Unlike the DUE which has a hardware random number generator, the ZERO requires a bit of work to generate strong random numbers. Walt Anderson developed an entropy generator for the UNO based on dueling clocks, see entropy lib. As a proof of concept, I utilized the ZERO's system clock (SysTick->VAL) and one of the RC oscillators (ULPOSC32K) to generate random bits, see github. The bit rate is about 10,000 bits per second. I collected a few million bits and verified the "randomness" with rngtest, ent, and NIST STS.
Other possible sources of randomness are unconnected ADC pins, though the analogRead() rate is slow, unless you adjust the firmware parameters for the ADC.