  The key step of syndrome-based decoding of Reed-Solomon codes up to half the
minimum distance is to solve the so-called Key Equation. List decoding
algorithms, capable of decoding beyond half the minimum distance, are based on
interpolation and factorization of multivariate polynomials. This article
provides a link between syndrome-based decoding approaches based on Key
Equations and the interpolation-based list decoding algorithms of Guruswami and
Sudan for Reed-Solomon codes. The original interpolation conditions of
Guruswami and Sudan for Reed-Solomon codes are reformulated in terms of a set
of Key Equations. These equations provide a structured homogeneous linear
system of equations of Block-Hankel form, that can be solved by an adaption of
the Fundamental Iterative Algorithm. For an $(n,k)$ Reed-Solomon code, a
multiplicity $s$ and a list size $\listl$, our algorithm has time complexity
\ON{\listl s^4n^2}.
