  Two rational primes p, q are called dual elliptic if there is an elliptic
curve E mod p with q points. They were introduced as an interesting means for
combining the strengths of the elliptic curve and cyclotomy primality proving
algorithms. By extending to elliptic curves some notions of galois theory of
rings used in the cyclotomy primality tests, one obtains a new algorithm which
has heuristic cubic run time and generates certificates that can be verified in
quadratic time.
  After the break through of Agrawal, Kayal and Saxena has settled the
complexity theoretical problem of primality testing, some interest remains for
the practical aspect of state of the art implementable proving algorithms.
