A subexponential-time algorithm for computing discrete logarithms over GF(p2)

Absrract-An algorithm for computing discrete logarithms over GF(p*), where p is a prime, in subexponential time is described. The algorithm is similar to the Merkle-Adleman algorithm for computing logarithms over GF( p ), but it uses quadratic fields as the appropriate algebraic structure. It also makes use of the idea of a virtual spanning set due to Hellman and Reyneri for computing discrete logarithms over GF(p”‘), for m growing and p fixed.