4.1 Primality Testing Continued

The obvious approach for designing an algorithm around this fact is to use the Schwartz-Zippel test to see if (x − a) − (x − a) is the zero polynomial. However, this fails for two reasons. The first is that if n is not prime then Zn is not a field (which we assumed in our analysis of Schwartz-Zippel); the second is that the degree of the polynomial is n, which is the same as the cardinality of Zn and thus too large (recall that Schwartz-Zippel requires that values be chosen from a set of size strictly larger than the degree).