The need for security in lightweight devices such as radio frequency identification tags is increasing and a pseudorandom number generator (PRNG) constitutes an essential part of the authentication protocols that provide security. The main aim of this research is to produce a lightweight PRNG for cryptographic applications in wireless identification and sensing platform family devices, and other related lightweight devices. This PRNG is produced with genetic programming methods using entropy calculation as the fitness function, and it is tested with the NIST statistical test suite. Moreover, it satisfies the requirements of the EPCGen2 standards.