In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. It relies on finding a relatively small factor base, for which most elements of the group can be expressed as products of elements in the factor base. Suitable techniques are known for, the multiplicative group of a finite field of order n. When n = 2m, the index-calculus algorithm is the best solution known for computing discrete logarithms. For n prime, a modification based on the general number field sieve provides better asymptotic performance.
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