Fast Computation of Discrete Logarithms in GF (q)
The Merkte-Adleman algorithm computes discrete logarithms in GF (q),the finite field with q elements, in subexponential time, when q is a prime number p. This paper shows that similar asymptotic behavior can be obtained for the logarithm problem when q = p m , in the case that m grows with p fixed. A method of partial precomputation, applicable to either problem, is also presented. The precomputation is particularly useful when many logarithms need to be computed for fixed values of p and m.
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