A subexponential-time algorithm for computing discrete logarithms overGF(p^2)

An algorithm for computing discrete logarithms over GF
(p^{2})
, 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^{m})
, for
m
growing and
p
fixed.