The efficient generation of public-key parameters is a prerequisite in public-key systems. A specific example is the requirement of a prime number p to define a finite field Zp for use in the Diffie-Hellman key agreement protocol and its derivatives (x12.6). In this case, an element of high order in Z p is also required. Another example is the requirement of primes p and q for an RSA modulus n = pq (x8.2).