Abstract
The fastest method known for factoring integers is the ‘number field sieve’. An analogous method over function fields is developed, the ‘function field sieve’, and applied to calculating discrete logarithms over GF(p n). An heuristic analysis shows that there exists a cε ℜ>0 such that the function field sieve computes discrete logarithms within random time: L p n[1/3, c] when log(p) ≤ n 9(n) where g is any function such that g: N → ℜ <.98>0 approaches zero as n → ∞.
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