Abstract
We present a method of generating primes r ≡ 1 (mod n), q and a Weil q-number π such that r divides Φ n (q) and r divides |A(𝔽 q )|, where A/𝔽 q is an ordinary abelian variety defined over a finite 𝔽 q corresponding to π. Such primes can be used for implementing pairing-based cryptographic systems.