Factor base discrete logarithms in Kummer extensions

The Discrete Logarithm Problem

“…In the first case we have r(X) = gX and in the second r(X) = g/X. See [23]. Numerical experiments suggest [1] that when k is close to q, one can find a rational function r(X) with denominator and numerator of degree at most 2, for which X q − r(X) is divisible by an irreducible degree k polynomial φ (X).…”

Adaptive two-filter smoothing based on second-order divided difference filter for distributed position and orientation system

“…Remark 1. Theorem 1 shows that the case of Artin-Schreier extensions is quite different with that of Kummer case [8].…”