate (only 2% error) and m-bit GCD-MR test is the fastest among three prime generation algorithms. More exactly, m-bit GCD-MR test is about 20% faster than the TD-MR combination.