This article is cited in 2 papers

Lifting of Solutions of an Exponential Congruence

I. A. Popovyan

M. V. Lomonosov Moscow State University

Abstract: 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.

Keywords: Polynomial algorithm, discrete logarithm, ring of algebraic integers, Fermat quotients, $\mathfrak{p}$-adic logarithm.

UDC: 511.225

Received: 16.06.2004
Revised: 23.01.2006

DOI: 10.4213/mzm2782

 English version: Mathematical Notes, 2006, 80:1, 72–82

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