Geodesic
Lifting of Solutions of an Exponential Congruence
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 76-86

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In the present paper, a polynomial algorithm is suggested for reducing the problem of taking the discrete logarithm in the ring of algebraic integers modulo a power of a prime ideal to a similar problem with the power equal to one. Explicit formulas are obtained; instead of the Fermat quotients, in the case of residues in the ring of rational integers, these formulas use other polynomially computable logarithmic functions, like the $\mathfrak{p}$-adic logarithm.
Mots-clés : Polynomial algorithm, Fermat quotients
Keywords: discrete logarithm, ring of algebraic integers, $\mathfrak{p}$-adic logarithm. 
@article{MZM_2006_80_1_a9,
     author = {I. A. Popovyan},
     title = {Lifting of {Solutions} of an {Exponential} {Congruence}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {76--86},
     publisher = {mathdoc},
     volume = {80},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a9/}
}
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I. A. Popovyan. Lifting of Solutions of an Exponential Congruence. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 76-86. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a9/